Дисертації з теми "Topological effects"

This thesis presents Topological Domain Theory as a powerful and flexible framework for denotational semantics. Topological Domain Theory models a wide range of type constructions and can interpret many computational features. Furthermore, it has close connections to established frameworks for denotational semantics, as well as to well-studied mathematical theories, such as topology and computable analysis. We begin by describing the categories of Topological Domain Theory, and their categorical structure. In particular, we recover the basic constructions of domain theory, such as products, function spaces, fixed points and recursive types, in the context of Topological Domain Theory. As a central contribution, we give a detailed account of how computational effects can be modelled in Topological Domain Theory. Following recent work of Plotkin and Power, who proposed to construct effect monads via free algebra functors, this is done by showing that free algebras for a large class of parametrised equational theories exist in Topological Domain Theory. These parametrised equational theories are expressive enough to generate most of the standard examples of effect monads. Moreover, the free algebras in Topological Domain Theory are obtained by an explicit inductive construction, using only basic topological and set-theoretical principles. We also give a comparison of Topological and Classical Domain Theory. The category of omega-continuous dcpos embeds into Topological Domain Theory, and we prove that this embedding preserves the basic domain-theoretic constructions in most cases. We show that the classical powerdomain constructions on omega-continuous dcpos, including the probabilistic powerdomain, can be recovered in Topological Domain Theory. Finally, we give a synthetic account of Topological Domain Theory. We show that Topological Domain Theory is a specific model of Synthetic Domain Theory in the realizability topos over Scott's graph model. We give internal characterisations of the categories of Topological Domain Theory in this realizability topos, and prove the corresponding categories to be internally complete and weakly small. This enables us to show that Topological Domain Theory can model the polymorphic lambda-calculus, and to obtain a richer collection of free algebras than those constructed earlier. In summary, this thesis shows that Topological Domain Theory supports a wide range of semantic constructions, including the standard domain-theoretic constructions, computational effects and polymorphism, all within a single setting.

Multicomponent polymer systems comprised of two or more chemically different polymer moieties provide an effective way to attain the desired properties from a limited palette of commodity polymers. Variations in macromolecular topologies often result in unique and unusual properties leading to novel applications. This dissertation addresses the effect of topology on properties of two multicomponent polymers systems: blends and polyrotaxanes. Blends of cyclic and linear polymers were compared to their topological counterparts, polyrotaxanes, in which cyclic components are threaded onto the linear polymer chains. The first part of the dissertation focuses on the synthesis and purification of cyclic polymers derived from linear (polyoxyethylene) (POE). Cyclic POEs of different cycle sizes were synthesized and then purified from their linear byproducts by inclusion complexation with alpha-cyclodextrin. Polystyrene was threaded through the resulting cycles by in situ free radical polymerization of styrene monomer in the presence of an excess of POE cycles. A bulky free radical initiator was utilized to endcap the polystyrene molecule at the two ends to prevent dethreading of cyclic moieties. In the second part of the dissertation, phase behavior, morphology and dynamics of cyclic POE and polystyrene blends were compared to linear POE and polystyrene blends. Advanced solid-state NMR techniques and differential scanning calorimetry were employed for this purpose. Cyclic POE was found to be much more miscible with polystyrene when compared to linear POE, resulting in nanometer-sized domains and significantly reduced mobilities of the cyclic POE components in the blends. The unusual behavior of cyclic POE in the blends was attributed to topological as well as end-group effects with the topological effects being predominant. Polyrotaxanes composed of polystyrene and cyclic POE components exhibited cyclic POE domain sizes similar to that of physical blends. Cyclic POE dynamics in polyrotaxanes were considerably hindered, however, due to the threaded architecture. Surface segregation studies of cyclic POE/polystyrene blends and polyrotaxanes did not show segregation of POE to the surface because of the improved miscibility and the topological constraints present in these systems.

Topological insulators are materials with their electronic band structure in bulk resembling that of an ordinary insulator, but the surface states are metallic. These surface states are topologically protected, meaning that they are robust against impurities. The topological phenomena of three dimensional topological insulators can be expressed within topological field theories, predicting axion electrodynamics and the topological magnetoelectric effect. An experiment have been suggested to measure the topological phenomena. In this thesis, the underlying theory and details around the experiment are explained and more detailed derivations and expressions are provided.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2006.
Includes bibliographical references.
The purpose of this study is to understand on atomic level the structural response of zircon (ZrSiO4) to irradiation using molecular dynamics (MD) computer simulations, and to develop topological models that can describe these structural changes. Topological signatures, encoded using the concepts of primitive-rings and local clusters, were developed and used to differentiate crystalline and non-crystalline atoms in various zircon structures. Since primitive-rings and local clusters are general concepts applicable to all materials, and the algorithms to systematically identify them are well-established, topological signatures based on them are easy to implement and the method of topological signatures is applicable to all structures. The method of topological signatures is better than the Wigner-Seitz cell method, which depends on the original crystalline reference grid that is unusable in heavily damaged structures or regions; it is also better than those methods based only on local structures limited to first coordination shell, since one can decide whether or not to include ring contents of large rings into the topological signatures, effectively controlling the range of the topological signatures. The early-stage evolution of non-crystalline disorder and the subsequent recrystallization in zircon collision cascade simulations were successfully modeled by using the topological signatures to identify non-crystalline atoms. Simply using the number of displaced atoms was unable to correctly show the initial peak of structural damage followed by the subsequent annealing stage. Using the topological signatures, amorphization within a single collision cascade was observed in zircon.
(cont.) In the radiation-induced amorphous zircon simulated in this study, the method of topological signatures was able to differentiate the amorphous region in the center of the simulation box and the crystalline region surrounding it. A few isolated remnant crystalline islands were identified in the amorphous region. About 5% of atoms in melted and melt-quenched structures were identified as crystalline atoms. Different amorphous zircon structures were found to be topologically different. Upon amorphization of zircon, the average ring size and the number of atoms in local cluster were found to increase. Larger average ring sizes were found in more pervasively amorphized structures. The radiation-induced amorphous structure was the least pervasively amorphized one, followed by the melt-quenched. The liquid-state amorphous structure was most pervasively amorphized and had the largest average ring size. Phase-separation of zircon into SiO2- and ZrO2-rich local regions was observed when zircon was amorphized in simulations, either thermally or by radiation. It was found in simulations using constant pressure ensembles that the zircon structure underwent abnormally huge volume swelling when it amorphized, which was attributed to the ion charges used in the potential model. Although the ion charges used in the originally chosen potential model were overall balanced, they were not balanced with regard to the phase decomposition products, and thus resulted in strong Coulombic repulsive force within locally SiO2- and ZrO2-rich regions when phase separation occurred. After the ion charges were re-balanced (and other potential parameters refitted), the volume expansion was found to be under control. The charge imbalance of SiO2 units was also found to produce unrealistically large fraction of 3-coordinated Si and shorter Si-O bond length.
(cont.) The issue of charge-balance with regard to phase decomposition products applies to all complex ceramics that decompose into separate phases upon amorphization. Threshold displacement energies in zircon were systematically determined. Many special directions, such as those directed toward neighboring atoms or open spaces surrounding the PKA, were considered. Cascade detail was extensively examined, including PKA trajectory, cascade extent, time scale, thermal spike, recoil density, distribution of PKA energy among sub-lattices and number of displaced atoms. The crystallographic features of the zircon structure were found to have profound implications for collision cascades. It was found that energetic PKAs were always deflected into the open channel along the z direction. Their displacements along the longitudinal x direction were never greater than about 4 nm in our simulations. The estimation of the cascade extent assuming homogeneous media thus greatly over-predicts the PKA displacement along the longitudinal direction. The effects of PKA mass on collision cascade were studied by comparing the cascades caused by Zr and U PKAs. The U atoms were simply "super-mass" Zr atoms in this study: U-Zr, U-Si and U-O interactions were the same as Zr-Zr, Zr-Si and Zr-O interactions, respectively. It was found that heavier PKAs produced longer cascades, more structural damage, and higher temperature in thermal spike. U also traveled further along the longitudinal x direction because it was less prone to change of velocity direction. The depleted regions in the core of the cascades surrounded by a densified shell, which were found in simulations by Trachenko et al., were not found in our study. After extensive tests of recently published zircon potentials, it was found that three out of the five tested potentials yielded poor elastic constants and appear to be unfit for serious simulations. Published simulation results using these potentials should accordingly be viewed cautiously.
by Yi Zhang.
Ph.D.

Cette thèse est consacrée à de nouveaux phénomènes en physique liées au spin et à la topologie des quasi-particules lumière-matière dans des hétérostructures. Elle est divisée en quatre parties. Chapitre 1 donne un fond nécessaire et introduit les propriétés fondamentales des polaritons et des excitons indirects dans des puits quantiques couplés. Chapitre 2 est concentré sur la dynamique de spin et sur formation de défauts topologiques dans des systèmes aux excitons indirects. Les 2 derniers chapitres considèrent les structures basées sur les microcavités. Chapitre 3 est consacré à la dynamique de spin des polaritons dans des oscillateurs paramétriques optiques. Finalement, chapitre 4 étudie les réseaux des microcavités en forme des piliers et introduit l’isolant topologique polaritonique
The present thesis manuscript is devoted to new phenomena in physics of light-matter quasiparticles in heterostructures, related to spin and topology. It is divided into four parts. Chapter 1 gives a necessary background, introducing basic properties of microcavity polaritons and indirect excitons in coupled quantum wells. Chapter 2 is focused on spin dynamics and topological defects formation in indirect exciton many-body systems. The last 2 chapters are related to microcavity-based structures. Chapter 3 is devoted to polariton spin dynamics in optical parametric oscillators. Finally, Chapter 4 studies pillar microcavity lattices and introduces the polariton topological insulator

Au cours des dernières décennies les besoins en capacité de stockage ont explosé avec l’avènement de l’ordinateur. La crise énergétique que nous traversons au 21eme siècle nécessite le développement de nouveaux matériaux pour le stockage de l’information. C’est dans ce but que les physiciens ont développé de nouvelles façons de stocker l’information de façon à réduire la taille, la consommation énergétique et le coût de fabrication des mémoires tout en augmentant leurs capacités et la vitesse de traitement de l’information. Les recherches réalisées au cours de cette thèse visent à améliorer le stockage de l’information à l'aide des deux champs de recherches suivants :- Le premier se base sur l’utilisation de matériaux émergents dans le domaine de la recherche scientifique : les isolants topologiques. Ces matériaux possèdent des textures de spin particulières susceptibles de générer une conversion très élevée entre courant de spin et courant de charge. Cet état de la matière (non trivial topologiquement) peut s’avérer complexe à stabiliser et à imager. C’est l’objectif de la première partie de cette thèse où des isolants topologiques provenant de la famille des demi-Heusler sont fabriqués par épitaxie par jets moléculaires. La caractérisation structurale par diffraction des rayons X et électronique ainsi que par microscopie à effet tunnel et microscopie électronique à transmission confirme la croissance épitaxiale dans la structure désirée prédite comme ayant une topologie non triviale. La spectroscopie photoélectrique résolue en angle révèle la présence d'états linéaires autour du point Γ de la zone de Brillouin. Néanmoins, les surfaces de Fermi obtenues sont complexes et ne permettent pas de tirer des conclusions claires sur la nature non triviale des composés. Des mesures de transport ont été effectuées pour tester l'efficacité potentielle d'interconversion de nos composés et les expériences de spin Seebeck révèlent une conversion spin/charge deux à trois fois plus élevée dans nos isolants toplogiques comparés à un échantillon témoin de Pt.- La seconde étude réalisée afin d'améliorer les mémoires magnétiques conventionnelles porte sur l’anisotropie magnétique. Ici encore les alliages d’Heusler offrent une grande variété de composés permettant de répondre à ce but. La famille de composés Mn3Z (Z = Ge, Ga) a beaucoup attiré l’attention du fait de sa maille élémentaire tetragonalisée permettant de stabiliser une aimantation perpendiculaire et cela même dans une géométrie de film mince. Dans cette thèse, nous étudions les alliages Mn(100-x)Ga(x) et Mn(100-x)Ge(x) et parvenons à les stabiliser dans leur structure D0(22) offrant une aimantation perpendiculaire. Un zoom est ensuite porté sur des empilements (bicouches et super-réseaux) à base de Mn3Ge et composés d'un second alliage d'Heusler aux propriétés remarquables, la famille Co2MnZ' (Z' = Si, Ge). Les composés Co2MnZ' ont un comportement semi-métallique leur conférant un faible amortissement magnétique et une polarisation en spin de 100% au niveau de Fermi, deux propriétés très souhaitées pour des applications basées sur le couple transfert de spin. Nous développons donc ici des hétérostructures Mn3Ge/Co2MnZ' (bicouches et super-réseaux) et parvenons à faire croître les deux composés dans les structures souhaitées. Le système global possède une aimantation perpendiculaire (amenée par Mn3Ge), la dernière couche de l'empilement est un demi-métal magnétique (amené par Co2MnZ') et les épaisseurs utilisées pour les deux couches permet d'accorder les propriétés magnétiques et d'obtenir 100% de rémanence
Over the last decades, the needs in storage capacity as shot up with computing development. The energy crisis that we are going through in the 21th century requires to develop new fundamental materials for data storage. It was with this purpose that physicist develop new ways to store information in order to reduce device’s scale, energy consumption and manufacturing cost while memories’ size and information’s speed has shot up. The research conducted in this thesis make use of two different ways to improve data storage:- The first one is by using emerging materials in science, called topological insulator, that host peculiar spin texture predicted to generate very high spin-to-charge interconversion. This non-trivial state of matter can be complex to stabilize and image. This is the goal of the first part of this thesis where topological insulators coming from the half-Heusler family are engineered by molecular beam epitaxy. Structural characterization are carried out by X-ray and electronic diffraction along with scanning tunneling microscopy and transmission electron microscopy that confirm an epitaxial growth in the desired structure predicted to host a non-trivial topology. Angle resolved photoemission spectroscopy is performed and reveals the presence of linear states around the Γ point of the Brillouin zone. Nonetheless, the complex Fermi surfaces imaged do not allow to draw clear conclusions on the non-trivial nature of both alloys. Transport measurements were performed to test the potential interconversion efficiency of our compounds and spin Seebeck experiments revealed a spin-to-charge conversion two to three times higher in our TIs compared to a Pt control sample.- The second way chosen to improve conventional magnetic memories is by playing with magnetic anisotropy. Here again, Heusler family offers a vast variety of compounds allowing to fulfill this goal. The Mn3Z family compounds has attracted a lot of attention owing to their tetragonalized unit cell that allows to stabilize perpendicular magnetic anisotropy (PMA) even in a thin film geometry. In this thesis, we investigate Mn(100-x)Ga(x) and Mn(100-x)Ge(x) alloys and manage to stabilize them in their D0(22) structure that offers PMA. A peculiar zoom is then done on Mn3Ge-based stacks composed of a second Heusler alloy with remarkable properties, the Co2MnZ’ family (Z' = Si, Ge). Co2MnZ’ compounds have a half-metallic behavior making them very suitable for spin transfer torque related applications due to their low magnetic damping and full spin polarization at the Fermi level. Here we develop Mn3Ge/Co2MnZ' heterostructures (bilayers and superlattices) and manage to grow both compounds in the desired structures. The overall system is perpendicularly magnetized (thanks to Mn3Ge), terminated with a half-metal magnet (thanks to Co2MnZ') and the thicknesses used for both layers allow to tune the magnetic properties and obtained 100% of remanence

