Littérature scientifique sur le sujet « Isolanti topologici »

Este trabalho apresenta o modelamento de dois novos Nós Lógicos para a norma IEC 61850. Estes modelos foram implementados no monitoramento de dois transformadores de transmissão e distribuição para a criação de um sistema de gestão destes ativos, cuja topologia foi elaborada com base na norma IEC 61850. Este trabalho contribui para a revisão do capítulo da norma que versa sobre monitoramento e supervisão de transformadores (IEC 61850-7-4) e inaugura modelos de Diagnostico e Expectativa de sua Vida Útil. A implementação foi realizada na área piloto do projeto (subestação Pilarzinho), de forma experimental e, avaliados e validados em campo, através da utilização de uma técnica não invasiva de avaliação da degradação do sistema de isolamento dos transformadores, a chamada Espectroscopia Dielétrica por Corrente de Polarização e Despolarização (PDC) e a Medida de Condutividade do Óleo Isolante (LCM). Foi implementado também o processo de secagem da parte ativa baseado em filtros moleculares e que consiste na remoção seletiva das moléculas de água do óleo isolante provocando um desequilíbrio entre a umidade dos materiais isolantes.

Topological relations and direction relations represent two pieces of the qualitative spatial reasoning triumvirate. Researchers have previously attempted to use the direction relation matrix to derive a topological relation, finding that no single direction relation matrix can isolate a particular topological relation. In this paper, the technique of topological augmentation is applied to the same problem, identifying a unique topological relation in 28.6% of all topologically augmented direction relation matrices, and furthermore achieving a reduction in a further 40.4% of topologically augmented direction relation matrices when compared to their vanilla direction relation matrix counterpart.

Multilayer networks continue to gain significant attention in many areas of study, particularly due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socioenvironmental ecosystems. However, clustering of multilayer networks, especially using the information on higher-order interactions of the system entities, still remains in its infancy. In turn, higher-order connectivity is often the key in such multilayer network applications as developing optimal partitioning of critical infrastructures in order to isolate unhealthy system components under cyber-physical threats and simultaneous identification of multiple brain regions affected by trauma or mental illness. In this paper, we introduce the concepts of topological data analysis to studies of complex multilayer networks and propose a topological approach for network clustering. The key rationale is to group nodes based not on pairwise connectivity patterns or relationships between observations recorded at two individual nodes but based on how similar in shape their local neighborhoods are at various resolution scales. Since shapes of local node neighborhoods are quantified using a topological summary in terms of persistence diagrams, we refer to the approach as clustering using persistence diagrams (CPD). CPD systematically accounts for the important heterogeneous higher-order properties of node interactions within and in-between network layers and integrates information from the node neighbors. We illustrate the utility of CPD by applying it to an emerging problem of societal importance: vulnerability zoning of residential properties to weather- and climate-induced risks in the context of house insurance claim dynamics.

The topological order of a quantum Hall state is mirrored by the gapless edge modes owing to bulk-edge correspondence. The state at the filling of ν = 5/2, predicted to host non-abelian anyons, supports a variety of edge modes (integer, fractional, neutral). To ensure thermal equilibration between the edge modes and thus accurately determine the state’s nature, it is advantageous to isolate the fractional channel (1/2 and neutral modes). In this study, we gapped out the integer modes by interfacing the ν = 5/2 state with integer states ν = 2 and ν = 3 and measured the thermal conductance of the isolated-interface channel. Our measured half-quantized thermal conductance confirms the non-abelian nature of the ν = 5/2 state and its particle-hole Pfaffian topological order. Such an isolated channel may be more amenable to braiding experiments.

Despite an evermore complete plethora of complex domain-specific semiempirical models, no succinct recipe for large-scale carbon nanotube electromechanical systems design has been formulated. To combine the benefits of these highly sensitive miniaturized mechanical sensors with the vast functionalities available in electronics, we identify a reduced key parameter set of carbon nanotube properties, nanoelectromechanical system design, and operation that steers the sensor’s performance towards system applications, based on open- and closed-loop topologies. Suspended single-walled carbon nanotubes are reviewed in terms of their electromechanical properties with the objective of evaluating orders of magnitude of the electrical actuation and detection mechanisms. Open-loop time-averaging and 1ωor 2ωmixing methods are completed by a new 4ωactuation and detection technique. A discussion on their extension to closed-loop topologies and system applications concludes the analysis, covering signal-to-noise ratio, and the capability to spectrally isolate the motional information from parasitical feedthrough by contemporary electronic read-out techniques.

