Dissertations / Theses on the topic 'String: topological'

Complex-oxides have seen an enormous amount of attention in the realm of Condensed Matter Physics and Materials Science/Engineering over the last several decades. Their ability to host a wide variety of novel physical properties has even caused them to be exploited commercially as dielectric, metallic and magnetic materials. Indeed, since the discovery of high temperature superconductivity in the “Cuprates” in the late 1980’s there has been an explosion of activity involving complex-oxides. Further, as the experimental techniques and equipment for fabricating thin films and heterostructures of these materials has improved over the last several decades, the search for new and more exotic properties has intensified. These properties stem from the interfaces formed by depositing these materials onto one another. Whether it be interfacial strain induced by the mismatch between the crystal structures, modified exchange interactions, or some combination of these and other interactions, thin films and heterostuctures provide an invaluable tool the modern condensed matter community. Simply put, a “complex-oxide” is any compound that contains Oxygen and at least two other elements; or one atom in two different oxidation states. Transition Metal Oxides (TMO’s) are a subset of complex-oxides which are of particular interest because of their strong competition between their charge, spin and orbit degrees of freedom. As we progress down the periodic table from 3d to 4d to 5d transition metals, the crystal field, electron correlation and spin-orbit energies become more and more comparable. Therefore, TMO thin films and heterostructures are indispensable to the search for novel physical properties. KTaO3 (KTO) is a polar 5d TMO which has been investigated for its high-k dielectric properties. It is a band insulator with a cubic perovskite crystal structure which is isomorphic to SrTiO3 (STO). This is important because non-polar STO is famous for forming a highly mobile, 2-Dimensional Electron Gas (2DEG) at the hetero-interface with polar LaAlO3 (LAO) as a result of the so-called “polar catastrophe”. Here, I use this concept of polarity to ask an important question: “What happens at hetero-interfaces where two different polar complex oxides meet?” From this question we propose that a hetero-interface between two polar complex-oxides with opposite polarity (I-V/III-III) should be impossible because of the strong Coulomb repulsion between the adjacent layers. However, we find that despite this proposed conflict we are able to synthesize KTO thin films on (110) oriented GdScO3 (GSO) substrates and the conflict is avoided through atomic reconfiguration at the hetero-interface. SrRuO3 (SRO) is a 4d TMO, and an itinerant ferromagnet that is used extensively as an electrode material in capacitor and transistor geometries and proof-of-concept devices. However, in the thin film limit the ferromagnetic transition temperature, TC, and conductivity drop significantly and even become insulating and lose their ferromagnetic properties. Therefore, we ask “Are the transport properties of SRO thin films inherently inferior to single crystals, or is there a way to maintain and/or enhance the metallic properties in the thin film limit?” We have fabricated SRO thin films of various thickness on GSO substrates (tensile strain) and find that all of our samples have enhanced metallic properties and even match those of single crystals. Finally, we ask “Can these enhanced metallic properties in SRO thin films allow us to observe evidence of a topological phase without the complexity of off-stoichiometry and/or additional hetero-structural layers?” Recent reports of oxygen deficient EuO films as well as hetero-structures and superlattices of SRO mixed with SrIrO3 or La0.7Sr0.3MnO3 have suggested that a magnetic skyrmion phase may exist in these systems. By measuring the Hall resistivity, we are able to observer a topological Hall effect which is likely a result of a magnetic skyrmion. We find that of the THE exists in a narrow temperature range and the proposed magnetic skyrmions range in size from 20-120 nm. Therefore, the SRO/GSO system can provide a more viable means for investigating magnetic skyrmions and their fundamental interactions.

The aim of this work is an optimalization of vector contact force sensor properties which prototype is at the moment designed. The principle of sensor is based on transformation active part of sensor using three tensiometers and following value indentification of loading force vector using neuron network. Sensor has a bad sensitivity when axis force load or near to axis of sensor. To solve this problem ''MKP'' model of sensor was used on which suitable optimalization method was applicated. From the result of optimalization modificated sensor will be proposed and will be made a utility verification using neuron network.

