Dans cette thèse, je présente une étude que j'ai réalisée à l'université Paris-sud sous la direction de Thierry Jolicœur sur les phases des Hall Quantiques Fractionnaire (HQF) dans la géométrie du cylindre.Après une rapide introduction dans le premier chapitre, je présente dans le second quelques concepts de base de l'effet HQF et j'introduit certains aspects de la géométrie cylindrique.Le chapitre 3 est consacré à l'étude de la limite du cylindre fin, c'est à dire lorsque la circonférence du cylindre est de l'ordre de quelques longueurs magnétiques. Dans cette limite, on sait que la fonction d'onde de Laughlin au remplissage 1/q se réduit à un cristal unidimensionnel, où une orbitale sur q est occupée. Dans le but d'étudier un limite intermédiaire, nous conservons les quatre premiers termes du développement de l’Hamiltonien lorsque la circonférence est petite devant la longueur magnétique. On trouve alors une expression exacte de l'état fondamental au moyen d'opérateurs de "squeezing" ou de produits de matrices. Nous trouvons également une écriture similaire pour les quasi- trous, les quasi-électron et la branche magnétoroton.Dans les chapitres 4 et 5, je me concentre sur l'étude des excitations de bord chirales des phases de HQF. Je présente une étude microscopique de ces états de bord dans la géométrie du cylindre, lorsque les quasi-particules peuvent passer d'un bord à l'autre par effet tunnel. J'étudie d'abord dans le chapitre 4 la phase de HQF principale dont l'état fondamental est bien décrit par la fonction d'onde de Laughlin. Pour un échelle d'énergie plus faible que le gap du volume, le théorie effective est donnée par un fluide d'électrons unidimensionnel bien particulier : un liquide de Luttinger chiral. À l'aide de diagonalisations numériques exactes, nous étudions le spectre des états de bord formé de le combinaison des deux bord contre-propageant sur chacun des cotés du cylindre. Nous montrons que les deux bords se combinent pour former un liquide de Luttinger non-chiral, où le terme de courant reflète le transfert de quasi-particules entre les bords. Cela nous permet d'estimer numériquement les paramètre de Luttinger pour un faible nombre de particules, et nous trouvons une valeur cohérente avec la théorie de X. G. Wen.J'analyse ensuite dans le chapitre 5 les modes de bord des phases de HQF au remplissage 5/2. À partir une construction basée sur la Théorie des Champs Conformes (TCC), Moore et Read (Nucl. Phys. B, 1991) ont proposé que la physique essentielle de cette phase soit décrite par un état apparié de fermion composites. Une propriété importante de cet état est que ses excitations émergentes permutent sous une statistique non-abéliène. Lorsqu'elles sont localisées sur les bords, ces excitations sont décrites par un boson chiral et un fermion de Majorana. Dans la géométrie du cylindre, nous montrons que le spectre des excitations de bord est fomé des tours conformes du modèle IsingxU(1). De plus, par une méthode Monte-Carlo, nous estimons les différentes dimensions d'échelle sur des grands systèmes (environ 50 électrons), et nous trouvons des valeurs en accord avec les prédictions de la TCC.Dans le dernier chapitre de ce manuscrit, je présente un travail que j'ai réalisé à UBC (Vancouver) en collaboration avec Marcel Franz sur les phase de Hall quantiques de spin induites dans le graphène par des adatomes. Dans ce système, les adatomes induisent un couplage spin-orbite sur les électrons des la feuille de graphène et introduisent du désordre qui est susceptible de détruire le gap spectral. Nous montrons dans ce chapitre que le gap spectral est préservé lorsque des valeurs réalistes de paramètres sont usités. De plus, au moyen de calculs analytiques à base énergie et de diagonalisations numériques exactes, nous identifions un signal caractéristique dans la densité d'états locale mettant en évidence la présence d'un gap topologique. Ce signal pourrait être observé au moyen d'un microscope à effet tunnel. / I present in this thesis a study that I did in the university Paris-sud under the supervision of Thierry Jolicœur onto Fractional Quantum Hall (FQH) phases in the cylinder geometry. After a short introduction in the first chapter, I present some basic concept relative to the FQH effect in the second one and introduce some essential features relative to the cylinder geometry, useful for the chapters 3, 4, and 5. The chapter 3 is dedicated to the study of the thin cylinder limit, i.e. when the circumference of the cylinder