The electronic and topological properties of materials are derived from the interplay between crystalline symmetry and dimensionality. Simultaneously introducing “forbidden” symmetries via quasiperiodic ordering with low dimensionality into a material system promises the emergence of new physical phenomena. Here, we isolate a two-dimensional (2D) chalcogenide quasicrystal and approximant, and investigate their electronic and topological properties. The 2D layers of the materials with a composition close to Ta1.6Te, derived from a layered transition metal dichalcogenide, are isolated with standard exfoliation techniques, and investigated with electron diffraction and atomic resolution scanning transmission electron microscopy. Density functional theory calculations and symmetry analysis of the large unit cell crystalline approximant of the quasicrystal, Ta21Te13, reveal the presence of symmetry-protected nodal crossings in the quasicrystalline and approximant phases, whose presence is tunable by layer number. Our study provides a platform for the exploration of physics in quasicrystalline, low-dimensional materials and the interconnected nature of topology, dimensionality, and symmetry in electronic systems.

We present a method for constructing from a given domain representation of a space X with underlying domain D, a domain representation of a subspace of compact subsets of X where the underlying domain is the Plotkin powerdomain of D. We show that this operation is functorial over a category of domain representations with a natural choice of morphisms. We study the topological properties of the space of representable compact sets and isolate conditions under which all compact subsets of X are representable. Special attention is paid to admissible representations and representations of metric spaces.

Tilapia lake virus (TiLV), a negative sense RNA virus with a 10 segment genome, is an emerging threat to tilapia aquaculture worldwide, with outbreaks causing over 90% mortality reported on several continents since 2014. Following a severe tilapia mortality event in July 2017, we confirmed the presence of TiLV in Bangladesh and obtained the near-complete genome of this isolate, BD-2017. Phylogenetic analysis of the concatenated 10 segment coding regions placed BD-2017 in a clade with the two isolates from Thailand, separate from the Israeli and South American isolates. However, phylogenetic analysis of individual segments gave conflicting results, sometimes clustering BD-2017 with one of the Israeli isolates, and splitting pairs of isolates from the same region. By comparing patterns of topological difference among segments of quartets of isolates, we showed that TiLV likely has a history of reassortment. Segments 5 and 6, in particular, appear to have undergone a relatively recent reassortment event involving Ecuador isolate EC-2012 and Israel isolate Til-4-2011. The phylogeny of TiLV isolates therefore depends on the segment sequenced. Our findings illustrate the need to exercise caution when using phylogenetic analysis to infer geographic origin and track the movement of TiLV, and we recommend using whole genomes wherever possible.

In this paper, we consider local moves on classical and welded diagrams of string links, and the notion of welded extension of a classical move. Such extensions being non-unique in general, the idea is to find a topological criterion which could isolate one extension from the others. To that end, we turn to the relation between welded string links and knotted surfaces in [Formula: see text], and the ribbon subclass of these surfaces. This provides a topological interpretation of classical local moves as surgeries on surfaces, and of virtual local moves as surgeries on ribbon surfaces. Comparing these surgeries leads to the notion of ribbon residue of a classical local move, and we show that up to some broad conditions there can be at most one welded extension which is a ribbon residue. We provide three examples of ribbon residues, for the self-crossing change, the Delta and the band-pass moves. However, for the latter, we note that the given residue is actually not an extension of the band-pass move, showing that a classical move may have a ribbon residue and a welded extension, but no ribbon residue which is an extension.

Automated generalization of road network data is of great concern to the map generalization community because of the importance of road data and the difficulty involved. Complex junctions are where roads meet and join in a complicated way and identifying them is a key issue in road network generalization. In addition to their structural complexity, complex junctions don’t have regular geometric boundary and their representation in spatial data is scale-dependent. All these together make them hard to identify. Existing methods use geometric and topological statistics to characterize and identify them, and are thus error-prone, scale-dependent and lack generality. More significantly, they cannot ensure the integrity of complex junctions. This study overcomes the obstacles by clarifying the topological boundary of a complex junction, which provides the basis for straightforward identification of them. Test results show the proposed method can find and isolate complex junctions in a road network with their integrity and is able to handle different road representations. The integral identification achieved can help to guarantee connectivity among roads when simplifying complex junctions, and greatly facilitate the geometric and semantic simplification of them.