La géométrie complexe est un outil puissant pour étudier les systèmes intégrables classiques, la physique statistique sur réseau aléatoire, les problèmes de matrices aléatoires, la théorie topologique des cordes, …Tous ces problèmes ont en commun la présence de relations, appelées équations de boucle ou contraintes de Virasoro. Dans le cas le plus simple, leur solution complète a été trouvée récemment, et se formule naturellement en termes de géométrie différentielle sur une surface de Riemann : la "courbe spectrale", qui dépend du problème. Cette thèse est une contribution au développement de ces techniques et de leurs applications.Pour commencer, nous abordons les questions de développement asymptotique à tous les ordres lorsque N tend vers l’infini, des intégrales N-dimensionnelles venant de la théorie des matrices aléatoires de taille N par N, ou plus généralement des gaz de Coulomb. Nous expliquons comment établir, dans les modèles de matrice beta et dans un régime à une coupure, le développement asymptotique à tous les ordres en puissances de N. Nous appliquons ces résultats à l'étude des grandes déviations du maximum des valeurs propres dans les modèles beta, et en déduisons de façon heuristique des informations sur l'asymptotique à tous les ordres de la loi de Tracy-Widom beta, pour tout beta positif. Ensuite, nous examinons le lien entre intégrabilité et équations de boucle. En corolaire, nous pouvons démontrer l'heuristique précédente concernant l'asymptotique de la loi de Tracy-Widom pour les matrices hermitiennes.Nous terminons avec la résolution de problèmes combinatoires en toute topologie. En théorie topologique des cordes, une conjecture de Bouchard, Klemm, Mariño et Pasquetti affirme que des séries génératrices bien choisies d'invariants de Gromov-Witten dans les espaces de Calabi-Yau toriques, sont solution d'équations de boucle. Nous l'avons démontré dans le cas le plus simple, où ces invariants coïncident avec les nombres de Hurwitz simples. Nous expliquons les progrès récents vers la conjecture générale, en relation avec nos travaux. En physique statistique sur réseau aléatoire, nous avons résolu le modèle O(n) trivalent sur réseau aléatoire introduit par Kostov, et expliquons la démarche à suivre pour résoudre des modèles plus généraux.Tous ces travaux soulignent l'importance de certaines "intégrales de matrices généralisées" pour les applications futures. Nous indiquons quelques éléments appelant à une théorie générale, encore basée sur des "équations de boucles", pour les calculer
Complex analysis is a powerful tool to study classical integrable systems, statistical physics on the random lattice, random matrix theory, topological string theory, … All these topics share certain relations, called "loop equations" or "Virasoro constraints". In the simplest case, the complete solution of those equations was found recently : it can be expressed in the framework of differential geometry over a certain Riemann surface which depends on the problem : the "spectral curve". This thesis is a contribution to the development of these techniques, and to their applications.First, we consider all order large N asymptotics in some N-dimensional integrals coming from random matrix theory, or more generally from "log gases" problems. We shall explain how to use loop equations to establish those asymptotics in beta matrix models within a one cut regime. This can be applied in the study of large fluctuations of the maximum eigenvalue in beta matrix models, and lead us to heuristic predictions about the asymptotics of Tracy-Widom beta law to all order, and for all positive beta. Second, we study the interplay between integrability and loop equations. As a corollary, we are able to prove the previous prediction about the asymptotics to all order of Tracy-Widom law for hermitian matrices.We move on with the solution of some combinatorial problems in all topologies. In topological string theory, a conjecture from Bouchard, Klemm, Mariño and Pasquetti states that certain generating series of Gromov-Witten invariants in toric Calabi-Yau threefolds, are solutions of loop equations. We have proved this conjecture in the simplest case, where those invariants coincide with the "simple Hurwitz numbers". We also explain recent progress towards the general conjecture, in relation with our work. In statistical physics on the random lattice, we have solved the trivalent O(n) model introduced by Kostov, and we explain the method to solve more general statistical models.Throughout the thesis, the computation of some "generalized matrices integrals" appears to be increasingly important for future applications, and this appeals for a general theory of loop equations

Doutoramento em Ciência e Engenharia de Materiais
The comprehensive study on the coupling of magnetism, electrical polarization and the crystalline lattice with the off-stoichiometric effects in self-doped multiferroic hexagonal h-LuMnxO3±δ (0.92≤x≤1.12) ceramic oxides was carried out for the PhD work. There is a complex coupling of the three ferroic degrees. The cancelation of the magnetic moments of ions in the antiferromagnetic order, electric polarization with specific vortex/antivortex topology and lattice properties have pushed researchers to find out ways to disclose the underlying physics and chemistry of magneto-electric and magneto-elastic couplings of h-RMnO3 multiferroic materials. In this research work, self-doping of Lu-sites or Mn-sites of h-LuMnxO3±δ ceramics prepared via solid state route was done to pave a way for deeper understanding of the antiferromagnetic transition, the weak ferromagnetism often reported in the same crystalline lattices and the ferroelectric properties coupled to the imposed lattice changes. Accordingly to the aim of the PhD thesis, the objectives set for the sintering study in the first chapter on experimental results were two. First, study