Aquest doctorat. El projecte cobreix les investigacions sobre aïllants topològics (TI) de la família Bi2Se3 amb diferents defectes i l'estudi d'efectes de proximitat de TI a la heteroestructura de grafè amb TI. La primera part d'aquest projecte se centra principalment en l'efecte del desordre en les propietats electròniques de TI amb gruix ultrafí (<3 nm). S’ha trobat que la manca de coincidència de rotació entre capes quíntuples de TI pot augmentar el “gap” de volum dels TI però preservar la textura d'espín tipus Rashba en l'estat de la superfície; mentre que la hidrogenació en una superfície de TI pot ajudar a reduir l'efecte túnel quàntic i tancar el “gap” de superfície en el punt Γ amb la textura d'espín tipus Rashba per a la pel·lícula TI ultrafina. A més, aquest esquema també pot crear un altre punt Dirac (DP) en el punt M amb textura de spin tipus Dresselhaus. La segona part del projecte investiga els efectes de proximitat de TI dins de la heteroestructura de grafè / TI i el DP en el grafè es plega des del punt K / K 'a Γ punt de la zona Brillouin, a causa del plegament de la banda, trobant que l'alineació entre el substrat de TI i el grafè té un paper clau en la formació de l'estructura de la banda i la textura d'espín del grafè. La configuració d'apilament "hollow" podria induir la distorsió d'unió de Kekulé a la capa de grafè, donant com a resultat l'engrandiment del “gap” (3.2 meV) i el Rashba SOC, el que dóna com a resultat la precessió d'espín propera al Γ punt . A més, aquesta textura atípica de Rashba espín fa que la component d'espín fora del pla disminueixi gradualment a mesura que el punt k s'allunya del punt Γ, el que porta a la anisotropia de gir a la capa de grafè. D'altra banda, la configuració d'apilament "bridge" o "top" podria portar l'evident divisió de la banda en direcció lateral, que podria ser l'origen de l'efecte Edelstein en la capa de grafè; no obstant, no hi ha una anisotropia d'espín evident en aquesta configuració. Totes les primeres dues parts s’han dut a terme a través del càlcul de teoria funcional de la densitat (DFT) i s’ha construït un model d'unió ajustada (TB) per als resultats de DFT per tal de proporcionar una explicació analítica de l'estructura de la banda i la textura de l'spin de grafè en el dispositiu de heteroestructura. L'última part d'aquest doctorat. L'activitat de recerca se centra en estudiar l'efecte d'impureses magnètiques i no magnètiques amb un esquema de dopatge aleatori sobre les propietats electròniques dels TI. El càlcul numèric basat en el model 3D Fu-Kane-Mele TB mostra que el dopatge no magnètic en la superfície de TI només pot induir el potencial in situ a la superfície DP i elevar-lo cap amunt, preservant la textura estàndard d'espín tipus Rashba; paral·lelament, el dopatge magnètic podria trencar la simetria d'inversió de temps i obrir el “gap” de superfície amb l'anisotropia d'espín també, el que significa que la component d'espín fora del pla en la superfície TI dopada magnèticament disminueix gradualment a mesura que el punt k s'allunya del Γ punt. Els treballs de recerca en aquest projecte podrien proporcionar una guia per a la llista d'experiments sobre les propietats electròniques de TI amb diferents tipus de defectes i impureses (magnètics i no magnètics); particularment, l'estudi dels efectes de proximitat en els TI podrien explicar el fenomen fonamental bàsic observat en aquest dispositiu per a l'estudi de la dinàmica d'espín en el laboratori.
Este doctorado. El proyecto cubre las investigaciones sobre aislantes topológicos (TI) de la familia Bi2Se3 con diferentes defectos y el estudio de efectos de proximidad de TI en la heteroestructura de grafeno con TI. La primera parte de este proyecto se centra principalmente en el efecto del desorden en las propiedades electrónicas de TI con espesor ultrafino (<3 nm). Se ha encontrado que la falta de coincidencia de rotación entre capas quíntuples de TI puede aumentar el “gap” de volumen de los TI pero preservar la textura de espín tipo Rashba en el estado de la superficie; mientras que la hidrogenación en una superficie de TI puede ayudar a reducir el efecto túnel cuántico y cerrar el “gap” de los estados de superficie en el punto Γ con la textura de espín tipo Rashba para la película TI ultrafina. Además, este esquema también puede crear otro punto Dirac (DP) en el punto M con textura de espín tipo Dresselhaus. La segunda parte del proyecto investiga los efectos de proximidad de TI dentro de la heteroestructura de grafeno/TI y el DP en el grafeno se pliega desde el punto K / K' a Γ punto en la zona Brillouin, debido al plegamiento de la banda, encontrando que la alineación entre el sustrato de TI y el grafeno desempeña un papel clave en la formación de la estructura de la banda y la textura de espín del grafeno. La configuración de apilamiento “hollow” podría inducir la distorsión de unión de Kekulé a la capa de grafeno, dando como resultado el agrandamiento del “gap” (3.2 meV) y el Rashba SOC, lo que da como resultado la precesión de espín cercana al Γ punto. Además, esta textura atípica de Rashba espín hace que la componente de espín fuera del plano disminuya gradualmente a medida que el punto k se aleja del punto Γ, lo que lleva a la anisotropía de giro en la capa de grafeno. Por otro lado, la configuración de apilamiento “bridge” o “top” podría traer la evidente división de la banda en dirección lateral, que podría ser el origen del efecto Edelstein en la capa de grafeno; sin embargo, no hay una anisotropía de espín evidente en dicha configuración. Todas las primeras dos partes se han llevado a cabo a través del cálculo de la teoría funcional de la densidad (DFT) y se ha construido un modelo de unión ajustada (TB) para los resultados de DFT con el fin de proporcionar una explicación analítica de la estructura de la banda y la textura del spin de grafeno en el dispositivo de heteroestructura. La última parte de este doctorado. La actividad de investigación se centra en estudiar el efecto de impurezas magnéticas y no magnéticas con un esquema de dopaje aleatorio sobre las propiedades electrónicas de los TI. El cálculo numérico basado en el modelo 3D Fu-Kane-Mele TB mostró que el dopaje no magnético en la superficie de TI solo podía inducir el potencial in situ en la superficie DP y elevarlo hacia arriba, preservando la textura estándar de espín tipo Rashba; mientras, el dopaje magnético podría romper la simetría de inversión de tiempo y abrir el “gap” de superficie con la anisotropía de espín también, lo que significa que la componente de espín fuera del plano en la superficie TI dopada magnéticamente disminuye gradualmente a medida que el punto k se aleja del Γ punto. Los trabajos de investigación en este proyecto podrían proporcionar una guía para la lista de experimentos sobre las propiedades electrónicas de TI con diferentes tipos de defectos e impurezas (magnéticos y no magnéticos); particularmente, el estudio de los efectos de proximidad en los TI podrían explicar el fenómeno fundamental básico observado en dicho dispositivo para el estudio de la dinámica de espín en el laboratorio.
This PhD. project covers the researches on the Bi2Se3-family topological insulators (TIs) with different defects and the study of the proximity effects of TI in the heterostructure of graphene with TI. The first part of this project mainly focuses on the effect of disorder on the electronic properties of TI with ultrathin thickness (< 3 nm). It was found that rotation mismatch between quintuple of TI can enlarge the bulk gap of TI but preserve the Rashba type spin texture on the surface state; while, the hydrogenation on one TI surface can help reduce the quantum tunneling effect and close the surface gap at Γ point with Rashba type spin texture for ultrathin TI film. Furthermore, this scheme can also create another Dirac point (DP) at M point with Dresselhaus type spin texture. The second part of the project investigates in the proximity effects of TI within the heterostructure of graphene/TI and the DP on graphene is folded from K/K' point to Γ point in Brillouin zone, due to the band folding, and it was found that the alignment between TI substrate and graphene played the key role in forming the band structure and the spin texture of graphene. Hollow configuration could induce the Kekulé bonding distortion to graphene layer, mainly resulting in the enlarged gap (3.2 meV), and the Rashba SOC, resulting in the spin precession close to the Γ point. Furthermore, this atypcial Rashba spin texture has the out-of-plane spin component decrease gradually as the k point moves away from the Γ point, leading to the spin anisotropy on graphene layer. While, the bridge or the top configuration could bring the evident band splitting in lateral direction, which could be the origin of the Edelstein effect in graphene layer; however, there is no evident spin anisotropy in such configuration. All the first two parts were carried out through density functional theory (DFT) calculation and a tight binding (TB) model was built up and fitted to the DFT results in order to provide an analytical explanation for the band structure and the spin texture of graphene in the heterostructure device. The last part of this PhD. research work was to study the effect of both non-magnetic and magnetic impurities with random doping scheme on the electronic properties of TI. Numerical calculation based on 3D Fu-Kane-Mele TB model showed that non-magnetic doping on TI surface could only induce the onsite potential on the surface state and lift the DP upwards, preserving the standard Rashba type spin texture; while, the magnetic doping could break the time reversal symmetry and open up the surface gap with the spin anisotropy as well, which means the out-of-plane spin component on magnetically doped TI surface decreases gradually as the k point moves away from the Γ point. Research works in this project could provide a guideline to the experimentlist on the electronic properties of TI with different kinds of defects and impurities (magnetic and non-magnetic ones); particularly, the study of the proximity effect of TI could explain the basic fundamental phenomenon observed in such device for spin dynamics study in the laboratory.

The working hypothesis for this study was that small elevation differences in field depressions affect the availability of redox active nutrients because the bottom of the depression remains waterlogged and in reducing conditions longer than the edge of the depression. Mn, Fe, S and P availabilities were investigated in a field depression with a 20 meter radius and 0.5 meter depth on a flood-prone, organic vegetable farm. One depression (Depression 1) was sampled seven times during three field seasons (May 2012-June 2014). The last two dates included sampling in an additional three depressions to allow a comparison among depressions on the same date. Sampling dates were categorized by the severity of flooding into the three following kinds of events: Post-Irene, Peak, and Non-Peak. The Post-Irene category includes sampling dates in the agricultural season following prolonged snow melt and flooding from Tropical Storm Irene in 2011. Sampling dates in the Peak category occurred within 30 days after one of the the top 12 greatest rainfalls, snowfalls, or heights of Winooski River Gage in the 30 month sampling period. Sampling on Non-Peak events occurred at least one month after a preceding Peak event. Repeated waterlogging events can increase redox cycling directly affecting the interchange of Mn, Fe, and S oxides and the soil solution. Indirectly, waterlogging can increase phosphorus release into the soil solution by reduction of iron. The results of this experiment indicate that some redox-sensitive soil nutrients correlated with elevation on some dates regardless of event type. Mn was more consistently affected by waterlogging events than Fe and S. Any relationship between sulfur and elevation may have been obscured by the strong relationship of sulfur with organic matter. This data suggests that phosphorus availability depended to some extent on available iron concentration.