I dispositivi elettronici che sfruttano proprietà legate allo spin elettronico costituiscono un settore molto promettente per lo sviluppo della nanoelettronica del futuro. Recentemente, gli isolanti topologici tridimensionali (IT-3D), quando posti a contatto con materiali ferromagnetici (FM), giocano un ruolo centrale nel contesto del miglioramento dell’efficienza di conversione tra spin e carica elettronici in eterostrutture di tipo FM/TI. L’oggetto principale di questa tesi è lo studio delle interazioni chimico-fisiche tra l’IT-3D Sb2Te3, nelle sue forme granulare ed epitassiale, con film di Fe e Co attraverso l’uso di tecniche di Diffrazione/Riflettività di raggi-X, spettroscopia di risonanza ferromagnetica (FMR) e pompaggio di spin in risonanza ferromagnetica (SP-FMR). In concomitanza con l’ottimizzazione delle proprietà dei materiali, un particolare interesse è stato rivolto verso l’impatto industriale della ricerca presentata. Per questo motivo, per la produzione di Sb2Te3 e di alcuni dei FM impiegati, sono state impiegate tecniche di deposizione di materiali su larga scala ( 4 pollici), quali la Metal Organic Chemical Vapor Deposition (MOCVD) e l’Atomic Layer Deposition (ALD) rispettivamente. Una approfondita caratterizzazione chimica, strutturale e magnetica dell’interfaccia Fe/ Sb2Te3-granulare ha evidenziato un marcato intermixing tra i materiali e una generale tendenza degli atomi di Fe nel legare con l’elemento calcogenuro quando presente in un IT. Attraverso trattamenti termici rapidi e a bassa temperatura sottoposti sui film di Sb2Te3 granulare prima della crescita del Fe, l’interfaccia Fe/Sb2Te3-granulare è risultata morfologicamente più netta e chimicamente stabile. Lo studio di film sottili di Co cresciuti attraverso ALD su Sb2Te3 granulare ha permesso la produzione di interfacce Co/Sb2Te3-granulare di alta qualità, con la possibilità inoltre di modificare le proprietà magneto-strutturali dei film di Co attraverso una selezione appropriata di substrati. Con l’obbiettivo di migliorare le proprietà dei film di Sb2Te3, dei trattamenti termici specifici sono stati condotti su Sb2Te3 granulare appena cresciuto, ottenendo film di Sb2Te3 altamente orientati con una qualità cristallina vicina al cristallo singolo di tipo epitassiale. Questi substrati di Sb2Te3 sono stati utilizzati per produrre eterostrutture di Au/Co/Sb2Te3-epitassiale e Au/Co/Au/Sb2Te3-epitassiale per studiare la loro risposta di FMR. I dati di FMR per il campione Au/Co/Sb2Te3-epitassiale sono stati interpretati considerando un contributo di Two Magnon Scattering (TMS) dominante, verosimilmente a causa della presenza di rugosità magnetica all’interfaccia Co/Sb2Te3-epitassiale. L’introduzione di un interlayer di Au per evitare il contatto diretto tra Co e Sb2Te3 si è dimostrato vantaggioso per la totale eliminazione del contributo di TMS. Misure di SP-FMR sono state condotte sulla struttura ottimizzata Au/Co/Au/Sb2Te3-epitassiale, sottolineando il ruolo giocato dallo strato di Sb2Te3-epitassiale nel processo di SP. I segnali di SP ricavati da campioni di Au/Co/Au/Si(111) e Co/Au/Si(111) sono stati utilizzati per determinare l’efficienza di conversione spin-carica ottenuta dall’introduzione dello strato di Sb2Te3. L’efficienza estratta è stata calcolata interpretando i dati di SP-FMR attraverso i modelli di effetto Edelstein inverso ed effetto di Spin-Hall inverso, i quali hanno dimostrato che l’IT-3D Sb2Te3 è un candidato promettente per essere impiegato nella prossima generazione di dispositivi spintronici.
Spin-based electronic devices constitute an intriguing area in the development of the future nanoelectronics. Recently, 3D topological insulators (TI), when in contact with ferromagnets (FM), play a central role in the context of enhancing the spin-to-charge conversion efficiency in FM/TI heterostructures. The main subject of this thesis is the study of the chemical-physical interactions between the granular and epitaxial Sb2Te3 3D-TI with Fe and Co thin films by means of X-ray Diffraction/Reflectivity, Ferromagnetic Resonance spectroscopy (FMR) and Spin Pumping-FMR. Beside the optimization of the materials properties, particular care was taken on the industrial impact of the presented results, thus large-scale deposition processes such as Metal Organic Chemical Vapor Deposition (MOCVD) and Atomic Layer Deposition (ALD) were adopted for the growth of the Sb2Te3 3D-TI and part of the FM thin films respectively. A thorough chemical, structural and magnetic characterization of the Fe/granular Sb2Te3 interface evidenced a marked intermixing between the materials and a general bonding mechanism between Fe atoms and the chalcogen element in chalcogenide-based TIs. Through rapid and mild thermal treatments performed on the granular Sb2Te3 substrate prior to Fe deposition, the Fe/granular-Sb2Te3 interface turned out to be sharper and chemically stable. The study of ALD-grown Co thin films deposited on top of the granular-Sb2Te3 allowed the production of high-quality Co/granular-Sb2Te3interfaces, with also the possibility to tune the magneto-structural properties of the Co layer through a proper substrate selection. In order to improve the structural properties of the Sb2Te3, specific thermal treatments were performed on the as deposited granular Sb2Te3, achieving highly oriented films with a nearly epitaxial fashion. The latter substrates were used to produce Au/Co/epitaxial-Sb2Te3 and Au/Co/Au/epitaxial-Sb2Te3 and the dynamic of the magnetization in these structures was investigated studying their FMR response. The FMR data for the Au/Co/Sb2Te3 samples were interpreted considering the presence of a dominant contribution attributed to the Two Magnon Scattering (TMS), likely due to the presence of an unwanted magnetic roughness at the Co/epitaxial-Sb2Te3 interface. The introduction of a Au interlayer to avoid the direct contact between Co and Sb2Te3 layers was shown to be beneficial for the total suppression of the TMS effect. SP-FMR measurements were conducted on the optimized Au/Co/Au/epitaxial-Sb2Te3 structure, highlighting the role played by the epitaxial Sb2Te3substrate in the SP process. The SP signals for the Au/Co/Au/Si(111) and Co/Au/Si(111) reference samples were measured and used to determine the effective spin-to-charge conversion efficiency achieved with the introduction of the epitaxial Sb2Te3 layer. The extracted SCC efficiency was calculated interpreting the SP-FMR data using the Inverse Edelstein effect and Inverse Spin-Hall effect models, which demonstrated that the Sb2Te3 3D-TI is a promising candidate to be employed in the next generation of spintronic devices.