of sintering off-stoichiometric samples within conditions reported in the bibliography and also extracted from the phase diagrams of the LuMnxO3±δ, with a multiple firings ending with a last high temperature step at 1300ºC for 24 hours. Second, explore longer annealing times of up to 240 hours at the fixed temperature of 1300 ºC in a search for improving the properties of the solid solution under study. All series of LuMnxO3±δ ceramics for each annealing time were characterized to tentatively build a framework enabling comparison of measured properties with results of others available in literature. XRD and Rietveld refinement of data give the evolution the lattice parameters as a function to x. Shrinkage of the lattice parameters with increasing x values was observed, the stability limit of the solid solution being determined by analysis of lattice parameters. The evolution of grain size and presence of secondary phases have been investigated by means of TEM, SEM, EDS and EBSD techniques. The dependencies of grain growth and regression of secondary phases on composition x and time were further characterized. Magnetic susceptibility of samples and magnetic irreversibility were extensively examined in the present work. The dependency of magnetic susceptibility, Neel ordering transition and important magnetic parameters are determined and compared to observation in other multiferroics in the following chapter of the thesis. As a tool of high sensitivity to detect minor traces of the secondary phase hausmannite, magnetic measurements are suggested for cross-checking of phase diagrams. Difficulty of previous studies on interpreting the magnetic anomaly below 43 K in h-RMnO3 oxides was discussed and assigned to the Mn3O4 phase, with supported of the electron microscopy. Magneto-electric coupling where AFM ordering is coupled to dielectric polarization is investigated as a function of x and of sintering condition via frequency and temperature dependent complex dielectric constant measurements in the final chapter of the thesis. Within the limits of solid solubility, the crystalline lattice of off-stoichiometric ceramics was shown to preserve the magneto-electric coupling at TN. It represents the first research work on magneto-electric coupling modified by vacancy doping to author’s knowledge. Studied lattices would reveal distortions at the atomic scale imposed by local changes of x dependent on sintering conditions which were widely inspected by using TEM/STEM methods, complemented with EDS and EELS spectroscopy all together to provide comprehensive information on cross coupling of distortions, inhomogeneity and electronic structure assembled and discussed in a specific chapter. Internal interfaces inside crystalline grains were examined. Qualitative explanations of the measured magnetic and ferroelectric properties were established in relation to observed nanoscale features of h-LuMnxO3±δ ceramics. Ferroelectric domains and topological defects are displayed both in TEM and AFM/PFM images, the later technique being used to look at size, distribution and switching of ferroelectric domains influenced by vacancy doping at the micron scale bridging to complementary TEM studies on the atomic structure of ferroelectric domains. In support to experimental study, DFT simulations using Wien2K code have been carried out in order to interpret the results of EELS spectra of O K-edge and to obtain information on the cation hybridization to oxygen ions. The L3,2 edges of Mn is used to access the oxidation state of the Mn ions inside crystalline grains. In addition, rehybridization driven ferroelectricity is also evaluated by comparing the partial density of states of the orbitals of all ions of the samples, also the polarization was calculated and correlated to the off-stoichiometric effect.
No trabalho de investigação para o doutoramento foi realizado um estudo abrangente dos efeitos do desvio estequiométrico sobre o comportamento magnético e o acoplamento do magnetismo com a polarização elétrica e a rede cristalina do óxido cerâmico multiferróico de rede hexagonal do LuMnxO3±δ auto-dopado no intervalo de composição (0.92≤x≤1.12). Existe um acoplamento complexo dos diferentes ordenamentos ferróicos. O cancelamento dos momentos magnéticos dos iões Mn no sistema antiferromagnético, a polarização elétrica com topologia específica de vórtice/antivórtice conduziram os investigadores a propor modelos para a física e química subjacentes ao acoplamento magneto-elétrico e magnetoelásticas dos materiais multiferróicos de h- RMnO3. Neste trabalho optou-se pela auto-dopagem das posições R e do Mn da rede cristalina dos cerâmicos h-LuMnxO3±δ preparados por reacção no estado sólido como caminho para uma compreensão mais completa da transição antiferromagnética, do ferromagnetismo fraco frequentemente observado nas mesmas redes cristalinas e das propriedades dieléctricas e ferroeléctricas associadas a alterações impostas à rede pela auto-dopagem. Em linha com o propósito traçado para a tese de doutoramento, foram dois os objectivos definidos para o estudo de sinterização no primeiro capítulo sobre resultados experimentais. Primeiro foi feito o estudo de sinterização das amostras com desvio de estequiometria em correspondência com condições do processamento relatadas na bibliografia e conformes com os diagramas de fases do LuMnO3, tendo-se optado por diversas etapas de reacção a temperatura elevada terminando com um último passo a 1300ºC durante 24 horas. Numa segunda parte, explorou-se o efeito do aumento do tempo de recozimento até às 240 horas à mesma temperatura fixa de 1300 ºC para melhorar as propriedades sob estudo da solução sólida. Caracterizaram-se todas as séries para cada tempo de recozimento dos cerâmicos de h-LuMnxO3±δ na tentativa de construir um referencial que permitisse a comparação das propriedades medidas nas composições com desvio de