Diamidines are compounds with antiparasitic properties that target the minor groove of DNA. The mechanism of action of these compounds is unknown, but topological changes to DNA structure are a possibility. In this study, we have developed a polyacrylamide gel based screening method to determine topological effects of diamidines on four target sequences: AAAAA, TTTAA, AAATT, and ATATA. The changes caused are sequence dependent, but generally the effect on AAAAA and AAATT is the same while the effect on TTTAA and ATATA is the same. A few compounds show interesting sequence dependent topological effects in the polyacrylamide screening method that could be caused by the compound forming a dimer. Mass spectrometry is used to determine the stoichiometry of DNA-compound complexes. Once compounds show topological effects in the screening method, a bent fragment of kinetoplast DNA is isolated to determine if the same effects occur with DNA from a parasite.

Les isolants topologiques sont des isolants qui ne peuvent être différenciés des isolants atomiques que par une grandeur physique non locale appelée invariant topologique. L'effet Hall quantique et son équivalent sans champ magnétique l'isolant de Chern sont des exemples d'isolants topologiques. En présence d'interactions fortes, des excitations exotiques appelées anyons peuvent apparaître dans les isolants topologiques. L'effet Hall quantique fractionnaire (EHQF) est la seule réalisation expérimentale connue de ces phases. Dans ce manuscrit, nous étudions numériquement les conditions d'émergence de différents isolants topologiques fractionnaires. Nous nous concentrons d'abord sur l'étude de l'EHQF sur le tore. Nous introduisons une méthode de construction projective des états EHQF les plus exotiques complémentaire par rapport aux méthodes existantes. Nous étudions les excitations de basse énergie sur le tore de deux états EHQF, les états de Laughlin et de Moore-Read. Nous proposons des fonctions d'onde pour les décrire, et vérifions leur validité numériquement. Grâce à cette description, nous caractérisons les excitations de basse énergie de l'état de Laughlin dans les isolants de Chern. Nous démontrons également la stabilité d'autres états de l'EHQF dans les isolants de Chern, tels que les états de fermions composites, Halperin et NASS. Nous explorons ensuite des phases fractionnaires sans équivallent dans la physique de l'EHQF, d'abord en choisissant un modèle dont l'invariant topologique a une valeur plus élevée, puis en imposant au système la conservation de la symétrie par renversement du temps, ce qui modifie la nature de l'invariant topologique
Topological insulators are band insulators which are fundamentally different from atomic insulators. Only a non-local quantity called topological invariant can distinguish these two phases. The quantum Hall effect is the first example of a topological insulator, but the same phase can arise in the absence of a magnetic field, and is called a Chern insulator. In the presence of strong interactions, topological insulators may host exotic excitations called anyons. The fractional quantum Hall effect is the only experimentally realized example of such phase. In this manuscript, we study the conditions of emergence of different types of fractional topological insulators, using numerical simulations. We first look at the fractional quantum Hall effect on the torus. We introduce a new projective construction of exotic quantum Hall states that complements the existing construction. We study the low energy excitations on the torus of two of the most emblematic quantum Hall states, the Laughlin and Moore-Read states. We propose and validate model wave functions to describe them. We apply this knowledge to characterize the excitations of the Laughlin state in Chern insulators. We show the stability of other fractional quantum Hall states in Chern insulators, the composite fermion, Halperin and NASS states. We explore the physics of fractional phases with no equivalent in a quantum Hall system, using two different strategies: first by choosing a model with a higher value of the topological invariant, second by adding time-reversal symmetry, which changes the nature of the topological invariant

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
Electromagnetic fields acting on particles have been extensively studied in different areas of physics. In quantum mechanics for example, effects such as Aharonov-Bohm, Landau levels and Hall conductivity, have always motivated new papers including analogous inertial models. Inertial effects play an important role in classical mechanics, but have been largely ignored in quantum mechanics. However, the analogy between inertial forces on mass particles and electromagnetic forces on charged particles is not new. Another factor that may influence the classical and quantum behavior of particles is geometry. An element related to geometry that has been extensively studied in several areas is the topological defect. Topological defects represent an interface between areas such as cosmology, gravitation, and condensed matter. Such defects in condensed matter can be developed through the classical theory of elasticity. However, due to the interdisciplinarity of this theme, approaches from gravitation can also describe them. Based on this analogy, the medium formed by a topological defect is characterized by a metric tensor. From this approach, several problems can be discussed by analyzing the influence of the topological defect in the solution of the problem. In this work, it will be discussed how magnetic field, rotation and topological defects, especially the disclination, influence in the Landau Levels and the Hall conductivity for a noninteracting planar two-dimensional electron gas. First we will discuss the influence of each of these elements and then the influence of all of them simultaneously.
A atuação de campos eletromagnéticos em partículas têm sido extensivamente estudada em diferentes áreas da física. Em mecânica quântica por exemplo, efeitos como Aharonov-Bohm, níveis de Landau e condutividade Hall, têm sempre motivado novos trabalhos inclusive para modelos análogos inerciais. Os efeitos inerciais desempenham um papel importante na mecânica clássica, mas tem sido largamente ignorados em mecânica quântica. No entanto, a analogia entre forças inerciais sobre partículas de massa e forças eletromagnéticas sobre partículas carregadas não é nova. Um outro fator que pode influenciar no comportamento clássico e quântico de partículas é a geometria. Um elemento relacionado a geometria e que tem sido bastante estudado em diversas áreas, é o defeito topológico. Os defeitos topológicos representam uma interface entre áreas como cosmologia, gravitação e matéria condensada. Tais defeitos em matéria condensada podem ser desenvolvidos através da teoria clássica da elasticidade. Contudo, devido a interdisciplinaridade desse tema, abordagens provenientes da gravitação podem também descrevê-los. Com base nessa analogia, caracteriza-se o meio formado por um defeito topológico mediante um tensor métrico. A partir dessa abordagem, diversos problemas podem ser discutidos analisando a influência do defeito topológico na solução do problema. Nesse trabalho, será discutido como campo magnético, rotação e defeitos topológicos, em especial a desclinação, influenciam os níveis de Landau e a condutividade Hall para um gás de elétrons bidimensional planar não interagente. Primeiramente discutiremos a influência de cada um desses elementos e em seguida a influência de todos simultaneamente. Será mostrado como a rotação quebra a degenerescência dos níveis de Landau aumentando consequentemente a condutividade Hall. Será mostrado também que acoplamento dos três elementos gera uma região para campos magnéticos fracos com sem estados ligados. Com um outro ponto de partida mostraremos também que a rotação pode ser utilizada para sintonizar a condutividade Hall.

Les couches minces d'oxyde présentent un large éventail de phénomènes physiques et riches diagrammes de phase, ajustables par l'ingénierie des déformations et des interfaces. Le CaMnO3, en particulier, est extrêmement sensible au dopage et aux contraintes d’épitaxie et, lorsqu'il est élaboré sous compression, il passe d'un état isolant et antiferromagnétique à un état métallique et faiblement ferromagnétique à seulement 2% de dopage au Ce.Nous avons utilisé une combinaison de spectroscopie de photoémission résolue en angle, de magnétotransport et de théorie de la fonctionnelle de la densité pour étudier les propriétés électroniques de ce matériau. Nous avons observé l'existence de deux porteurs de charge distincts, les électrons légers et les polarons lourds, dont la nature diffère en raison de leur couplage radicalement différent aux phonons. Nous attribuons ces différences à un remplissage relatif différent de la bande en raison des corrélations, qui améliorent considérablement le couplage aux phonons de la bande des polarons lourds. Les expériences de magnétotransport révèlent que la bande polaire domine le transport malgré sa mobilité réduite.La compression épitaxiale donne également lieu à une forte anisotropie magnétique qui stabilise des bulles magnétiques et s’accompagnent d’un effet Hall topologique. Cela suggère que ces bulles ont un caractère topologique. L'effet Hall topologique diverge lorsque la manganite s'approche de la transition métal-isolant à faible dopage. Nous avons utilisé une théorie récemment développée pour interpréter ce comportement, et nous concluons que des corrélations peuvent entrer en jeu, augmentant la masse effective des porteurs et par conséquent l'effet Hall topologique.Comme cette manganite est très sensible aux changements de densités de porteurs, nous avons développé des transistors à effet de champ ferroélectriques BiFeO3/(Ca,Ce)MnO3. Lors de la commutation de la polarisation ferroélectrique de la couche supérieure de BiFeO3, nous n'avons pu observer de changement notable dans les propriétés des couches de manganite sous-jacentes. Nous avons utilisé la microscopie électronique en transmission pour étudier les propriétés de ces bicouches avec une résolution atomique, et nous avons observé que l'épinglage de polarisation à l’interface BiFeO3/(Ca,Ce)MnO3 empêche une commutation complète de la polarisation et réduit ainsi la capacité opérationnelle de ces dispositifs. Néanmoins, nous avons pu détecter l’influence de la polarisation ferroélectrique sur les propriétés électroniques de la manganite à l’échelle atomique
Oxide thin films feature a wide range of physical phenomena and rich phase diagrams tunable by strain and interface engineering. CaMnO3, in particular, is extremely sensitive to both doping and strain and, when grown with compressive strain, transitions from an insulating and antiferromagnetic state to a metallic and weakly ferromagnetic state at only 2% Ce doping.We used a combination of angle-resolved photoemission spectroscopy, magnetotransport, and density functional theory to study the electronic properties of this material. We observed the existence of two separate charge carriers, light electrons and heavy polarons, whose physical nature differs because of drastically different couplings to phonons. We ascribe these differences to a different relative band filling due to correlations, which enhance greatly the coupling to phonons of the heavy polarons band. Magnetotransport experiments reveal that the polaron band dominates transport despite its lower mobility.Compressive strain also gives rise to a strong magnetic anisotropy which stabilizes magnetic bubbles that accompany a topological Hall effect. This suggests that these bubbles have topological character, i.e. are skyrmion bubbles. The topological Hall effect diverges as the manganite approaches the metal-insulator transition at low dopings. We used a recently developed theory in order to interpret this behavior, and we conclude that correlations may come into play, enhancing the effective mass of the carriers, and in turn the topological Hall effect.As this manganite is highly sensitive to changes in doping and carrier density, we grew BiFeO3/(Ca,Ce)MnO3 ferroelectric field-effect transistors. Upon switching the ferroelectric polarization of the BiFeO3 top layer, we could not observe any sizable changes in the properties of the underlying manganite layers. We used transmission electron microscopy to study the properties of these bilayers with an atomic resolution, and we observed that polarization pinning at the BiFeO3/(Ca,Ce)MnO3 impedes a complete switch of the polarization and so reduces the operational capabilities of these devices. Nevertheless, we could detect modifications of the electronic properties of the manganite induced by polarization reversal at the atomic scale

Cette thèse traite de l'application des approches topologiques de la liaison chimique à des systèmes contenant des éléments lourds sujets aux effets relativistes, notamment ceux dépendant du spin. Elle présente deux volets principaux : (i) l'évaluation des effets du couplage spin-orbite (SO) sur la structure électronique à l'aide d'une analyse combinée des propriétés de la fonction ELF et de l'approche QTAIM en deux composantes et (ii) la rationalisation des distorsions structurales pour des molécules impliquant des éléments lourds et le rôle du couplage SO dans ces distorsions. Nous avons pu mettre en évidence différentes situations pour lesquelles le couplage SO peut avoir une influence très importante, modérée ou négligeable. Un résultat important de ce travail démontre la dépendance du couplage SO à son environnement chimique. Pour le second volet, nous avons élaboré une approche qui a consisté à établir une corrélation entre les interactions électrostatiques locales entre régions liantes et non liantes (bassins ELF et QTAIM) et la géométrie moléculaire du système dans l'esprit des modèles VSEPR et du Ligand Close Packing (LCP). Cette approche a notamment mis en évidence la connexion entre la structure moléculaire et les répulsions des paires non-liantes de l'atome central avec leur environnement
This thesis deals with the aplication of topological approaches of the chemical bonding by means of analysing properties of density-based functions like Electron Localization Function (ELF) and the Quantum Theory of Atoms in Molecumes (QTAIM) to systems involving heavy elements such as 6p elements or actinides . It is divided into two main parts: (i) the evaluation of the spin-orbit coupling (SOC) effects on the electronic structure by means of combination of the QTAIM and ELF topological analyses in the field of quasirelativistic quantum calculations, and (ii) the rationalization of structural distorsions on molecules containing heavy atoms, and the role of the SOC on these distorsions. We were able to emphasize different situations for which SOC has strong, moderate or tiny influence on the chemical bonding, depending on the chemical environnement on which the heavy element is involved. In the second part of this thesis we tested our approach consisting of ELF/QTAIM interbasin repulsion energy analysis in connection with the molecular geometry of the system, in the spirit of the VSEPR and LCP models