Cette thèse a pour but de développer et d'utiliser un cadre cohérent permettant de caractériser les phases topologiques dans des milieux spatialement périodiques induites par une perturbation dépendant périodiquement du temps ("phases topologiques de Floquet" ou "isolants topologiques de Floquet"), en présence de symétries. Ces phases sont des généralisation des isolants topologiques apparues lors de l'étude d'isolants topologiques induits par la lumière ainsi que d'analogues ondulatoires des isolants topologiques (en acoustique, mécanique et optique). De nouveaux invariants topologiques caractérisant ces systèmes sont définis, en particulier en présence d'un renversement du temps fermionique. Les cas, déjà connus dans des situations particulières, des classes complexes A et AIII de Cartan-Altland-Zirnbauer sont généralisés à toutes les dimensions, et leur survivance dans les classes réelles est discutée. Les conséquences physiques potentielles dans des systèmes électroniques sont explorées par des simulations de transport résolues en temps, qui concluent à l'existence de conductances différentielles moyennes quantifiées en présence d'un état de bord topologique
This thesis aims at developing and using a coherent framework to characterize topological states in spatially periodic media stemming from a time-periodic drive (« topological Floquet states » or « Floquet topological insulators »), when symmetries are present. Such states are a generalization of topological insulators, which appeared from the study of the control by light of topological insulators, and from the study of the wave-physics versions of topological insulators (in acoustics, mechanics and optics). New invariants characterizing such systems are defined, in particular when fermionic time-reversal is present. The cases of complex classes A and AIII in the Cartan-Altland-Zirnbauer classification, which are already known in particular cases, are generalized to any space dimension, and their survival in real classes is discussed. Potential physical consequences in electronic systems are explored by time-resolved numerical simulation of transport properties, which show evidence of quantized average differential conductances when a topological edge state is present

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

Les isolants topologiques 3D sont un nouvel état de la matière décrit par un volume iso-lant électriquement et recouvert par des états de surface métalliques. Une jonction Joseph-son topologique (TJJ) formée autour de ces états de surface peut théoriquement contenirun mode lié d’Andreev ayant une périodicité doublée par rapport aux modes liés d’An-dreev conventionnels 2p périodiques. Le mode d’Andreev 4p périodique serait la briqueélémentaire de l’ordinateur quantique topologique. Ainsi, nous étudions la dynamique dece mode particulier lors de mesures de Shapiro sur des jonctions Josephson fabriquées surdes isolants topologiques à base de bismuth.A?n d’identi?er les e?ets d’un mode 4p-périodique dans une mesure de Shapiro, nousutilisons un model phénoménologique permettant de simuler la caractéristique courant-tension d’une TJJ lors de telles mesures. Nous prédisons deux signatures du mode 4p-périodique et estimons leur robustesse face aux e?ets de chau?age par e?et Joule et face àun modèle d’empoisonnement thermiquement activé du mode 4p-périodique.Par des mesures de Shapiro, nous étudions la dynamique des TJJ basées sur le matériausimple qu’est le Bi2Se3. L’observation des deux mêmes signatures précédemment anticipéespar nos simulations, à savoir un ordre d’apparition non conventionnel des pas de Shapiroainsi que la persistance d’un supercourant à la fermeture du plateau de Shapiro n = 0prouve la présence d’un mode 4p-périodique.Notre étude s’est également portée sur un autre isolant topologique le BiSbTeSe2. Nousavons e?ectué sa croissance par cristallisation liquide-solide et avons mis en évidence,par des mesures d’interférométrie supraconductrice une supraconductivité de surface sanstransport électronique par le volume
Three dimensional topological insulators (3D TI) are a new state of matter composedof an electrically insulating bulk covered by metallic surface states. Theoretically, a topo-logical Josephson junction composed of these surface states can host an Andreev Boundstate (ABS) that has twice the periodicity of the conventional 2p periodic ABSs. The4p periodic ABS is expected to be the building block of topological quantum computing.Therefore, we study the dynamic of this particular ABS by performing Shapiro measure-ment on Josephson junctions built with bismuth based 3D TI.To identify the e?ects of a 4p periodic ABS in a Shapiro measurement, we use a phe-nomenological model that simulates the voltage-current characteristics of a TJJ. We predicttwo signatures of the 4p periodic ABS and estimate their robustness against Joule heatingand thermally activated quasiparticle poisoning of the 4p periodic mode.We study the Josephson junctions dynamics by performing Shapiro measurements onjunctions built on Bi2Se3. We observe the two previously anticipated signatures, whichare the non-conventional appearance order of the Shapiro steps and the remaining of asupercurrent at the closing of the Shapiro step n = 0. They prove the presence of a 4pperiodic ABS.We also study the topological insulator BiSbTeSe2 that we have grown by using themelting growth method. By superconducting interferometric measurements, we show asuperconducting surface transport without bulk electronic conduction