estequiometria com os resultados de outros estudos da bibliografia. A difracção de raios-X (DRX) e o refinamento de Rietveld dão a evolução dos parâmetros de rede em função de x tendo-se observado uma retracção nos parâmetros de rede com o aumento dos valores de x e identificado em primeira aproximação o limite de estabilidade da solução sólida pela análise dos mesmos parâmetros de rede. As evoluções do tamanho do grão e a da quantidade de fases residuais detectadas foram investigadas por técnicas de TEM, SEM, EDS e EBSD. Foram ainda caracterizadas as dependências do crescimento de grão e da diminuição de teor em fases secundárias em função da composição x e tempo de processo. A susceptibilidade magnética das amostras e a irreversibilidade magnética são caracterizadas e avaliadas extensivamente no capítulo seguinte da tese. Foram determinadas as dependências da susceptibilidade magnética, da temperatura de Néel da transição antiferromagnética e dos parâmetros principais do comportamento magnético e comparadas com observações feitas em outros multiferróicos. Como ferramenta de alta sensibilidade para detectar vestígios menores da fase magnética hausmannite, sugere-se que as medidas magnéticas podem ser úteis na confirmação dos diagramas de fase dos óxidos RMnO3. São discutidas dificuldades patentes em estudos anteriores sobre as interpretações dadas à anomalia magnética nos óxidos h-RMnO3 abaixo de 43 K sendo esta atribuída à fase Mn3O4 com suporte na microscopia eletrónica. No capítulo final da tese é investigado o acoplamento magneto-eléctrico com o ordenamento AFM acoplado às fronteiras de domínio da polarização dielétrica e com a determinação da constante dielétrica complexa em função da frequência e temperatura. Dentro do limite de estabilidade da solução sólida do h-LuMnxO3±δ, o acoplamento magneto-eléctrico em TN continua a observar-se em todo o intervalo do desvio estequiométrico. Tanto quanto o autor tem conhecimento este estudo representa o primeiro trabalho de investigação sobre acoplamento magneto-eléctrico modificado por auto-dopagem com lacunas nas redes de h-RMnO3. A observação das redes cristalinas revela distorções à escala atómica criadas pelas variações locais da razão x na composição do LuMnxO3±δ, dependentes das condições de sinterização as quais foram analisadas em detalhe por TEM/STEM, complementado com EDS e espectroscopia EELS por forma a obterem-se informações mais completas sobre relações cruzadas entre distorção, falta de homogeneidade composicional e estrutura eletrónica. Estes resultados encontram-se reunidos e são discutidos num capítulo específico da tese. Foram encontradas interfaces internas nas secções finas TEM dos grãos cristalinos de várias tipologias. São propostas explanações qualitativas para as propriedades magnéticas e ferroelétricas medidas correlacionando-as com as observações feitas à nano-escala nos cerâmicos de LuMnxO3±δ. Os domínios ferroelétricos e defeitos topológicos estão presentes tanto em imagens de TEM como de AFM/PFM. Esta última técnica é utilizada para a caracterização do tamanho, distribuição e comutação de polaridade dos domínios ferroelétricos na escala do mícron em relação com potenciais efeitos da dopagem por lacuna e fazendo a ponte com os estudos TEM sobre a estrutura atómica dos mesmos domínios ferroelétricos. Como suporte ao estudo experimental, foram feitas simulações DFT usando o código Wien2K a fim de interpretar os espectros de EELS da banda K do oxigénio e para obter informação sobre a hibridização dos catiões com o oxigénio. As linhas das bandas L3,2 do Mn nos espectros de EELS são utilizadas para estabelecer o estado de oxidação dos iões Mn no interior dos grãos cristalinos. Além disso, a ferroelectricidade induzida por re-hibridização é também avaliada por comparação com a densidade parcial de estados dos orbitais do conjunto de iões da estrutura cristalina e a polarização elétrica é computada e correlacionada com efeitos do desvio estequiométrico.

Strongly correlated systems on geometrically frustrated lattices can stabilize a large number of interesting phases that includes a wide array of novel Mott insulators in both bosonic and electronic systems. Charge fluctuations in a Mott insulator are suppressed due to strong mutual interaction among the particles. The presence of frustration is of particular importance as the physics it offers is often rich, unexpectedly complicated, and continues to raise many open questions. The thesis elucidates some of these issues on a kagome lattice where strong interactions among the particles in the Mott phase impose non-trivial local constraints depending on the filling fraction on the lattice. These Mott insulators, in addition to featuring unusual magnetic and/or charge ordering, can also harbor topologically ordered states of quantum matter, e.g., resonating valence bond liquids realized in certain quantum dimer models on non-bipartite lattices. The dimer models can be regarded as low-energy effective theories for different types of bosonic models in the strong-coupling limit. Exploring this connection is a central theme of this thesis with the aim of realizing novel strongly correlated ground states. Past studies of these models have revealed the existence of various ordered and disordered phases with distinct signatures. Among these low-energy phases, the presence of a stable topological liquid at a particular point, known as Rokhsar-Kivelson point, in the phase diagram is notable. The classical versions of the dimer model are also known to have garnered a vast interest in various fields ranging from problems of pure mathematical origin to ones in physical chemistry as well as statistical physics. Pioneered by Kasteleyn, several analytical works came forward to exactly calculate the partition function of the problem from which other physical observables can be derived. Classical numerical methods are extensively