The search for a Majorana Fermion has been an area of intense interest in condensed matter research of late. This elusive particle, predicted to exist in 1937, has been sought after for both fundamental and practical reasons. On the fundamental level, no particle to date has been observed to be a Majorana fermion, meanwhile on the practical level a Majorana fermion, if found, would represent a non-abelian anyon and could thus be used to build a quantum computer. The search for a Majorana Fermion has recently shifted to topological superconductivity. Topological superconductors are categorized by the nontrivial winding of their order parameter phase and for this reason are expected to support Majorana Fermions in their vortex cores. Owing to this, the study of topological superconductors has intensified in recent years. Current proposals for a device that may behave as a topological superconductor are based on semiconductor heterostructures, where the spin-orbit coupled bands of a semiconductor are split by a band gap or Zeeman field and superconductivity is induced by proximity to a conventional superconductor. In this setup, topological superconductivity is obtained in the semiconductor layer and the proposed heterostructures typically include two or three layers of different materials. In this thesis we propose a simplification to these types of devices, suggesting a way in which the superconducting layer can be replaced. Part of our proposal includes a model Hamiltonian for these types of systems. This thesis will also develop several different methods to analyze this model Hamiltonian in various different parameter regimes with the ultimate goal of classifying its topology.
Récemment, une région d'intérêt en la recherché de la matière condensée est le recherche pour les "Majorana Fermions". Les physiciens sont fascinés avec cette particule pour des raisons fondamentales et pratiques. Fondamentalement, une particule se comporte comme un Majorana Fermion n'a jamais été trouvée avant. Pratiquement, un Majorana Fermion pourrait être utilisé pour la construction d'un ordinateur quantique. Dans les dernières années, les chercheurs ont commencé à chercher pour des Majorana Fermions dans les supraconducteurs. En particulier, les supraconducteurs topologiques sont crus de supportes les Majorana Fermions dans leur vortex cores et de ce fait des nombreux dispositifs supraconducteurs topologiques ont été proposées. Les propositions récemment sont basées sur les hétérostructures de trois ou deux couches. Dans ces hétérostructures, les bandes d'un semiconducteur avec le couplage de spin-orbit sont séparées par le champ Zeeman d'une couche ferromagnétique (ou un champ appliqué). Après cette, supraconductivité topologique est établie dans la couche de semiconductrice en raison de la proximité d'une couche de supraconducteur ordinaire. Dans cette thèse nous proposons une simplification des dispositifs décrits ci-dessus; nous suggérons un moyen d'enlever la couche de supraconductivité. Nous commençons par proposer un Hamiltonian du cette système et procède à développer des nombreuses méthodes pour analyser cette Hamiltonian avec l'objectif ultime de classifier la topologie de ce système.

Les isolants topologiques constituent une nouvelle classe de matériaux caractérisés par l'association d'un volume isolant et de surfaces conductrices. Avec des propriétés électroniques similaires au graphene, notamment un transport régit par des particules à énergie de dispersion linéaire couramment appelés fermions de Dirac ainsi qu'une protection topologique empêchant tout phénomène de rétrodiffusion, ces matériaux suscitent un intérêt grandissant dans la quête d'une électronique de faible consommation. En effet, la production de courants de spin non-dissipatifs et polarisés ainsi que la formation de courants de spin purs en l'absence de matériaux magnétiques constituent une partie des attentes de ces matériaux topologiques.L'objectif de cette thèse a été de démontrer expérimentalement le potentiel de l'isolant topologique HgTe pour des applications notamment dans le domaine de la l'électronique de spin ou spintronique.Pour ce faire, d'importants efforts ont été mis en œuvre pour améliorer le procédé de croissance par épitaxie par jets moléculaires.La composition chimique, la contrainte ainsi que la qualité des interfaces de la couche de HgTe ont été identifiées comme des axes majeurs de travail et d'optimisation afin d'obtenir une structure de bande inversée, l'ouverture d'un gap de volume, ainsi que pour protéger les propriétés électroniques des états de surface topologiques. Fort de ces caractéristiques, notre matériau possède à priori toutes les qualités nécessaires pour permettre de sonder les propriétés topologiques. Accéder à ces propriétés particulières est en particulier possible par des mesures d'effet Hall quantique sur des structures de type barres de Hall. La fabrication de ces dispositifs a néanmoins requis une attention particulière à cause de la forte volatilité du mercure et a nécessité le développement d'un procédé de nanofabrication à basses températures.Des mesures d'effet Hall quantique à très basses températures ont ensuite été réalisées dans un cryostat à dilution. Tout d'abord des couches épaisses de HgTe ont été mesurées et ont démontrées des mécanismes de transport très complexes mêlant les états de surface topologiques à d'autres contributions attribuées au volume et aux états de surface latéraux. La réduction de l'épaisseur des couches de HgTe a permis de limiter l'impact de ces contributions en les rendant négligeable pour les couches les plus fines. Dans ces conditions, ces structures ont affiché les propriétés attendues de l'effet Hall quantique avec notamment une annulation de la résistance. Avec ces propriétés, l'analyse en température de l'effet Hall quantique a permis de démontrer la nature des porteurs circulant sur les états de surface topologiques et de les identifier à des fermions de Dirac.Avec la mise en évidence de la nature topologique de notre système, l'étape suivante a été d'utiliser les propriétés topologiques et plus particulièrement le blocage entre le moment et le spin d'un électron pour tester le potentiel du système 3D HgTe/CdTe pour la spintronique. Premièrement, des mesures de pompage de spin ont été réalisées et ont mis en exergue la puissance de ces structures pour l'injection et la détection de spin. Deuxièmement, ces structures ont été implémentéessous la forme de jonction p-n dans l'idée de réaliser un premier dispositif de spintronique qui présente à ce jour des premiers signes de fonctionnement
With graphene-like transport properties governed by massless Dirac fermions and a topological protection preventing from backscattering phenomena, topological insulators, characterized by an insulating bulk and conducting surfaces, are of main interest to build low power consumption electronic building-blocks of primary importance for future electronics.Indeed, the absence of disorder, the generation of dissipation-less spin-polarized current or even the possibility to generate pure spin current without magnetic materials are some of the promises of these new materials.The objective of this PhD thesis has been to experimentally demonstrate the eligibility of HgTe three dimensional topological insulator system for applications and especially for spintronics.To do so, strong efforts have been dedicated to the improvement of the growth process by molecular beam epitaxy.Chemical composition, strain, defect density and sharpness of the HgTe interfaces have been identified as the major parameters of study and improvement to ensure HgTe inverted band structure, bulk gap opening and to emphasize the resulting topological surface state electronic properties. Verification of the topological nature of this system has then been performed using low temperature magneto-transport measurements of Hall bars designed with various HgTe thicknesses. It is worth noting that the high desorption rate of Hg has made the nanofabrication process more complex and required the development of a low temperature process adapted to this constraint. While the thicker samples have evidenced very complex transport signatures that need to be further investigated and understood, the thickness reduction has led to the suppression of any additional contributions, such as bulk or even side surfaces, and the demonstration of quantum Hall effect with vanishing resistance. Consequently, we have managed to demonstrate direct evidences of Dirac fermions by temperature dependent analysis of the quantum Hall effect. The next step has been to use the topological properties and especially the locking predicted between momentum and spin to test the HgTe potential for spintronics. Spin pumping experiments have demonstrated the power of these topological structures for spin injection and detection. Moreover, the implementation of HgTe into simple p-n junction has also been investigated to realize a first spin-based logic element

We investigate theoretically the topological Kondo effect (TKE) and related non-Fermi-liquid (NFL) phenomena in correlated mesoscopic devices containing Majorana fermions. Using the numerical renormalisation group (NRG), we confirm and extend results obtained by conformal field theory (CFT) and we calculate numerically exact conductance curves for several different devices over large temperature ranges, which could be compared directly to future experiments. Our calculations uncover a wide range of physics in these mesoscopic devices and we derive several effective models to explain this behaviour. We first consider the prototypical model proposed by Béri and Cooper [B. Béri and N. R. Cooper. Phys. Rev. Lett., 109, 156803 (2012).] in which a non-local spin-1/2 is coupled to spin-1 conduction electrons. This model was proposed as the minimal model for the TKE, arising as the low-energy effective model of a superconducting grain connected to three leads containing Majorana fermions at the ends. We study the model in detail, confirming asymptotic CFT results and calculating the full conductance curves. We show that the NFL physics is robust to asymmetric Majorana-lead couplings, and uncover a duality between weak- and strong-coupling regimes using Abelian bosonisation. We also show how inter-Majorana couplings destabilise the NFL behaviour. We next consider the device beyond the effective spin-1/2 model, working instead with an Anderson-type model where charge fluctuations can be taken into account. We consider various possibilities for the energy levels on the superconducting grain and calculate and compare the behaviour in each case. We show that the NFL physics is robust to charge fluctuations, and is not restricted only to the regime of a non-degenerate ground state on the superconductor with large charging energy. We also derive various low-energy effective models for the different charging states. Finally, we investigate the device with a fourth lead attached. This gives rise to an effective two-channel Kondo model, but the device geometry means that the conductance is distinct from that studied previously. We also consider the full Anderson model, showing again that the conductance results are robust to charge fluctuations.

In this thesis, we investigate the quantum transport properties of disordered three dimensional topological insulator (3DTI) nanostructures of BiSe and BiTe in detail. Despite their intrinsic bulk conductivity, we show the possibility to study the specific transport properties of the topological surface states (TSS), either with or without quantum confinement. Importantly, we demonstrate that unusual transport properties not only come from the Dirac nature of the quasi-particles, but also from their spin texture. Without quantum confinement (wide ribbons), the transport properties of diffusive 2D spin-helical Dirac fermions are investigated. Using high magnetic fields allows us to measure and separate all contributions to charge transport. Band bending is investigated in BiSe nanostructures, revealing an inversion from upward to downward bending when decreasing the bulk doping. This result points out the need to control simultaneously both the bulk and surface residual doping in order to produce bulk-depleted nanostructures and to study TSS only. Moreover, Shubnikov-de-Haas oscillations and transconductance measurements are used to measure the ratio of the transport length to the electronic mean free path ltr/le. This ratio is measured to be close to one for bulk states, whereas it is close to 8 for TSS, which is a hallmark of the anisotropic scattering of spin-helical Dirac fermions. With transverse quantum confinement (narrow wires or ribbons), the ballistic transport of quasi-1D surface modes is evidenced by mesoscopic transport measurements, and specific properties due to their topological nature are revealed at very low temperatures. The metallic surface states are directly evidenced by the measure of periodic Aharonov-Bohm oscillations (ABO) in 3DTI nanowires. Their exponential temperature dependence gives an unusual power-law temperature dependence of the phase coherence length, which is interpreted in terms of quasi-ballistic transport and decoherence in the weak-coupling regime. This remarkable finding is a consequence of the enhanced transport length, which is comparable to the perimeter. Besides, the ballistic transport of quasi-1D surface modes is further evidenced by the observation of non-universal conductance fluctuations in a BiSe nanowire, despite the long-length limit (L > ltr) and a high metallicity (many modes). We show that such an unusual property for a mesoscopic conductor is related to the limited mixing of the transverse modes by disorder, as confirmed by numerical calculations. Importantly, a model based on the modes' transmissions allows us to describe our experimental results, including the full temperature dependence of the ABO amplitude.

From the alignment of magnets to the melting of ice, the transition between different phases of matter underpins our exploitation of materials. Both a quantum and a classical phase can undergo an instability into another state. In this thesis, we study the stability of matter in both contexts: topological states and crystalline solids. We start with the stability of fractional quantum Hall states on a lattice, known as fractional Chern insulators. We investigate, using exact diagonalization, fractional Chern insulators in higher Chern bands of the Harper-Hofstadter model, and examine the robustness of their many-body energy gap in the effective continuum limit. We report evidence of stable states in this regime; comment on two cases associated with a bosonic integer quantum Hall effect; and find a modulation of the correlation function in higher Chern bands. We next examine the stability of molecules using variational and diffusion Monte Carlo. By incorporating the matrix of force constants directly into the algorithms, we find that we are able to improve the efficiency and accuracy of atomic relaxation and eigenfrequency calculation. We test the performance on a diverse selection of case studies, with varying symmetries and mass distributions, and show that the proposed formalism outperforms existing restricted Hartree-Fock and density functional theory methods. Finally, we analyze the stability of three-dimensional crystals. We note that for repulsive Coulomb crystals of point nuclei, cubic systems have a zero matrix of force constants at second order. We investigate this by constructing an analytical model in the tight-binding approximation, and present a phase diagram of the most stable crystal structures, as we tune core and valence orbital radii. We reconcile our results with calculations in the nearly free electron regime, as well as current research in condensed matter and plasma physics.

The conventional Casimir effect manifests itself as a quantum mechanical force between two plates, that arises from the quantization of the electromagnetic field in the enclosed vacuum. In this thesis the existence is discussed of an extra, topological term in the Casimir energy at finite temperatures. This topological Casimir effect emerges due to the nontrivial topological features of the gauge theory: the extra energy is the result of tunneling transitions between states that are physically the same but topologically distinct. It becomes apparent when examining, for instance, periodic boundary conditions. I explicitly calculate the new term for the simplest example of such a system, a Euclidean 4-torus. By dimensional reduction, this system is closely related to two dimensional electromagnetism on a torus, which is well understood. It turns out that the topological term is extremely small compared to the conventional Casimir energy, but that the effect is very sensitive to an external magnetic field. The external field plays the role of a topological theta parameter, analogous to the theta vacuum in Yang-Mills theory. The topological Casimir pressure and the induced magnetic field show a distinctive oscillation as a function of the external field strength, something that can hopefully be observed experimentally.