La découverte de l'effet Hall quantique par von Klitzing en 1980 a ouvert la voie à ce qui sera connu plus tard comme la théorie topologique des bandes. Dans le cadre de cette théorie, on ne s'intéresse plus uniquement à la relation de dispersion énergétique des électrons dans les cristaux, mais aussi à l'organisation topologique de la structure de bande. Cette théorie a permis la découverte d'une nouvelle phase de la matière, représentée par les isolants topologiques. Ces isolants topologiques ont de particulier qu'ils se comportent comme des isolants normaux dans le bulk, mais présentent des états de surface conducteurs. Dans cette thèse, on s'intéresse particu- lièrement aux isolants topologiques dits Z2, pour lesquels les états de surface sont protégés par la symétrie de renversement du temps : ils ne peuvent disparaître en présence d'une perturbation qui préserve cette symétrie sans que le système ne traverse une transition de phase quantique. Pour les isolants topologiques à trois dimensions, nous proposons dans cette thèse, un critère expérimental utilisant les oscillations quantiques magnétiques, permettant d'identifier un type particulier d'isolants topologiques : les isolants topologiques forts. Pour les systèmes à deux dimensions, nous nous sommes intéressés aux phénomènes liés à la rupture de la symétrie par renversement du temps à cause de la présence d'un ordre antiferro- magnétique. Dans ce cas, la symétrie d'importance devient le renversement du temps fois une translation. Dans ce contexte, nous avons tout d'abord établi analytiquement l'expression d'un invariant topologique pour les systèmes présentant aussi la symétrie d'inversion. Nous avons ensuite adapté trois méthodes numériques normalement utilisées dans le cadre des isolants topo- logiques invariants par renversement du temps : la méthode de la phase de jonction, la méthode des centres de charge des fonctions de Wannier et la construction explicite des états de bord. Nous avons montré qu'elles permettaient de tester la nature triviale ou topologique de plusieurs modèles théoriques pour lesquelles aucune méthode n'existait, par exemple les systèmes sans symétrie d'inversion
The discovery of the quantum Hall effect by von Klitzing in 1980 paved the way for what is now known as topological band theory. In this theory, we are interested not only in the energy spectra of the electrons in crystals, but also in the topological structure of the bands. A new phase of matter was discovered thanks to this theory : the topological insulators. Topological insulators are unique in the sense that they behave like trivial insulators in the bulk, but possess metallic edge states. In this thesis, we are particularly interested in so-called Z2 topological insulators, whose edge states are protected by time reversal symmetry : they cannot disappear in the presence of a perturbation that respects this symmetry, without the system undergoing a quantum phase transition. For three-dimensional topological insulators, we propose an experimental criterion based on magnetic quantum oscillations to identify a special kind of topological insulators : the strong topological insulator. In two dimensions, we study the consequences of time reversal symmetry breaking due to anti-ferromagnetic order. In this case, the important symmetry is time reversal times a trans- lation. In this context, we first establish an analytical expression for systems that also have inversion symmetry. We then adapt three numerical methods usually employed for time reversal symmetric systems : the reconnection phase method, the Wannier charge center method and the explicit construction of edge states. We show that they are useful to probe the topology of models for which no methods were available ; such as non-centrosymmetric systems