applied to these models to verify the analytical predictions. We introduce a new classical algorithm here to compute the correlation functions of a classical dimer model on a square (bipartite) and a triangular (non-bipartite) lattice based on a tensor network construction. The method, called tensor network renormalization group, turns out to be a powerful tool for simulating short-ranged gapped systems as inferred from our results benchmarked against the classical Monte-Carlo technique and compared with past analytical studies. One should note that the quantum dimer model at the Rokhsar-Kivelson point can also be described as an infinite temperature canonical ensemble of classical dimers because of the particular structure of the ground state which is an equal weight superposition in the configuration manifold. The geometry of the lattice plays a pivotal role in deciding the nature of the phases that arise in the dimer models. Many physical properties of the dimer liquid phase can be extracted in the simple classical setting which certainly allows for a deep understanding of the classical models to be developed. The liquid phase is gapped on non-bipartite lattices and gapless on bipartite lattices, which is reflected in the decay of correlation functions with spatial distances. In general on non-bipartite lattices, the topological nature of the dimer liquid is characterized by a Z2 topological order which survives even when the model is perturbed away from the Rokhsar-Kivelson point. Stability of this liquid phase not only depends on the lattice geometries but notably on dimer concentrations also. In this context, we focus on a particular variant of the dimer model on a triangular lattice which is known as the quantum fully packed loop model. The model is composed of nonintersecting closed loops made of dimers and governed by the same Hamiltonian as the quantum dimer model. The loop model provides an effective low-energy description of a strongly correlated bosonic system at 1/3 filling on the kagome lattice. The corresponding Bose-Hubbard Hamiltonian consists of nearest-neighbor hopping and all possible repulsive interactions within a hexagonal plaquette. Conspicuous features of the zero-temperature phase diagram for this model include (i) presence of a stable Z2 liquid even without any Rokhsar-Kivelson potential term (in distinction to the standard quantum dimer model), and (ii) an unconventional phase transition from the liquid phase to a novel crystalline phase that has nematic order (dubbed lattice nematic). For a deeper understanding of the physics, a mapping to an Ising gauge theory is presented. The gauge theoretic description provides a useful way to predict the nature of the quantum phase transition to lie in the O(3) universality class. Finally a fermionic model at the same 1/3 filling is considered in which the ground state exhibits a number of exotic local orderings resulting from the spin-charge interplay of electrons. The Hamiltonian comprises nearest-neighbor hopping, strong on-site Coulomb interaction, and repulsive interaction terms only between nearest-neighbors. In the strong correlation limit, this fermionic problem maps to a two-color fully packed loop model – a model in which the loop segments carry an additional quantum number as color on a honeycomb lattice. The effective theory is governed by coherent three-particle ring exchanges and nearest-neighbor antiferromagnetic spin exchanges. The competition between these two leads to a phase diagram composed of a novel plaquette ordered state (known as the plaquette phase) that undergoes phase transition to a new kind of charge ordered state which we call a short loop phase. From our numerical analysis, we conclude that the plaquette phase features an unusual antiferromagnetic order with gapless spin excitations while the charge-ordered state is subjugated by spin fluctuations of localized electrons arranged in small hexagonal loops on the kagome lattice.

La réalisation de supraconducteurs topologiques constitue un des principaux enjeux actuels de la physique de la matière condensée. Il a en effet été prédit que ces systèmes devaient abriter des fermions de Majorana. Ces fermions de Majorana disposent à la fois d’une statistique non-abélienne et, du fait de leur origine topologique, d’une robustesse face au désordre local, ce qui les rend très attrayants pour des applications en informatique quantique. Une approche susceptible de conduire à de la supraconductivité topologique consiste à considérer des systèmes supraconducteurs à fort couplage spin-orbite et brisant la symétrie d’inversion. C’est dans cette optique que, dans le cadre de cette thèse, j’ai effectué des mesures de microscopie et spectroscopie par effet tunnel sur des matériaux quasi-bidimensionnels : (LaSe)1,14(NbSe2)2 et Sr2IrO4.J’ai tout d’abord étudié les propriétés électroniques du matériau incommensurable (LaSe)1,14(NbSe2)2, proche parent du composé dichalcogénure de métaux de transition 2HNbSe2. (LaSe)1,14(NbSe2)2 est une hétérostructure faite d’alternances de biplans NbSe2 à géométrie prismatique trigonale et de biplans de LaSe avec une structure de sel de roche. Le fort couplage spin-orbite ainsi que la non-centrosymétrie présents dans les plans NbSe2 font de (LaSe)1,14(NbSe2)2 un potentiel candidat pour de la supraconductivité topologique. Dans cette thèse, je présente des résultats de spectroscopie montrant que la structure électronique de (LaSe)1,14(NbSe2)2 est similaire à celle de la monocouche de NbSe2 avec un dopage de type électron accompagné par un déplacement du potentiel chimique de 0,3 eV, jusqu’alors inégalé. J’ai également pu démontrer la nature quasi–bidimensionnelle de (LaSe)1,14(NbSe2)2 et notamment la présence d’un fort couplage spin-orbite de type Ising. De plus, la faible robustesse de la supraconductivité vis à vis du désordre non magnétique couplée à des mesures