The aim of this thesis was to identify topologically protected states in the materials SnTe and Fe3Sn2. Such states are currently receiving a large amount of interest due to their applications for spintronic devices. Recently SnTe was discovered to be a crystalline topological insulator, a state of matter where its surface is highly conducting while the bulk remains insulating. However detection of these surface states is difficult using transport measurements, since the bulk is not totally insulating but still contains a large number of free carriers. SnTe undergoes a rhombohedral structural distortion on cooling caused by a soft transverse optic phonon, with the exact Tc strongly dependent on the carrier concentration. The distortion acts to lower crystal symmetry removing some of the symmetries that protect the surface state. Single crystal samples displaying the structural transition were grown and investigated using inelastic X-ray scattering to measure the phonon softening previously reported by other authors. The soft phonon was seen to recover again after distortion indicative of a 2nd order ferroelectric transition. This is the first reported discovery of the recovery showing the distortion is ferroelectric in nature. Shubnikov de Haas quantum oscillations were measured to study the Fermi surface under ambient and high hydrostatic pressure conditions. A distortion of the Fermi surface caused by the structural transition was evident, resulting in 4 distinct oscillation frequencies. However at applied pressures above 6 kbar, the transition was suppressed and only 1 oscillation measured. A two component Hall response also becomes apparent under high pressure. The possible origin of this and its relation to possible surface states is discussed. The anomalous Hall effect was also measured in the ferromagnet Fe3Sn2 which has a bilayer Kagome structure. Previous measurements on polycrystalline Fe3Sn2 suggested a non-collinear spin rotation from the spins pointing along the c-axis at high temperature to lying in the a-b plane below 80 K. A spin glass phase is then expected below 80 K. Single crystal magnetisation measurements carried out in this thesis show the spins are in the a-b plane at high temperatures and begin to display a ferromagnetic component along the c-axis approaching 80 K. The difference is accounted for by considering the demagnetising factor in the plate shaped single crystals. For this temperature range an applied field along the c-direction however rotates the moments towards c. At intermediate fields there are strong features evident in both the anomalous Hall effect and magnetoresistance. These features may be due to a topological Hall effect caused by a non-collinear spin structure. The possible existence of Skyrmion excitations was also recently discussed theoretically in Fe3Sn2. Our data is more suggestive of static Skyrmions known to cause topological Hall effects in MnSi.

Cette thèse poursuit deux directions dans le domaine des isolants et supraconducteurs topologiques.Dans la première partie de la thèse nous étudions des isolants en deux dimensions sur réseau, présentant un effet Hall quantique anormal (c'est-à-dire en l'absence d'un champ magnétique externe), induit par la présence d'un flux magnétique inhomogène dans la maille. Le système possède des phase isolantes caractérisés par un invariant topologique, le nombre de Chern, qui est lié à la conductance portée par le bord états. Nous montrons que les modèles à deux bandes admettent des phase à nombre de Chern arbitraire, ou, de façon équivalente, un nombre arbitraire d'états de bord, quand on augmente la portée des couplages sur réseau. Cette compréhension est rendue possible grâce à la démonstration d'une formule montrant que le nombre de Chern d'une bande dépend de certains propriétés d'un ensemble discret de points dans la zone de Brillouin, les points de Dirac en l'absence du gap. Ces idées sont rendues plus concrètes dans l'étude du modèle de Haldane et dans la création d'un modèle artificiel avec cinq phases de Chern dont les états de bord sont déterminés en détail. La deuxième partie de la thèse porte sur les supraconducteurs topologiques unidimensionnels qui exhibent des états exotiques d'énergie zéro: les états liés de Majorana. Nous étudions ici la présence de fermions de Majorana dans des fils de semiconducteurs à fort couplage spin-orbite sous l’effet de proximité d'un supraconducteur d'onde s. Nous montrons que la polarisation de spin des degrés de liberté électroniques dans la fonction d'onde Majorana dépend du poids relatif du couplage spin-orbite Dresselhaus et Rashba. Nous étudions également les fermions de Majorana dans des jonctions linéaires longues supraconducteur-normal et supraconducteur-normal-supraconducteur (SNS) où ils apparaissent comme des états étendus dans la jonction normale. En outre, la géométrie d'anneaux peut être mise en correspondance avec une jonction SNS, et, sous l'action de gradients dans la phase supraconductrice, des fermions Majorana étendus se forment encore à l'intérieur du fil normal. Enfin, un modèle à deux bandes avec des fermions de Majorana multiples est traité. Nous démontrons que les jonctions Josephson construites à partir de ce modèle maintiennent l'une des signatures remarquables des fermions de Majorana, à savoir la périodicité 4π de l'effet Josephson fractionnaire
This thesis follows two threads in the field of topological insulators and superconductors. The first part of the thesis is devoted to the study of two-dimensional quantum anomalous Hall insulators on a lattice, in the absence of an external magnetic flux, but induced by an inhomogeneous flux in the unit cell. The system possesses several gapped phases characterized by a topological invariant, the Chern number, that is related to the conductance carried by the edge states. Here we show that two-band models admit an arbitrary large number of Chern phases or, equivalently, an arbitrary number of edge states, by adding hopping between distant neighbor sites. This result is based on a formula proving that the Chern number of a band depends on certain properties of a finite set of points in the Brillouin zone, i.e. the Dirac points for the gapless system. These ideas are made more concrete in the study of a modified Haldane model, and also by creating an artificial model with five Chern phases, whose edge states are determined in detail. The second part of the thesis focuses on one-dimensional topological superconductors with exotic zero-energy edge states: the Majorana bound states. Here we investigate the presence of Majorana fermions in spin-orbit coupled semiconducting wire in proximity to an s-wave superconductor. We show that the spin-polarization of the electronic degrees of freedom in the Majorana wave function depends on the relative weight of Dresselhaus and Rashba spin-orbit couplings. We also investigate Majorana fermions in linear superconductor-normal and long superconductor-normal-superconductor (SNS) junctions where they appear as extended states in the normal junction. Furthermore, ring geometries can be mapped to an SNS junction, and, we have shown that under the action of superconducting phases gradients, extended Majorana fermions can form again inside the normal wire. Finally a two-band model with multiple Majorana fermions is treated and we show that Josephson junctions built from this model maintain the 4π periodicity for the fractional Josephson effect, one of Majorana fermions signatures

This thesis is a study of three categories of problems in fermionic systems for which topology plays an important role: (i) The properties of zero modes arising in systems of fermions interacting with a bosonic background, with a special focus on Majorana modes arising in the superconductor state. We propose a method for counting Majorana modes and we study a mechanism for controlling their number parity in lattice systems, two questions that are of relevance to the protection of quantum bits. (ii) The study of dispersionless bands in two dimensions as a platform for correlated physics, where it is shown the possibility of stabilizing the fractional quantum Hall effect in a flat band with Chern number. (iii) The extension of the hierarchy of quantum Hall fluids to the case of time-reversal symmetric incompressible ground states describing a phase of strongly interacting topological insulators in two dimensions.
Physics

Since their experimental discovery in 2008, topological insulators have been catapulted to the forefront of condensed matter physics research owing to their potential to realize both exciting new technologies as well as novel electronic phases that are inaccessible in any other material class. Their exotic properties arise from a rare quantum organization of its electrons called ``topological order,'' which evades the conventional broken symmetry based-classification scheme used to categorize nearly every other state of ordered matter. Instead, topologically ordered phases are classified by topological invariants, which characterize the phase of an electron's wavefunction as it moves through momentum space. When a topologically ordered phase is interfaced with an ordinary phase, such as the vacuum, a novel metallic state appears at their shared boundary. In topological insulators, this results in the formation of a two-dimensional metallic state that spans all of its surfaces. The surface state electronic spectrum is characterized by a single linearly dispersing and helically spin-polarized Dirac cone that is robust against disorder. The helical nature of the surface Dirac cone is highly novel because the Dirac electrons carry a net magnetic moment and are capable of transporting 100% spin-polarized electrical currents, which are the long-sought electronic properties needed for many spin-based electronic applications. However, owing to the small bulk band gap and intrinsic electronic doping inherent to these materials, isolating the surface electronic response from the bulk has proven to be a major experimental obstacle. In this thesis, we demonstrate the means by which light can be used to isolate and study the surface electronic response of topological insulators using optoelectronic and nonlinear optical techniques. In chapter 1, we overview the physics of topological order and topological insulators. In chapter 2, we show how polarized light can be used to generate and control surface electrical currents that originate from the helical Dirac cone. In chapter 3, we demonstrate that the nonlinear second harmonic generation of light from a topological insulator is a sensitive surface probe and can be used to detect the breaking of space-time symmetries and monitor changes in the surface carrier density.
Physics

L'utilisation de matériaux ferromagnétiques a longtemps été l'unique méthode pour détecter et produire des courants de spin. Cependant, depuis le milieu des années 2000 des méthodes alternatives ont été proposées. Un champ émergent de la spintronique, appelé spin-orbitronique, s'attelle à l'utilisation du couplage spin orbite pour détecter et produire des courants de spin en l'absence de matériaux ferromagnétiques. Une interconversion efficace entre courant de spin et courant de charge a pu être obtenues à l'aide de l'effet Hall de spin dans les métaux lourds tels que le Platine ou le Tantale. Une telle conversion peut aussi être obtenue en utilisant l'effet Edelstein dans les interfaces Rashba et les isolants topologiques.La conversion de courant de spin à courant de charge par effet Hall de spin et effet Edelstein inverse peut être étudiée par la méthode dite du pompage de spin par résonance ferromagnétique. Ce manuscrit présente ces différents effets de conversion ainsi que la technique utilisée basée sur une mesure électrique effectuée à la résonance ferromagnétique. Y sont présentés des résultats de conversion spin charge dans les métaux, les interfaces Rashba à base d'oxydes ainsi que dans les isolants topologiques. Parmi ces systèmes nous avons montré la possibilité de moduler à l'aide d'une grille électrostatique la conversion spin charge dans un gaz d'électron bidimensionel obtenu à la surface de l'oxyde SrTiO3. De plus il est possible de moduler, de façon rémanente, la conversion dans SrTiO3 grâce à la ferroélectricité obtenue à des températures cryogéniques.Parmi les autres systèmes étudiés les isolants topologiques HgTe et Sb2Te3 présentent des propriétés de conversion spin vers charge prometteuses à température ambiante. En particulier dans le cas de HgTe, en utilisant une couche de protection de HgCdTe nous avons pu obtenir des niveaux de conversion un ordre de grandeur plus élevé que dans le Platine.Ces résultats suggèrent que les gaz d'électrons bidimensionnels aux interfaces d'oxydes ainsi que les isolants topologiques sont des systèmes prometteurs pour la détections de courants de spin pour des applications au delà de la logique CMOS
Using a ferromagnetic layer has been the first method to obtain and detect spin currents, allowing to modify the magnetization state of an adjacent layer using spin transfer torque. However, in recent years, an alternative way to manipulate spin currents has been proposed. An emerging field of spintronics, called spin-orbitronics, exploits the interplay between charge and spin currents enabled by the spin-orbit coupling (SOC) in non-magnetic systems. An efficient current conversion can be obtained through the Spin Hall Effect in heavy metals such as Platinum or Tantalum. The conversion can also be obtained by exploiting the Edelstein Effect in Rashba interfaces and topological insulators.The spin to charge conversion by means of Inverse Edelstein Effect and inverse Spin Hall Effect can be studied by the spin pumping by ferromagnetic resonance technique. This manuscript present these two conversion mechanisms as well as the technique that was used to measure them, which is based on an electrical detection of the ferromagnetic resonance. Results on the spin to charge current conversion obtained in metals, oxide-based Rashba interfaces and topological insulators will be presented. Among these systems we have demonstrated the possibility to tune the conversion efficiency by using a gate voltage in a two-dimensional electron gas at the surface of an oxide SrTiO3. Moreover it is possible to tune this effect, a remanent way, thanks to the ferroelectricity obtained in SrTiO3 at cryogenic temperatures.Other studied systems such as topological insulators HgTe and Sb2Te3 also have promising properties for an efficient spin to charge current conversion at room temperature. In particular we showed than in HgTe by using a thin HgCdTe protective layer, it is possible to obtain a spin to charge current conversion efficiency one order of magnitude larger than in Pt.These results suggest that stwo dimensional electron gases at oxide interfaces and topological insulators have a strong potential for the efficient detection of spin currents for possible beyond CMOS applications