Nessa tese de doutorado apresentamos um estudo da estrutura eletronica de materiais isolantes topologicos. A teoria fundamental dos isolantes topologicos foi abordada atraves de invariantes topologicos Z2, assim como os seus metodos para o calculo desses invariantes topologicos e as consequencias da topologia de bandas nao-trivial. Assim como as propriedades atomisticas e energeticas, as propriedades eletronicas de alguns isolantes topologicos foram calculadas atraves de metodos de primeiros principios baseados na Teoria do Funcional da Densidade. Apresentamos nessa tese o estudo de quatro sistemas de interesse fisico: (1) Em isolantes topologicos do tipo Bi2Se3 e Bi2Te3 com falhas de empilhamentos, encontramos que o Bi2Te3 com falhas de empilhamentos apresentam estados metalicos na regiao do defeito; (2) Na interface Bi2Se3/GaAs com tratamento de Se na regiao do GaAs, encontramos que a interacao entre o cone de Dirac do Bi2Se3 com a banda de valencia do GaAs abre um gap de energia no ponto ; (3) Em nanoestradas de germaneno imersas em germanano com interfaces zigzag, encontramos que a partir de uma largura critica podemos observar o efeito Hall quantico de spin; e (4) nas ligas desordenadas hexagonais de SixGe1-x em duas dimensoes, o sistema desordenado compartilha a mesma topologia de bandas do siliceno e do germaneno, enquanto que a liga ordenada Si0.5Ge0.5 e um isolante trivial. As estruturas eletronicas desses sistemas foram investigadas no intuito de entender as consequencias fisicas da topologia de bandas nao-trivial nos estados de Bloch de bulk e de superficies/interfaces.
In this doctoral thesis we present a study of the electronic structure of topological insulators materials. The fundamental theory of topological insulators was addressed through the Z2 topological invariants, as well as their methods to calculate these topological invariants and the consequences of non-trivial band topology. Just as atomistic and energetic properties, the electronic properties of some topological insulators were calculated using first-principles methods based upon Density Functional Theory. We present in this thesis the study of four systems of physical interest: (1) In topological insulators like Bi2Se3 and Bi2Te3 with stacking faults, we found that the Bi2Te3 with stacking faults presents metallic states in the region of the defect; (2) For Bi2Se3/GaAs interface with Se-treatment in the GaAs region, we found that the interaction between the Dirac cone of the Bi2Se3 and the valence band of the GaAs opens a bandgap at the -point; (3) In germanene nanoroads embedded on germanane with zigzag interfaces/edge, we found that from a critical width we can observe the quantum spin Hall effect; and (4) For SixGe1x two-dimensional hexagonal disordered alloy, the system shares the same non-trivial band topology of the silicene and germanene, while the ordered alloy Si0.5Ge0.5 is a trivial insulator. The electronic structures of these systems were investigated in order to understand the physical consequences of non-trivial band topology in the bulk and surfaces/interfaces Bloch states.