d’interférences de quasiparticules m’a permis de mettre en avant le caractère non conventionnel du paramètre d’ordre supraconducteur dans (LaSe)1,14(NbSe2)2. Cette étude permet d’envisager l’utilisationd’hétérostructures incommensurables telles que (LaSe)1,14(NbSe2)2 pour explorer la physique des dichalcogénures de métaux de transition dans la limite bidimensionnelle, pour laquelle de nombreuses études théoriques ont prédit une supraconductivité topologique. Dans cette thèse, je présente également une étude des effets du dopage sur les propriétés électroniques de l’oxyde d’iridium Sr2IrO4. Sr2IrO4 est un isolant de Mott non conventionnel puisqu’il doit cette propriété à la présence d’un fort couplage spin-orbite. Du fait d’une brisure locale de la symétrie d’inversion, certaines prédictions théoriques ont pu montrer que Sr2IrO4 devrait devenir un supraconducteur topologique une fois dopé. Ici, je montre qu’avec le dopage, Sr2IrO4 subit une transition de phase inhomogène à l’échelle nanométrique entre un état isolant de Mott et un état pseudo-métallique. Ce travail justifie la pertinence d’utiliser une sonde locale telle que le microscope à effet tunnel afin de venir compléter des résultats sur la physique de Mott obtenus par des méthodes intégratives comme la spectroscopie électronique résolue en angle
The realization of topological superconductors is one of the main current goals of condensed matter physics. It was indeed predicted that such systems should host Majorana fermions. These Majorana fermions possess both a non-Abelian statistics and, because of their topological origin, a certain robustness against local disorder, which makes them attractive for quantum computing applications. One approach likely to lead to topological superconductivity consists in considering superconducting systems with strong spin-orbit coupling and with broken inversion symmetry. It is in this framework that, during this thesis, I performed scanning tunneling microscopy and spectroscopy measurements on quasi-2D materials : (LaSe)1,14(NbSe2)2 and Sr2IrO4. I first studied the electronic properties of misfit compound LaNb2Se5, which is a parent of transition metal dichalcogenide 2H-NbSe2. (LaSe)1,14(NbSe2)2 is a heterostructure made out of alternations of NbSe2 bilayers with trigonal prismatic geometry and LaSe bilayers with rocksalt structure. (LaSe)1,14(NbSe2)2 is a potential candidate for topological superconductivity because of the presence of both a strong spin-orbit coupling and of broken inversion symmetry in NbSe2 planes. Here, I present spectroscopic results showing that the electronic structure of(LaSe)1,14(NbSe2)2 is very similar to the one of electron-doped monolayer NbSe2 with a shift of the chemical potential of 0,3 eV, priorly never reached. I could also demonstrate the quasi- 2D nature of (LaSe)1,14(NbSe2)2 and more particularly the presence of a strong Ising spinorbit coupling. Moreover, the observed weakness of superconductivity against non-magnetic disorder combined with quasiparticle interferences measurements allowed me to exhibit the unconventional nature of (LaSe)1,14(NbSe2)2 superconducting order parameter. This study opens the possibility to use misfit heterostructures such as (LaSe)1,14(NbSe2)2 to study thephysics of transition metal dichalcogenides in the 2D limit, for which many theoretical studies predict topological superconductivity. In this thesis, I also present a study on the effects of doping on the electronic properties of iridate compound Sr2IrO4. Sr2IrO4 is a spin-orbit induced Mott insulator. Because inversion symmetry is locally broken in Sr2IrO4, some theoretical predictions suggest that Sr2IrO4 should turn into a topological superconductor once doped. Here, I exhibit a nanometer-scaleinhomogeneous doping-driven Mott insulator to pseudo-metallic phase transition. This work further justifies the importance of using a local probe such as scanning tunnelling microscopy in order to complete results on Mott physics obtained by integrative methods like angle-resolved photoemission spectroscopy

As famílias Anosov foram introduzidas por P. Arnoux e A. Fisher, motivados por generalizar a noção de difeomorfismo de Anosov. A grosso modo, as famílias Anosov são sequências de difeomorfismos (fi)i∈Z definidos em uma sequencia de variedades Riemannianas compactas (Mi)i∈Z, em que fi: Mi ->Mi+1 para todo i ∈ Z, tal que a composição fi+no· · ·ofi, para n >=1, tem comportamento assintoticamente hiperbólico. Esta noção é conhecida como um sistema dinâmico não-estacionário ou um sistema dinâmico não-autônomo. Sejam M a união disjunta de cada Mi, para i ∈ Z, e Fm(M) o conjunto consistente das famílias de difeomorfismos (fi)i∈Z de classe Cm definidos na sequência (Mi)i∈Z. O propósito principal deste trabalho é mostrar algumas propriedades das famílias Anosov. Em particular, mostraremos que o conjunto destas famílias é aberto em Fm(M), em que Fm(M) é munido da topologia forte (ou topologia Whitney); a estabilidade estrutural de certa classe de famílias Anosov, considerando conjugações topológicas uniformes; e várias versões para os Teoremas de variedades estáveis e instáveis. Os resultados que serão apresentados aqui generalizam alguns outros resultados obtidos em Sistemas Dinâmicos Aleatórios, os quais serão mencionados ao longo do trabalho. Além do anterior, será introduzida a entropia topológica para elementos em Fm(M) e mostraremos algumas das suas propriedades. Provaremos que esta entropia é contínua em Fm(M) munido da topologia forte. Porém, ela é descontínua em cada elemento de Fm(M) munido da topologia produto. Também apresentaremos um resultado que pode ser uma ferramenta de muita utilidade no estudo da continuidade da entropia topológica de difeomorfismos definidos em variedades compactas. Finalizaremos o trabalho dando uma lista de problemas que surgiram ao longo desta pesquisa e que serão analisados em um trabalho futuro.