Orientador: Pascoal José Giglio Pagliuso
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin
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Resumo: A ideia de topologia na Física da Matéria da Condensada, apesar de ter surgido com o efeito Hall quântico inteiro, só voltou a ser explorada recentemente na busca de novas fases da matéria depois do surgimento dos Isolantes Topológicos (ITs) 2D. Após a previsão teórica, e a descoberta experimental, foi proposto que esta nova fase poderia ser generalizada para sistemas 3D, em que o volume do material seria isolante com estados metálicos de superfície que possuiriam canais de spin polarizados. Apesar de diversos experimentos e o surgimento de outras fases topológicas da matéria subsequentes, ainda há dúvidas sobre a natureza dos ITs 3D. Os efeitos topológicos mais claros ainda não foram observados de forma inequívoca e reprodutível experimentalmente e ainda seria de extrema valia encontrar técnicas experimentais que possam complementar os mais discutidos experimentos de ARPES. Nesta dissertação foram estudadas duas famílias distintas de materiais propostas como possíveis ITs 3D: os binários Bi2Se3 e Sb2Te3 e o half-Heusler YPdBi. Utilizando a técnica de auto-fluxo e a fusão estequiométrica, os sistemas foram sintetizados dopados com os terras-rara Gd3+, Nd3+ e Er3+ para realizar estudos de ressonância de spin eletrônico (RSE) e do papel dos efeitos de campo cristalino (CEF) - no caso do half-Heusler. Para o ternário YPdBi foram feitos dois estudos. Na família dos half-Heuslers, a ordem topológica surge da relação entre o acoplamento spin-órbita e a hibridização, que está ligada com a mudança do parâmetro de rede, então os efeitos de CEF poderiam estar refletindo a transição entre a trivialidade e a não-trivialidade. A partir das medidas de susceptibilidade magnética em função da temperatura das amostras dopadas com Nd3+ e Er3+ combinadas com os estudos de RSE, foi possível extrair os parâmetros de campo cristalino (CFP) de quarta e sexta ordem. Comparando esses dados com resultados anteriores para o material, supostamente, não-trivial YPtBi, observou-se uma mudança sistemática no sinal dos CFP. Resultados prévios para as amostras de YPtBi dopadas com Nd3+ mostram uma evolução não usual para uma forma de linha difusiva com a potência de micro-onda. Neste trabalho também foi realizado um estudo da forma de linha em função da potência. Apenas a ressonância do Nd3+ para os monocristais de 10% de Nd em YPdBi mostrou uma forma de linha difusiva que evolui com a potência da micro-onda. No caso dos binários Bi2Se3 e Sb2Te3, o objetivo era otimizar a rampa de tratamento térmico para obter monocristais melhores que poderiam permitir a observação de um espectro totalmente resolvido do Gd3+. Após mudanças no crescimento dos monocristais, o espectro totalmente resolvido foi obtido para as amostras de Bi2Se3. No caso do Sb2Te3 apenas uma linha central com a estrutura fina colapsada foi observada. Acompanhando o deslocamento g e a evolução da largura de linha dH da RSE do Gd3+ com a temperatura, o comportamento negativo do deslocamento g para toda a faixa de temperatura indica que elétrons do tipo p são os grandes responsáveis pela formação da superfície de Fermi residual destes sistemas. Um aumento no coeficiente angular de dH em função da temperatura, a taxa Korringa b, foi observado em baixas temperaturas, logo diferentes concentrações de Gd3+ foram utilizadas para estudar este comportamento. Novamente observou-se um comportamento anômalo em baixas temperaturas, o que poderia estar relacionado com a evolução dos CFP com a temperatura. Todos esses resultados foram discutidos levando-se em conta a possibilidade de existência de topologia não-trivial na estrutura eletrônica desses materiais, com foco particular na relação da interação spin-órbita e os efeitos de campo cristalino com a manifestação da topologia não trivial nesses sistemas
Abstract: The idea of topological systems in Condensed Matter Physics, although already explored in the Quantum Hall Effect, has recently become a topic of intense scientific investigation. In particular, great efforts have been dedicated to the search for new quantum phases since the proposal of the Topological Insulators (TIs) in 2D. After the theoretical prediction and the experimental discovery of the TIs in the 2D case, the existence of the Quantum Hall Spin Effect in 3D, 3D TIs, was proposed, where an insulator bulk and metallic surface states with spin polarized channels could be experimentally realized. Although many experiments have been performed, and some groups claimed the direct observation of such new topological phases, there is still a lot of controversy about the nature of the 3D TIs and about the actual microscopic origin of the metallic states on the surface of the studied materials. Other signatures of the topological phases have not been unambiguously and repeatedly measured yet and there is an obvious lack of a supplementary lab technique to be compared to the most used technique to probe these states, which is ARPES. In this work we have studied two different classes of 3D TIs: the binaries Bi2Se3 and Sb2Te3 and the half-Heusler YPdBi. We have been able to grow single crystals of these materials pure and rare-earth doped with Gd3+, Nd3+ and Er3+ using the self-flux technique and the stoichiometric melting. The aim was to use these crystals to study Electron Spin Resonance (ESR) as a potential probe to investigate the existence of the metallic surface states and to explore the possible of the crystalline electrical field (CEF) effects on the formation of the non-trivial electronic structure of these materials. Regarding the YPdBi, our ESR and magnetization studies have revealed that, in the half-Heusler family, the topological order emerges from the interplay between spin-orbit coupling and the hybridization, which is connected with the changes on the lattice parameter. Thus, the CEF effects could reflect the transition from trivial to nontrivial topology. From the magnetic susceptibility data as a function of temperature from the Nd3+ and Er3+ doped samples combined with the ESR studies, it was possible to extract the fourth and sixth order crystal field parameters (CFP). Comparing our data with the previous results from YPtBi, which is a putative non-trivial material, a systematic change in the sign of the CFP was observed. Previous results with the YPtBi Nd-doped samples show an unusual evolution of the Nd3+ ESR line to a diusive-like line shape as a function of the microwave power. In this work we have performed a similar study of the Nd3+ ESR line shape as a function of the microwave power. Only for the single crystal of 10% Nd in YPdBi resonance shows a diffusive-like line shape that evolves with the microwave power. In the case of the binaries Bi2Se3 e Sb2Te3, the aim of this work was to optimize the heat treatment used in previous works of our group to obtain better single crystals that could allow the observation of the full resolved spectra from Gd3+. After many changes in the single crystal growth method, we were able to observe fully resolved Gd3+ ESR spectra in the Bi2Se3 samples. Regarding the Sb2Te3 single crystals, only a single Gd3+ Dysonian ESR line was observed. Following the Gd3+ ESR dg and dH as a function of temperature, the observed negative behavior of dg, in the whole temperature range studied, indicates that p-type electrons are the main source for the formation of the small the Fermi surface of these materials. An increase of the angular coefficient of dH as a function of temperature, the Korringa rate b, at low temperatures was observed and different concentrations of Gd3+ were required to investigate this anomaly. Again this anomalous behavior at low temperatures was observed for the all Gd-doped samples, which could be related to an evolution of CFP with temperature. We discuss our results taking into account the existence of non-trivial topological states in our samples and the role of spin-orbit and CEF effects might have in the formation of such states
Mestrado
Física
Mestre em Física
132653/2015-0
CNPQ
CAPES
FAPESP

This Thesis is devoted to the study of topological phases of matter in optical platforms, focusing on non-Hermitian systems with gain and losses involving nonreciprocal elements, and fractional quantum Hall liquids where strong interactions play a central role.In the first part we investigated nonlinear Taiji micro-ring resonators in passive and active silicon photonics setups. Such resonators establish a unidirectional coupling between the two whispering-gallery modes circulating in their perimeter. We started by demonstrating that a single nonlinear Taiji resonator coupled to a bus waveguide breaks Lorentz reciprocity. When a saturable gain is added to a single Taiji resonator, a sufficiently strong unidirectional coupling rules out the possibility of lasing in one of the whispering-gallery modes with independence of the type of optical nonlinearity and gain saturation displayed by the material. This can be regarded as a dynamical time-reversal symmetry breaking. This effect is further enhanced by an optical Kerr nonlinearity. We showed that both ring and Taiji resonators can work as optical isolators over a broad frequency band in realistic operating conditions. Our proposal relies on the presence of a strong pump in a single direction: as a consequence four-wave mixing can only couple the pump with small intensity signals propagating in the same direction. The resulting nonreciprocal devices circumvent the restrictions imposed by dynamic reciprocity. We then studied two-dimensional arrays of ring and Taiji resonators realizing quantum spin-Hall topological insulator lasers. The strong unidirectional coupling present in Taiji resonator lattices promotes lasing with a well-defined chirality while considerably improving the slope efficiency and reducing the lasing threshold. Finally, we demonstrated that lasing in a single helical mode can be obtained in quantum spin-Hall lasers of Taiji resonators by exploiting the optical nonlinearity of the material. In the second part of this Thesis we dived into more speculative waters and explored fractional quantum Hall liquids of cold atoms and photons. We proposed strategies to experimentally access the fractional charge and anyonic statistics of the quasihole excitations arising in the bulk of such systems. Heavy impurities introduced inside a fractional quantum Hall droplet will bind quasiholes, forming composite objects that we label as anyonic molecules. Restricting ourselves to molecules formed by one quasihole and a single impurity, we find that the bound quasihole gives a finite contribution to the impurity mass, that we are able to ascertain by considering the first-order correction to the Born-Oppenheimer approximation. The effective charge and statistical parameter of the molecule are given by the sum of those of the impurity and the quasihole, respectively. While the mass and charge of such objects can be directly assessed by imaging the cyclotron orbit described by a single molecule, the anyonic statistics manifest as a rigid shift of the interference fringes in the differential scattering cross section describing a collision between two molecules.

Dans cette thèse, j'adresse le sujet fascinant et attirant du transport de charge électrique et de chaleur dans les systèmes Hall quantiques, qui sont parmi l'exemple le plus célèbre des phases topologiques de la matière, en présence de potentiels électriques dépendantes du temps. L'effet Hall se produit dans des systèmes électroniques bidimensionnels dans la limite de forts champs magnétiques perpendiculaires. Le cachet de systèmes de Hall quantiques est l'apparition d'états de bord métalliques unidimensionnels sur les frontières du système.La longueur de cohérence assurée par la protection topologique garantit d’avoir accès à la nature ondulatoire des électrons. Ces propriétés ont inspiré un nouveau domaine de la recherche, connu comme la l'optique quantique électronique. Une source d’électrons individuels peut être réalisée en s'appliquant à un système de Hall quantique impulsions Lorentzian. En considérant l'application d'un train périodique d'impulsions Lorentzian à un système Hall quantique, j'examine la densité de charge d'un état composé par beaucoup de levitons dans le régime de Hall quantique fractionnaire, constatant ainsi qu'il est réarrangé dans une configuration réguliere de sommets et des vallées. Alors, j'analyse les propriétés de transport de chaleur des levitons dans les systèmes Hall quantiques, qui représente un nouveau point de vue sur l'optique quantique électronique, étendant et généralisant les résultats obtenus dans le transport de charge
In this thesis, I address the intriguing and appealing topic of charge and heat transport in quantum Hall systems, which are among the most famous example of topological phases of matter, in presence of external time-dependent voltages. Quantum Hall effect occurs in two-dimensional electron systems in the limit of strong perpendicular magnetic fields. The hallmark of quantum Hall systems is the emergence of one-dimensional metallic edge states on the boundary. Along these edge states particles propagate with a definite direction. The coherence length ensured by topological protection guarantees to access wave-like nature of electrons. This properties inspired a new field of research, known as electron quantum optic. Single-electron source can be realized by applying to a quantum Hall system a periodic train of Lorentzian-shaped pulses.Plateaus of the Hall resistance appear also at fractional values of the resistance quantum. The physical explanation of fractional quantum Hall effect cannot neglect the correlation between electrons and this phase of matter is inherently strongly-correlated. By considering the application of a periodic train of Lorentzian pulses to a quantum Hall system, I investigate the charge density of a state composed by many levitons in the fractional quantum Hall regime, thus finding that it is re-arranged into a regular pattern of peaks and valleys, reminiscent of Wigner crystallization in strongly-interacting electronic systems. Then, I analyze heat transport properties of levitons in quantum Hall systems, which represent a new point of view on electron quantum optics, extending and generalizing the results obtained in the charge domain