Cette thèse porte sur l'exploration de différentes phases topologiques présentes dans des hétérostructures à base de mercure, cadmium et tellure (HgCdTe). Ces systèmes sont de parfaits cas d'études des états topologiques dans la matière condensée. En effet, leur structure de bande peut aisément être modifiée d'inversée à non-inversée par le biais de paramètres internes ou externes.Lorsqu'un système présente une structure de bande inversée, il a une topologie non triviale. Il est impossible de modifier cet ordre topologique sans fermer son gap, ce qui inévitablement entraîne l'apparition de particules sans masse dans son volume. Un système présentant une structure de bande inversée et un gap d'énergie finie dans lequel se trouve le niveau de Fermi, est appelé isolant topologique. Ce nouveau type de matériau est isolant dans son volume, mais abrite des états métalliques sans gap sur ses bords. Ces derniers ont une relation de dispersion linéaire et sont protégés des effets liés au désordre et de la rétrodiffusion par des impuretés non magnétiques. Ces états particuliers apparaissent à l'interface de matériaux présentant des ordres topologiques différents. Ainsi, un isolant topologique 2D se caractérise par des canaux 1D de conductance polarisés en spin à ses bords, alors qu'un isolant topologique 3D accueille des fermions de Dirac 2D, polarisés en spin, aux surfaces.L'existence de fermions sans masse 2D et 3D a déjà été démontrée expérimentalement. Cependant, la transition de phase topologique durant laquelle apparaissent les particules sans masse n'a que très peu été explorée. Il est possible de modifier la structure de bande de HgCdTe d'inversée à non inversée par le biais de la composition chimique, la pression, la température ou le confinement quantique. Ces paramètres permettent ainsi de sonder le système au voisinage de différentes transitions de phase topologiques. Dans ce travail, l'utilisation de la température comme paramètre d'ajustement continu du gap permet d'étudier au point de transition de phase l'apparition de fermions semi-relativistes de Dirac (2D) et de Kane (3D) ainsi que leurs propriétés.Les systèmes étudiés au cours de ces travaux de recherche sont des cristaux massifs de Hg1-xCdxTe et des puits quantiques HgTe/CdTe présentant des structures de bandes inversées et non inversées, ainsi que des couches minces de HgTe contraintes pouvant être considérées comme des isolants topologiques 3D ayant un confinement quantique résiduel. Tous ces systèmes possèdent des propriétés topologiques. L'interprétation des résultats s'appuie sur les prédictions théoriques basées sur le modèle de Kane. En annexe, une vue d'ensemble des puits quantiques composites InAs/GaSb, structures également identifiées comme isolants topologiques, est présentée, comportant les résultats préliminaires obtenus sur ces dernières.Toutes les structures ont été étudiées par magnétospectroscopie en transmission dans les domaines de fréquence terahertz et infra-rouge moyen à l'aide d'un dispositif expérimental spécifiquement conçu pour permettre des mesures sur une large plage de températures
This thesis presents an investigation of different topological phases in mercury-cadmium-telluride (HgCdTe or MCT) based heterostructures. These solid state systems are indeed a perfect playground to study topological states, as their band structure can be easily varied from inverted to non-inverted, by changing internal or external parameters.If a system has an inverted band ordering, its electronic structure has a non-trivial topology. One cannot change its topological order without closing the band gap, which is inevitably accompanied with the appearance of massless particles in the bulk. A system, that has an inverted band structure and a finite gap in which the Fermi level is positioned, is called a topological insulator. These novel materials are insulators in the bulk, but host gapless metallic states with linear dispersion relation at boundaries, protected against disorder and backscattering on non-magnetic impurities. These states arise at the interfaces between materials characterized by a different topological order. A 2D topological insulator is thus characterized by a set of 1D spin-polarized channels of conductance at the edges, while a 3D topological insulator supports spin-polarized 2D Dirac fermions on its surfaces.The 2D and 3D massless fermions have already been demonstrated experimentally in HgCdTe-based heterostructures. However, the topological phase transitions during which the massless particles appear remain barely explored. The HgCdTe band structure can be tuned from inverted to non-inverted using chemical composition, pressure, temperature, or quantum confinement. These parameters therefore allow to probe the system in the vicinity of different topological phase transitions. In this thesis, the use of temperature as continuous band gap tuning parameter allows to study the appearance and the parameters of semi-relativistic 2D Dirac and 3D Kane fermions emerging at the points of phase transitions.The systems investigated were Hg$_{1-x}$Cd$_x$Te bulk systems and HgTe/CdTe quantum wells characterized by an inverted and regular band order, and strained HgTe films which can be considered as 3D topological insulators with a residual quantum confinement. All these systems exhibit topological properties, and the experimental results are interpreted according to theoretical predictions based on the Kane model. This thesis is complemented by an overview and the preliminary results obtained on a different compound -- a InAs/GaSb broken-gap quantum well, which was also identified as a topological insulator. The structures were studied by means of terahertz and mid-infrared magneto-transmission spectroscopy in a specifically designed experimental system, in which temperature could be tuned in a broad range

La thèse porte sur l'étude théorique des propriétés électroniques à la surface de l’oxyde de métal de transition SrTiO3. Ce matériau est la pierre angulaire de l'électronique des oxydes, un nouveau domaine de recherche qui a pour but d'enquêter sur les oxydes de métaux de transition en tant que candidats post-silicium pour une émergence future de nouveaux composants électroniques. Le SrTiO3 est en soi un système étonnant : dans sa plus pure composition chimique, c’est un bon isolant avec une large bande interdite. Cependant, en le dopant avec de petites quantités d'autres éléments, il se transforme en un métal à haute mobilité d'électrons. Le SrTiO3 a également saisi l'attention en raison de sa capacité à accueillir des gaz d'électrons bidimensionnels (2DEGs) quand il est interfacé avec certains oxydes polaires. Ces 2DEGs présentent des propriétés fascinantes, la plus visible étant la coexistence du magnétisme et de la supraconductivité.La surface du SrTiO3 peut également accueillir des 2DEGs, sans avoir besoin de s'interfacer avec d'autres matériaux ; dans ce cas, les électrons participant aux transports sont générés par des lacunes d'oxygène créées à la surface. Cette observation est remarquable, car le SrTiO3 offre une structure simple où les propriétés des 2DEGs peuvent être étudiées.Cette thèse s’articule autour des deux axes. Tout d'abord, elle étudie la bicouche STO orientée 111, formée de seulement deux cellules unitaires. Deuxièmement, elle analyse les puits quantiques générés par les postes vacants de l'oxygène à la surface 111 du STO. Les deux sujets sont abordés en utilisant des modèles de liaison forte, dans lesquels le Hamiltonien incorpore différents termes liés aux énergies sur place, aux interactions de saut et au couplage spin-orbite. A partir de ces calculs, j’ai réalisé une analyse exhaustive des propriétés, du caractère et de la parité des orbitaux des bandes de valence et de conduction, ainsi que des états de bord dans la bicouche 111
The thesis is focused on the theoretical study of the electronic properties at the surface of the transition metal oxide STO. This material is the cornerstone of oxide electronics, an emerging research area that has the goal of investigating transition metal oxides as post-silicon candidates for a future emerging new electronics. STO is in itself an astounding system; in its purest chemical composition is a good ban-insulator with a wide bandgap. Nevertheless, upon doing it with tiny amounts of other elements it transforms itself in a metal with high electron mobility. Even more remarkably, at the lowest temperatures, typically below 300mK, it goes superconductor. And adding to these properties, strain induces also ferroelectricity in this material. Over the last years, STO has also grabbed attention because of its ability of hosting two-dimensional electron gas (2DEGs) when it is interfaced with some polar oxides. Such 2DEGs exhibit fascinating properties, the most conspicuous is the coexistence of magnetism and superconductivity.The surface of STO can host 2DEGs too, without need of interfacing it to other materials; in this case the electrons participating in transport are generated by oxygen vacancies created at the surface. This is remarkable observation, as it affords a simpler structure where the 2DEGs properties can be studied. In spite of the accumulated knowledge, still a better fundamental comprehension is required of the electronic structure of the quantum wells at the surfaces oriented along the 111 direction, for which the perovskite structure is reminiscent of the celebrated honeycomb-like structure of graphene. Contrary to the latter, in which electrons are in s- and p- states, 111 quantum wells in STO would host electrons in d-bands. Higher electronic correlations are then expected, that may bring new fascinating physics.The outline of this Thesis has two main branches: first, it studies the 111-oriented STO bilayer, formed by just two unit cells; secondly it analyzes the quantum wells generated by Oxygen vacancies at the 111-surface of STO. Both subjects are approached using tight-binding models in which the Hamiltonian incorporates different terms related to on-site energies, hopping interactions or spin-orbit coupling. From these calculations, I have carried out an exhaustive analysis of the orbital character and parity properties of valence and conduction bands, as well as edge states in the 111 bilayer. Tight-binding calculations have also shed light on the orbital character, space location and extension and energy of electronic states generated by oxygen vacancies at the 001 surface of STO