Anosov families were introduced by P. Arnoux and A. Fisher, motivated by generalizing the notion of Anosov dieomorphisms. Roughly, Anosov families are sequences of dieomorphisms (fi)i∈Z dened on a sequence of compact Riemannian manifolds (Mi)i∈Z, where fi: Mi -> Mi+1 for all i ∈ Z, such that the composition fi+n o · · · o fi, for n >=1, has asymptotically hyperbolic behavior. This notion is known as a non-stationary dynamical system or a non-autonomous dynamical system. Let M be the disjoint union of each Mi, for each i ∈ Z, and Fm(M) the set consisting of families of Cm-dieomorphisms (fi)i∈Z dened on the sequence (Mi)i∈Z. The main goal of this work is to explore some properties of Anosov families. In particular, we will show that the set consisting of these families is open in Fm(M), where Fm(M) is endowed with the strong topology (or Whitney topology); the structural stability of a certain class of Anosov families, considering uniform topological conjugacies; and some versions of stable and unstable manifold theorems. The results that will be presented here generalize some results obtained in Random Dynamical Systems, which will be mentioned throughout the work. In addition to the above mentioned theorems, the topological entropy for elements in Fm(M) will be introduced, and we will show some of its properties. We will prove that this entropy is continuous on Fm(M) endowed with strong topology. However, it is discontinuous at each element of Fm(M) endowed with the product topology. We will also present a result that can be a very useful tool in the study of the continuity of the topological entropy of dieomorphisms dened on compact manifolds. We will nish the work by giving a list of problems that have arisen throughout this research and that will be analyzed in a future work.

The thesis deals with the behaviour of a cracked rail wheel. The aim was to perform the strain analysis of intact wheel as well as the fracture analysis of the primary direct cracked wheel. Solution includes an analysis of operating conditions, assessment of the substantiality of articular components of load, stiffness of the wheel, a comprehensive analysis of fracture of the selected railway wheel profile and optimization of the wheel shape depending on the matching fracture properties.

Dans cette thèse, nous introduisons deux nouvelles approches pour calculer l'homologie persistante(HP) d'une séquence de complexes simpliciaux. L'idée de base est de simplifier les complexes de la séquence d'entrée en utilisant des types spéciaux de collapses (effondrement), les collapses forts et les collapses d'arêtes, et de calculer l'HP d'une séquence réduite de plus petite taille qui a la même HP que la séquence initiale. Notre première approche utilise les collapses forts introduits par J. Barmak et E. Miniam [DCG (2012)]. Un collapse fort supprime les sommets dits dominés d'un complexe simplicial. Notre approche utilisant les collapses forts a plusieurs caractéristiques qui la distinguent des travaux antérieurs. La méthode n'est pas limitée aux filtrations (c'est-à-dire aux séquences de sous-complexes simpliciaux imbriqués) mais fonctionne pour d'autres types de séquences comme les tours et les zigzags. Par ailleurs, pour implémenter les collapses forts, il suffit de représenter les simplexes maximaux du complexe, et pas l'ensemble de tous ses simplexes, ce qui économise beaucoup d'espace et de temps. De plus, les complexes de la séquence peuvent être collapsés indépendamment et en parallèle.Dans le cas des complexes en drapeaux (flag complexes), les collapses forts peuvent être réalisés sur le 1-squelette du complexe et le complexe résultat est également un complexe en drapeau. Nous montrons que si l'on restreint la classe des complexes simpliciaux aux complexes en drapeaux, on peut améliorer la complexité en temps et en espace de facon décisive par rapport aux travaux antérieurs. Lorsque les collapses forts sont appliqués aux complexes d'une tour de complexes en drapeau, nous obtenons une séquence réduite qui est aussi une tour de complexes en drapeau que nous appelons le coeur de la tour. Nous convertissons ensuite le coeur de la tour en une filtration équivalente pour calculer son HP. Là encore, nous n'utilisons que les 1-squelettes des complexes. La méthode résultante est simple et extrêmement efficace.Nous étendons la notion de sommet dominé au cas de simplexes de dimension quelconque. Le concept d'arête dominée apparait très puissant et nous l'étudions dans le cas des complexes en drapeaux de faconplus détaillée. Nous montrons que les collapses d'arêtes (suppression des arêtes dominées) dans un complexe en drapeaux peut être effectué, comme précédemment, en utilisant uniquement le 1-squelette du complexe. En outre, le complexe résiduel est également un complexe de drapeaux. Ensuite, nous montrons que, comme dans le cas des collapses forts, on peut utiliser les collapses d'arêtes pour réduire une filtration de complexes en drapeaux en une filtration de complexes en drapeaux plus petite qui a la même HP. Là encore, nous utilisons uniquement le 1-squelettes des complexes.Comme l'ont démontré de nombreuses expériences sur des données publiques, les approches développées sont extrêmement rapides et efficaces en mémoire. En particulier, la méthode utilisant les collapses d'arêtes offre de meilleures performances que toutes les méthodes connues, y compris l'approche par collapses forts. Enfin, nous pouvons faire des compromis entre précision et temps de calcul en choisissant le nombre de complexes simpliciaux de la séquence à collapser