Dans cette thèse, j'adresse le sujet fascinant et attirant du transport de charge électrique et de chaleur dans les systèmes Hall quantiques, qui sont parmi l'exemple le plus célèbre des phases topologiques de la matière, en présence de potentiels électriques dépendantes du temps. L'effet Hall se produit dans des systèmes électroniques bidimensionnels dans la limite de forts champs magnétiques perpendiculaires. Le cachet de systèmes de Hall quantiques est l'apparition d'états de bord métalliques unidimensionnels sur les frontières du système.La longueur de cohérence assurée par la protection topologique garantit d’avoir accès à la nature ondulatoire des électrons. Ces propriétés ont inspiré un nouveau domaine de la recherche, connu comme la l'optique quantique électronique. Une source d’électrons individuels peut être réalisée en s'appliquant à un système de Hall quantique impulsions Lorentzian. En considérant l'application d'un train périodique d'impulsions Lorentzian à un système Hall quantique, j'examine la densité de charge d'un état composé par beaucoup de levitons dans le régime de Hall quantique fractionnaire, constatant ainsi qu'il est réarrangé dans une configuration réguliere de sommets et des vallées. Alors, j'analyse les propriétés de transport de chaleur des levitons dans les systèmes Hall quantiques, qui représente un nouveau point de vue sur l'optique quantique électronique, étendant et généralisant les résultats obtenus dans le transport de charge
In this thesis, I address the intriguing and appealing topic of charge and heat transport in quantum Hall systems, which are among the most famous example of topological phases of matter, in presence of external time-dependent voltages. Quantum Hall effect occurs in two-dimensional electron systems in the limit of strong perpendicular magnetic fields. The hallmark of quantum Hall systems is the emergence of one-dimensional metallic edge states on the boundary. Along these edge states particles propagate with a definite direction. The coherence length ensured by topological protection guarantees to access wave-like nature of electrons. This properties inspired a new field of research, known as electron quantum optic. Single-electron source can be realized by applying to a quantum Hall system a periodic train of Lorentzian-shaped pulses.Plateaus of the Hall resistance appear also at fractional values of the resistance quantum. The physical explanation of fractional quantum Hall effect cannot neglect the correlation between electrons and this phase of matter is inherently strongly-correlated. By considering the application of a periodic train of Lorentzian pulses to a quantum Hall system, I investigate the charge density of a state composed by many levitons in the fractional quantum Hall regime, thus finding that it is re-arranged into a regular pattern of peaks and valleys, reminiscent of Wigner crystallization in strongly-interacting electronic systems. Then, I analyze heat transport properties of levitons in quantum Hall systems, which represent a new point of view on electron quantum optics, extending and generalizing the results obtained in the charge domain

Coupling Majorana fermions to metallic conduction electrons will lead to the so-called topological Kondo effect, which is an embodiment of the exotic non-local properties that Majorana fermions possess. Using its minimal setup, this thesis studies the influence of this effect on the scattering properties of conduction electrons by analysing the component of the electron tunnelling density of states (tDOS) which oscillates at twice the Fermi wavenumber kF. We find that at zero bias this 2kF-tDOS displays a non-monotonic behaviour as the temperature is lowered. Starting from the exponential suppression at temperatures much larger than the characteristic Kondo temperature, the 2kF-tDOS may show a Kondo logarithmic peak before it crosses over to a T"3 decay, depending on the ratio of the junction-to-tunnelling distance at which the tDOS is being measured and the characteristic Kondo length. This then provides a way to estimate the extent of the Kondo screening cloud. At energies much below the Kondo temperature, the 2kF-tDOS is described by a universal scaling function indicative of strong correlations. The non-Fermi-liquid scattering occurs in this energy regime, which can be identified by the vanishing of single-particle-to-single-particle scattering at topological Kondo fixed point that in turn manifests in the complete suppression of the 2kF-tDOS at zero temperature and bias. Furthermore, we also have provided a practical method to use the 2kF-tDOS to extract information about the single-particle scattering matrix for more general quantum impurity systems.

Dans cette thèse, nous étudions d'un point de vue théorique différents aspects de la matière topologique. Ces systèmes présentent des propriétés résistantes aux éventuelles perturbations grâce à une topologie non-triviale de leur structure de bandes. En particulier, des excitations exotiques, par exemple des fermions de Majorana, peuvent apparaitre à leurs bords.L'entropie d'intrication, ainsi que le spectre d'intrication ont été fondamentaux dans l'étude théorique de ces systèmes, et plus généralement des phases libres. Il est cependant difficile de les mesurer expérimentalement. L'étude des fluctuations de charge bipartites a été proposée afin de remédier à ce problème, et celles-ci permettent une mesure faible de l'intrication, en particulier pour des modèles unidimensionnels libres. Nous généralisons les précédents travaux sur les Liquides de Luttinger à des familles génériques de supraconducteurs et isolants topologiques en une et deux dimensions, systèmes dans lesquels la charge observée n'est plus conservée. Nous montrons que les transitions de phases topologiques sont caractérisées par certains coefficients universels dans les fluctuations et les fonctions de corrélations. Les systèmes bidimensionnels que nous étudions présentent des cônes de Dirac, et ces coefficients dépendent de leur enroulement. Cela nous permet de caractériser la topologie de ces points critiques. Dans tous les cas, les fluctuations suivent une loi de volume, qui a un comportement non-analytique aux transition de phase.Dans un second temps, nous nous intéressons aux systèmes en interactions. Nous montrons tout d'abord que certaines des signatures des transitions topologiques survivent en leur présence, dans les supraconducteurs topologiques. Nous étudions ensuite le diagramme de phase de deux fils supraconducteurs couplés par une interaction Coulombienne. Celle-ci mène à la création de phases exotiques grâce à la compétition avec la supraconductivité non-conventionnelle. Nous montrons en particulier l'apparition de phases de Mott brisant spontanément la symétrie de renversement du temps et présentant des courant orbitaux non-triviaux, ainsi que celle d'une phase de fermions libres, qui est l'extension de deux chaînes de Majorana critiques en interaction.Enfin, nous nous intéressons aux effets de la présence de fermions de Majorana sur le transport électronique. Nous étudions un îlot supraconducteur où plusieurs de ces fermions existent. Ce système pourrait être l'un des composants élémentaires d'un éventuel ordinateur quantique. Les fermions de Majorana changent les statistiques d'échange des porteurs de charges, ce qui se traduit par une fractionnalisation de la conductance. Celle-ci se révèle très robuste face aux anisotropies et autres perturbations. Nous étendons les études précédentes au cas où le nombre d'électrons dans la boîte peut fluctuer, et montrons l'équivalence de ce problème avec le modèle Kondo à plusieurs canaux. Nous réinterprétons alors ce modèle en terme du déplacement d'une particule dans un réseau fictif dissipatif
In this thesis, we study theoretically different aspects of topological systems. These models present resilient properties due to a non-trivial topology of their band structures, and in particular exotic edge excitations such as Majorana fermions.Entanglement entropy and entanglement spectrum have been fundamental to the study of these systems and of gapless systems in general, but are difficult to measure experimentally. Bipartite charge fluctuations were proposed as a weak measurement of this entanglement, in particular for one-dimensional gapless phases. We extend previous results on standard Luttinger Liquids to generic families of one- and two-dimensional non-interacting topological systems. Through exact computations, we show that their critical points are characterized by universal coefficients that reveal the topological aspect of the transitions. In two dimensions, the Dirac cones give quantized contributions to the fluctuations and various correlation functions. These contributions depend on their winding numbers, allowing for a precise determination of the topological structure of the gapless points. A volume law is also present and linked to the Quantum Fisher information, with characteristic non-analyticities at the phase transitions.In a second time, we include interactions and show that some of these signatures are preserved in topological superconductors even in their presence. Through analytical (bosonization, renormalization group) and numerical (exact diagonalization and DMRG) methods, we study the phase diagram of two Coulomb-coupled topological superconducting wires. We are interested in their behavior when the interactions are strong enough to break the topological protection: the interplay between unconventional superconductivity and interactions leads to exotic phases. We show the appearance of phases spontaneously breaking the time-reversal symmetry, with non-trivial orbital currents, and of an unusual gapless phase that is the extension of two critical interacting Majorana modes.Finally, we are interested in electronic transport mediated by Majorana fermions. We study a floating superconducting island carrying several such impurities. This device is thought to be a potential building block for a quantum computer. The Majorana fermions affect the statistics of the charge carriers, which leads to very resilient fractionalized transport. We extend previous studies to the charge degenerate case, where the total number of fermions in the island is not fixed, and map it to the well-known Multi-Channel Kondo model at large interaction. We reinterpret this standard model in terms of a particle moving in a highly dimensional, dissipative lattice

Heterogeneous ferromagnetic-superconducting systems such as a regular array of ferromagnetic nano dots deposited on the top of a superconducting thin film have attracted many research teams both experimental and theoretical. The interest in these systems does not only stem from being good candidates for technological applications, but also because they represent a new class of physical systems where two competing order parameters can coexist. This work focuses on the theoretica laspects of these systems by studying the static and dynamics of few model systems. In the first part, the static properties of a superconducting thin film interacting with a ferromagnetic texture are considered within the London approximation. In particular, the ferromagnetic textures considered here are a circular dot of submicrometer size with in-plane magnetization, an elliptical dot magnetized in the direction perpendicular to the superconductor, and a ferromagnetic dot magnetized in the direction normal to the superconducting film and containing non magnetic cavities. I also consider the interaction of vortices in the superconductor with a ferromagnetic columnar defect which penetrates the supercondcting film. In each case the vector potential and magnetic field of the ferromagnet in the presence of the superconductor are calculated. Afterward the presence of vortices in the superconductor is assumed and the energy of vortex-texture system is found. The pinning potential and force supplied by the texture are then derived from the energy of interaction between the ferromagnet and superconductor. I show that if the magnetization of the ferromagnet exceeds a critical value then vortices are spontaneously created in the ground state of the system. Such spontaneous creation of vortices is possible mostly in a close vicinity of the superconducting transition temperature Ts. For every case, the threshold value of the magnetization at which vortices start to be spontaneously created in the SC is calculated as a function of the parameters of the texture geometry. The phase diagrams for transitions from vortexless regime to regimes with one or more vortices are determined for all cases. In the second problem, the transport properties of a ferromagnetic superconducting bilayer with alternating magnetization and vortex density are studied within a phenomenological model. I show that pinning forces do not appear for continuous distribution of vortices, so a discrete model for the bilayer system is constructed. Afterward, I calculate the pinning forces acting on vortices and antivortices resulting from highly inhomogeneous distribution of flux lines and prove that this system has strong transport anisotropy. In the absence of random pinning, the system displays a finite resistance for the current in the direction perpendicular to the domains while its resistance vanishes for the parallel current. The transport anisotropy strongly depends on temperature. I study this dependence and show that the ratio of parallel to perpendicular critical current is largest close to the superconducting transition temperature Ts and the vortex disappearance temperature Tv while it has a minimum in between them.

Si espone la teoria quantistica non relativistica dei sistemi di particelle identiche, costruendo un opportuno spazio delle configurazioni la cui struttura è coerente con la loro indistinguibilità. Si impiegano nozioni di topologia algebrica per la formulazione di una meccanica quantistica su tale spazio, mostrando che in due dimensioni spaziali esiste una continuità di statistiche quantistiche. Le particelle con queste statistiche intermedie tra bosoni e fermioni sono chiamate anioni. Si illustra l'importanza che hanno assunto nella spiegazione dell'effetto Hall quantistico e nell'attuale ricerca sulla possibilità di creare un computer quantistico topologico.

Cette thèse est consacrée à la description de la physique à une particule ainsi qu'à celle de fluides quantiques bosoniques dans des systèmes topologiques. Les deux premiers chapitres sont introductifs. Dans le premier, nous introduisons des éléments de théorie des bandes et les quantités géométriques et topologiques associées : tenseur métrique quantique, courbure de Berry, nombre de Chern. Nous discutons différents modèles et réalisations expérimentales donnant lieu à des effets topologiques. Dans le second chapitre, nous introduisons les condensats de Bose-Einstein ainsi que les excitons-polaritons de cavité.La première partie des résultats originaux discute des phénomènes topologiques à une particule dans des réseaux en nid d'abeilles. Cela permet de comparer deux modèles théoriques qui mènent à l'effet Hall quantique anormal pour les électrons et les photons dû à la présence d'un couplage spin-orbite et d'un champ Zeeman. Nous étudions aussi l'effet Hall quantique de vallée photonique à l'interface entre deux réseaux de cavités avec potentiels alternés opposés.Dans une seconde partie, nous discutons de nouveaux effets qui émergent due à la présence d'un fluide quantique interagissant décrit par l’équation de Gross-Pitaevskii dans ces systèmes. Premièrement, il est montré que les interactions spin anisotropes donnent lieu à des transitions topologiques gouvernées par la densité de particules pour les excitations élémentaires d’un condensat spineur d’exciton-polaritons.Ensuite, nous montrons que les tourbillons quantifiés d'un condensat scalaire dans un système avec effet Hall quantique de vallée, manifestent une propagation chirale le long de l'interface contrairement aux paquets d'ondes linéaires. La direction de propagation de ces derniers est donnée par leur sens de rotation donnant lieu à un transport de pseudospin de vallée protégé topologiquement, analogue à l’effet Hall quantique de spin.Enfin, revenant aux effets géométriques linéaires, nous nous sommes concentrés sur l’effet Hall anormal. Dans ce contexte, nous présentons une correction non-adiabatique aux équations semi-classiques décrivant le mouvement d’un paquet d’ondes qui s’exprime en termes du tenseur géométrique quantique. Nous proposons un protocole expérimental pour mesurer cette quantité dans des systèmes photonique radiatifs
This thesis is dedicated to the description of both single-particle and bosonic quantum fluid Physics in topological systems. After introductory chapters on these subjects, I first discuss single-particle topological phenomena in honeycomb lattices. This allows to compare two theoretical models leading to quantum anomalous Hall effect for electrons and photons and to discuss the photonic quantum valley Hall effect at the interface between opposite staggered cavity lattices.In a second part, I present some phenomena which emerge due to the interplay of the linear topological effects with the presence of interacting bosonic quantum fluid described by mean-field Gross-Pitaevskii equation. First, I show that the spin-anisotropic interactions lead to density-driven topological transitions for elementary excitations of a condensate loaded in the polariton quantum anomalous Hall model (thermal equilibrium and out-of-equilibrium quasi-resonant excitation configurations). Then, I show that the vortex excitations of a scalar condensate in a quantum valley Hall system, contrary to linear wavepackets, can exhibit a robust chiral propagation along the interface, with direction given by their winding in real space, leading to an analog of quantum spin Hall effect for these non-linear excitations. Finally, coming back to linear geometrical effects, I will focus on the anomalous Hall effect exhibited by an accelerated wavepacket in a two-band system. In this context, I present a non-adiabatic correction to the known semiclassical equations of motion which can be expressed in terms of the quantum geometric tensor elements. We also propose a protocol to directly measure the tensor components in radiative photonic systems

The present thesis aims to investigate the electronic transport of the helical states flowing at the edges of a 2D Topological Insulator (TI). A particular interest is devoted to the problem of electron tunnelling between helical edge states. This can for instance be realized with a set up where tunnelling is induced by a constriction etched in a quantum well of a Quantum Spin Hall Effect (QSHE) system. I investigate this problem by taking into account two types of tunnelling: spin preserving (it reverses the group velocity of the electron) and spin flipping (it flips the spin orientation) coupling coefficients. As first I analyse how the currents and the multi-terminal conductance depend on the physical features of the tunnel junction and how they can be controlled. I then consider the role of disorder in the tunnel junction and address to the analysis of the spin preserving transmission coefficients in the Anderson localization regime.