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

Questa tesi si occupa di approfondire lo studio di possibili fasi topologiche in un sistema costituito da due catene di spin caratterizzate entrambe da un'interazione alternata forte e debole. Infatti è interessante capire se questo tipo di interazione può portare a termini topologici non nulli nella funzione di partizione, termini che invece sono assenti per due catene accoppiate quando l'interazione tra spin vicini è sempre la stessa. Quello che si scopre dal punto di vista analitico è che, quando l'interazione su una catena è traslata di un sito rispetto a quella sull'altra catena, il nostro modello, nel limite del continuo, si può mappare nel modello sigma non lineare più un termine topologico diverso da zero. In corrispondenza di un certo valore critico del termine topologico si ha una transizione di fase tra due fasi isolanti differenti. Tale valore critico corrisponde a un certo valore critico del parametro che caratterizza l'interazione alternata sulle catene. L'analisi numerica, basata sul metodo DMRG, conferma questa previsione teorica. Inoltre, dal confronto tra i risultati numerici per i livelli energetici ottenuti con condizioni al contorno aperte e chiuse, si può già notare che una delle due fasi sembra avere proprietà topologiche non triviali. E' dunque molto interessante chiedersi se queste fasi siano caratterizzate da un qualche tipo di ordine topologico, rilevabile attraverso parametri d'ordine non locali. Le simulazioni numeriche confermano questa ipotesi: il parametro d'ordine non locale di stringa è non nullo nella fase caratterizzata da proprietà topologiche non triviali, che è dunque identificata come un isolante di Haldane, e il parametro d'ordine non locale di parità è non nullo nella fase topologicamente triviale, che è dunque identificata come un isolante di Mott. Si ha dunque una transizione di fase tra l'isolante di Mott e l'isolante di Haldane.

Abstract Noise and vibration are undesirable side effects associated with the use of spur gears in drivetrains. With market pressures for higher power densities, the development of high performance drivetrains with reduced noise and vibration thresholds forms a generic problem in the power transmission and gearing fields. In this paper, a process to reduce mesh stiffness variation in a spur gear set through the use of Differential Crowning™ technology, with concomitant reductions in acoustic noise and structure borne vibration, is presented. Through certain topological modifications to the profile of the gear teeth, mesh stiffness variation can be consistently minimized over a range of input loads. Analytical predictions for the mesh stiffness variation and transmission error in a conventional baseline drivetrain, and in one optimized through Differential Crowning™, are discussed. Design and operating parameters are used as inputs in a “design of experiments test protocol” so as to isolate those parameters which most influence performance. Controlled testing is performed in an acoustically-treated chamber, and sound pressure, sound intensity, vibration, and transmission error data are obtained for the baseline and optimized drivetrains. The test results are correlated with the predictions, and they demonstrate a mean reduction of 8 dB in total sound power for the optimized drivetrain over the six input speeds and loads that were considered.