In this thesis, we introduce two new approaches to compute the Persistent Homology (PH) of a sequence of simplicial complexes. The basic idea is to simplify the complexes of the input sequence by using special types of collapses (strong and edge collapse) and to compute the PH of an induced sequence of smaller size that has the same PH as the initial one.Our first approach uses strong collapse which is introduced by J. Barmak and E. Miniam [DCG (2012)]. Strong collapse comprises of removal of special vertices called \textit{dominated} vertices from a simplicial complex.Our approach with strong collapse has several salient features that distinguishes it from previous work. It is not limited to filtrations (i.e. sequences of nested simplicial subcomplexes) but works for othertypes of sequences like towers and zigzags. To strong collapse a simplicial complex, we only need to store the maximal simplices of the complex, not the full set of all its simplices, which saves a lot ofspace and time. Moreover, the complexes in the sequence can be strong collapsed independently and in parallel.In the case of flag complexes strong collapse can be performed over the $1$-skeleton of the complex and the resulting complex is also a flag complex. We show that if we restrict the class of simplicial complexes to flag complexes, we can achieve decisive improvement in terms of time and space complexities with respect to previous work. When we strong collapse the complexes in a flag tower, we obtain a reduced sequence that is also a flag tower we call the coreflag tower. We then convert the core flag tower to an equivalent filtration to compute its PH. Here again, we only use the 1-skeletons of the complexes. The resulting method is simple and extremelyefficient. We extend the notions of dominated vertex to a simplex of any dimension. Domination of edges appear to be very powerful and we study it in the case of flag complexes in more detail. We show that edge collapse (removal of dominated edges) in a flag complex can be performed using only the 1-skeleton of the complex as well. Furthermore, the residual complex is a flag complex as well. Next we show that, similar to the case of strong collapses, we can use edge collapses to reduce a flag filtration F to a smaller flag filtration F^c with the same persistence. Here again, we only use the 1-skeletons of the complexes. As a result and as demonstrated by numerous experiments on publicly available data sets, our approaches are extremely fast and memory efficient in practice. In particular the method using edge collapse performs the best among all known methods including the strong collapse approach. Finally, we can compromizebetween precision and time by choosing the number of simplicial complexes of the sequence we strong collapse

Neste trabalho estudamos as iteradas de aplicações do plano no plano. Usando as técnicas da dinâmica simbólica em aplicações do plano no plano, tendo sempre por base a teoria de amassamento de Milnor e Thurston e o formalismo da dinâmica simbólica desenvolvido por Sousa Ramos, abordamos diferentes aspectos qualitativos da dinâmica das aplicações de Lozi. Assim, através da dinâmica simbólica introduzida por Yutaka Ishii, começamos por refor-mular a fronteira do espaço dos parâmetros correspondente às aplicações de Lozi equivalentes à ferradura de Smale. No seguimento, apresentamos um método que permite a construção da bacia de atracção para o atractor de uma qualquer aplicação de Lozi. Ainda usando a dinâmica simbólica para as aplicações de Lozi, apresentamos um método que fazendo uso de expansões em fracções contínuas, nos permite calcular o maior dos expoentes de Lyapunov de uma aplicação de Lozi. Com a introdução do conceito de ponto crítico e subsequentemente de sequência de amassamento para as aplicações de Lozi, partimos para uma a construção de uma partição de Markov do seu espaço de fases. Desse modo, é possível a caracterização completa do espaço dos parâmetros através da introdução do conceito de curva de amassamento, que mostramos serem curvas isentrópicas. Consequentemente, obtemos a descrição em termos da entropia topológica da família das aplicações de Lozi. ### Abstract - In this work, we study the iterations of two dimensional maps. Using symbolic dynamics techniques for two dimensional maps, based on both the kneading theory of Milnor and Thurston and the formalism of symbolic dynamics developed by Sousa Ramos, we studied the qualitative aspects of the dynamics of Lozi maps. Thus, through the symbolic dynamics introduced by Yutaka Ishii, through the correction of symbolic sequence that characterized the first tangency between stable and unstable manifolds, we reformulate the border for the Smale horseshoes. Following this work, we present a method that allows the construction of the basin of attraction for the Lozi attractor. Even using the symbolic dynamics, we introduce a new method, using continuous fractions expansions that allow us to compute the largest Lyapunov exponent. Through the kneading sequence for Lozi map, we characterize the region in the parameter space were we have the kneading curves and we also give a method to the construction of a partition of Markov for the Lozi attractors. Consequently we characterize the topological entropy for the Lozi map, and costruct a new topological invariant, the second invariant.