Alors que le nœud critique des circuits intégrés (CI) entre dans la phase 1 nm, les matériaux tridimensionnels traditionnels ne peuvent pas conserver leurs propriétés physiques d'origine et ne peuvent donc pas répondre aux besoins des processus de fabrication des circuits intégrés. Parallèlement, la diminution de la largeur des lignes entraîne également une augmentation inévitable de la consommation d'énergie statique. Par conséquent, la recherche de nouveaux matériaux et de nouvelles technologies pour briser le « mur de taille » et le « mur de puissance » est devenue une direction cruciale dans l'industrie des circuits intégrés. En tant que nouveau membre de la famille des matériaux bidimensionnels (2D), les aimants 2D peuvent maintenir leur ordre magnétique à longue portée à l'échelle atomique avec leurs propriétés physiques facilement contrôlées par des stimuli externes, ce qui constitue une plate-forme idéale pour la haute densité et les dispositifs spintroniques de faible puissance. Cependant, en raison de l'effet dimensionnel, le magnétisme 2D ne peut pas exister à haute température. Bien que plusieurs méthodes puissent améliorer la température de Curie (Tc) des aimants 2D (comme le dopage, l'intercalation ionique ou le pompage laser), elles sont loin d'être faciles à contrôler et à haut rendement. Plus important encore, la méthode de préparation largement utilisée par exfoliation mécanique abandonne le mérite de l'effet interfacial 2D, qui s'est avéré être une approche importante pour une manipulation magnétique 2D efficace. Par conséquent, l'étude de l'effet interfacial dans les aimants 2D épitaxiaux est considérée comme un domaine clé pour obtenir un ordre ferromagnétique 2D stable, à grande échelle, à haute Tc, facile à contrôler. L'isolant topologique (TI) est un autre matériau 2D avec un fort couplage spin-orbital. Les états de surface protégés par la topologie ont fourni à TI de nombreux effets fascinants liés au spin, tels que le verrouillage de l'impulsion de spin, l'effet d'échange de spin, etc., ce qui fait de ce matériau un candidat potentiel pour fabriquer des dispositifs spintroniques efficaces. De plus, le TI peut être intégré à des aimants 2D pour former une hétérostructure 2D, dans laquelle non seulement le magnétisme peut être amélioré via l'effet d'interface, mais également les propriétés liées au spin de l'hétérostructure peuvent être manipulées grâce aux avantages de ces aimants
With the critical node of integrated circuits (IC) entering the 1 nm stage, traditional three-dimensional materials cannot maintain their original physical properties, and thus cannot meet the needs of IC manufacturing processes. Meanwhile, the shrinking line width also introduces an inevitable increase in static power consumption. Therefore, researching new materials and new technologies to break through the "Size Wall" and "Power Wall" has become a crucial direction in the IC industry. As a new member of the two-dimensional (2D) material family, the 2D magnets can maintain its long-range magnetic order at the atomic scale with its physical properties easily controlled by external stimuli, which provides an ideal platform for the high-density and low-power spintronic devices. However, due to the dimensional effect, 2D magnetism cannot exist at high temperatures. Although several methods can enhance the Curie temperature (Tc) of 2D magnets (such as doping, ion intercalation, or laser pumping), they are far from easy-controllability and high-efficiency. More importantly, the widely-used preparation method via mechanical exfoliation abandons the merit of 2D interfacial effect, which was proved to be an important approach to efficient 2D magnetic manipulation. Therefore, studying the interfacial effect in epitaxial 2D magnets is regarded as a key field to achieving large-scale, high-Tc, easy-controlling, and stable 2D ferromagnetic order. Topological insulator (TI) is another 2D material with strong spin-orbital coupling. The topology-protected surface states provided TI with numerous fascinates spin-related effects, such as spin-momentum locking, spin exchange effect, etc., which makes this material a potential candidate to fabricate effective spintronic devices. In addition, the TI can be integrated with 2D magnets to form a 2D heterostructure, in which not only the magnetism can be enhanced via the interfacial effect, but also the spin-related properties of the heterostructure can be manipulated due to the advantages of these two materials

The discovery of the fractional quantum Hall effect for two-dimensional electron gases immersed in a strong orthogonal magnetic field represents a cornerstone of modern physics. The states responsible for the appearance of the fractional quantum Hall effect have been found to be part of a whole new class of phases of matter, characterized by an internal order with unprecedented properties and known as topological order. This fact opened up a completely new territory for physical studies, paving the way towards many of the current hot topics in physics, such as topological phases of matter, topological order and topological quantum computing. As it happens for most topologically-ordered phases, fractional quantum Hall states are breeding ground for the observation of many exotic physical phenomena. Important examples include the appearance of degenerate ground states when the system in placed on a space with non-trivial topology, the existence of chiral gapless edge excitations which unidirectionally propagate without suffering of back-scattering processes, and the possibility of hosting elementary excitations, known as quasiparticles and quasiholes, carrying fractional charge and anyonic statistics. Even though for years since their discovery fractional quantum Hall states have been studied only in electronic systems, the recent advances made in the domains of quantum simulators and artificial gauge fields opened the possibility to realize bosonic analogs of these states in platforms based on ultracold atoms and photons. Reaching the appropriate conditions for the simulation of the fractional quantum Hall effect with neutral particles (such as atoms and photons) has required decades of both theoretical and experimental efforts and passed through the implementation of many topological models at the single-particle level. However, we strongly believe that the stage is set finally and that bosonic fractional quantum Hall states will be realized soon in different set-ups. Motivated by this fact, we dedicate this Thesis to the study of the edge and quasihole excitations of bosonic fractional quantum Hall states with the goal of guiding near future experiments towards exciting discoveries such as the observation of anyons. In the first part of the Thesis we focus our attention on the behavior of the edge excitations of the bosonic $ u=1/2$ Laughlin state (a paradigmatic wave function for the fractional quantum Hall effect) in the presence of cylindrically symmetric hard-wall confining potentials. With respect to electronic devices, atomic and photonic platforms offers indeed a more precise control on the external potential confining the systems, as confirmed by the recent realization of flat-bottomed traps for ultracold atoms and by the flexibility in designing optical cavities. At the same time, most of the theoretical works in this direction have considered harmonic confinements, for which the edge states have been found to display the standard chiral Luttinger liquid behavior, leaving the field open for our analysis of new physics beyond the Luttinger paradigm. In the second part we propose a novel method to probe the statistical properties of the quasihole excitations on top of a fractional quantum Hall state. As compared to the previous proposals, it does not rely on any form of interference and it has the undeniable advantage of requiring only the measurements of density-related observables. As we have already mentioned, although the existence of anyons have been theoretically predicted long time ago, it still lacks a clear-cut experimental evidence and this motivated people working with ultracold atoms and photons to push their systems into the fractional quantum Hall regime. However, while there exist plenty of proposals for the detection of anyons in solid-state systems (mostly based on interferometric schemes in which currents are injected into the system and anyons travel along its edges), in the present literature the number of detection schemes applicable in ultracold atomic and/or photonic set-ups is much smaller and they are typically as demanding as those proposed in the electronic context. Finally, in the last part of the Thesis we move to the lattice counterparts of the fractional quantum Hall states, the so-called fractional Chern insulators. Still with the purpose of paving the way for future experimental studies with quantum simulators, we focus our attention of the simplest bosonic version of these states and, in particular, on the properties of its quasihole excitations. Although this topic has already been the subject of intense studies, most of the previous works were limited either to system sizes which are too small to host anyonic excitations, or to unphysical conditions, such as periodic geometries and non-local Hamiltonians. Our study investigates for the first time the properties of genuine quasihole excitations in experimentally relevant situations.

The discovery of the fractional quantum Hall effect for two-dimensional electron gases immersed in a strong orthogonal magnetic field represents a cornerstone of modern physics. The states responsible for the appearance of the fractional quantum Hall effect have been found to be part of a whole new class of phases of matter, characterized by an internal order with unprecedented properties and known as topological order. This fact opened up a completely new territory for physical studies, paving the way towards many of the current hot topics in physics, such as topological phases of matter, topological order and topological quantum computing. As it happens for most topologically-ordered phases, fractional quantum Hall states are breeding ground for the observation of many exotic physical phenomena. Important examples include the appearance of degenerate ground states when the system in placed on a space with non-trivial topology, the existence of chiral gapless edge excitations which unidirectionally propagate without suffering of back-scattering processes, and the possibility of hosting elementary excitations, known as quasiparticles and quasiholes, carrying fractional charge and anyonic statistics. Even though for years since their discovery fractional quantum Hall states have been studied only in electronic systems, the recent advances made in the domains of quantum simulators and artificial gauge fields opened the possibility to realize bosonic analogs of these states in platforms based on ultracold atoms and photons. Reaching the appropriate conditions for the simulation of the fractional quantum Hall effect with neutral particles (such as atoms and photons) has required decades of both theoretical and experimental efforts and passed through the implementation of many topological models at the single-particle level. However, we strongly believe that the stage is set finally and that bosonic fractional quantum Hall states will be realized soon in different set-ups. Motivated by this fact, we dedicate this Thesis to the study of the edge and quasihole excitations of bosonic fractional quantum Hall states with the goal of guiding near future experiments towards exciting discoveries such as the observation of anyons. In the first part of the Thesis we focus our attention on the behavior of the edge excitations of the bosonic $ u=1/2$ Laughlin state (a paradigmatic wave function for the fractional quantum Hall effect) in the presence of cylindrically symmetric hard-wall confining potentials. With respect to electronic devices, atomic and photonic platforms offers indeed a more precise control on the external potential confining the systems, as confirmed by the recent realization of flat-bottomed traps for ultracold atoms and by the flexibility in designing optical cavities. At the same time, most of the theoretical works in this direction have considered harmonic confinements, for which the edge states have been found to display the standard chiral Luttinger liquid behavior, leaving the field open for our analysis of new physics beyond the Luttinger paradigm. In the second part we propose a novel method to probe the statistical properties of the quasihole excitations on top of a fractional quantum Hall state. As compared to the previous proposals, it does not rely on any form of interference and it has the undeniable advantage of requiring only the measurements of density-related observables. As we have already mentioned, although the existence of anyons have been theoretically predicted long time ago, it still lacks a clear-cut experimental evidence and this motivated people working with ultracold atoms and photons to push their systems into the fractional quantum Hall regime. However, while there exist plenty of proposals for the detection of anyons in solid-state systems (mostly based on interferometric schemes in which currents are injected into the system and anyons travel along its edges), in the present literature the number of detection schemes applicable in ultracold atomic and/or photonic set-ups is much smaller and they are typically as demanding as those proposed in the electronic context. Finally, in the last part of the Thesis we move to the lattice counterparts of the fractional quantum Hall states, the so-called fractional Chern insulators. Still with the purpose of paving the way for future experimental studies with quantum simulators, we focus our attention of the simplest bosonic version of these states and, in particular, on the properties of its quasihole excitations. Although this topic has already been the subject of intense studies, most of the previous works were limited either to system sizes which are too small to host anyonic excitations, or to unphysical conditions, such as periodic geometries and non-local Hamiltonians. Our study investigates for the first time the properties of genuine quasihole excitations in experimentally relevant situations.

In this overview I describe the simplest models for the quantum Hall and quantum spin Hall effects, and give some general indications as to the description of topological insulators. As a background to the theoretical models I will first trace the development leading up to the description of topological insulators . Then I will present Laughlin's original model for the quantum Hall effect and briefly discuss its limitations. After that I will describe the Kane and Mele model for the quantum spin Hall effect in graphene and discuss its relation to a general quantum spin Hall system. I will conclude by giving a conceptual description of topological insulators and mention some potential applications of such states.