is of the order of a few magnetic length. In this limit, it is known that the Laughlin wave function at the filling factor 1/q is reduced to a one dimensional crystal in the lowest Landau level orbitals where one every q orbitals is occupied. We Taylor expand the Hamiltonian when the circumference is small compare to the magnetic length in order to study an intermediate limit. When only the first four terms of the development are kept, it is possible to find exact representations of the ground state with "squeezing" operators or matrix products. We also find similar representations for quasiholes, quasielectrons and the magnetorton branch. These results have been published in the article Phys. Rev. B 85, 155116 (2012). In the chapter 4 and 5 I focus onto the gapless chiral edge excitations of FQH phases. I present a microscopic study of those edges states in the cylindrical geometry where quasiparticles are able to tunnel between edges. I first study the principal FQH phase at the filling fraction 1/3 whose ground state is well described by the Laughlin wave function in the chapter 4. For an energy scale lower than the bulk gap, the effective theory is given by a very peculiar one dimensional electron fluid localized at the edge: a chiral Luttinger liquid. Using numerical exact diagonalizations, we study the spectrum of edge modes formed by the two counter-propagating edges on each side of the cylinder. We show that the two edges combine to form a non-chiral Luttinger liquid, where the current term reflects the transfer of quasiparticles between edges. This allows us to estimate numerically the Luttinger parameter for a small number of particles and find it coherent with the one predicted by X. G. Wen theory. We published this work in Phys. Rev. B 86, 115214 (2012). I then analyze edge modes of the FQH phase at filling fraction 5/2 in the chapter 5. From a Conformal Field Theory (CFT) based construction, Moore and Read (Nucl. Phys. B, 1991) proposed that the essential physics of this phase is described by a paired state of composite fermions. A striking property of this state is that emergent excitations braid with non-Abelian statistics. When localized along the edge, those excitations are described through a chiral boson and a Majorana fermion. In the cylinder geometry, we show that the spectrum of edge excitations is composed of all conformal towers of the IsingxU(1) model. In addition, with a Monte Carlo method, we estimate the various scaling dimensions for large systems (about 50 electrons), and find them consistent with the CFT predictions.In the last chapter of my manuscript, I present a work that I did in UBC (Vancouver) in collaboration with Marcel Franz onto quantum spin Hall phases in graphene induced by adatoms. In this system, adatoms induce a spin orbit coupling for electrons in the graphene sheet and create some disorder which might be responsible for destruction the spectral gap. We show in this chapter and in the article [Phys. Rev. B 89, 201410(R) (2014)] that the spectral gap remains open for a realistic range of parameters. In addition, with analytical computations in the low energy approximation and numerical exact diagonalizations, we find characteristic signal in the local density of states highlighting the presence of topological gap. This signal might be observed in scanning tunneling spectroscopy experiments.

Neste trabalho foram estudadas as fases topológicas não triviais presentes em sistemas formados pela deposição de átomos de grafeno. Encontramos que quando um átomo hibridiza fortemente com o grafeno, apresenta um momento magnético e um forte spin-órbirta é possível a formação de uma rede hexagonal de baricentros que efetivamente gera uma estrutura de bandas característica de um efeito hall quântico anômalo. Especificamente, determinamos que o Ru satisfaz estas características. Quando este metal é depositado em uma configuração triangular no grafeno ocorrem picos na densidade de estados localizados no centro geométrico (baricentro) dos triângulos formados pelos Ru. Estes picos estão distribuídos de forma hexagonal e efetivamente geram uma estrutura de bandas que nas proximidades do nível de Fermi apresenta uma configuração de spin característica do efeito Hall quântico anômalo. Adicionalmente, encontramos que o sistema composto pela absorção de Ba ou Sr no grafeno favorece a formação do efeito Hall quântico de spin. Neste sistema, o acoplamento spin-órbita (SOC) gera um gap mais de 1000 vezes maior ao período no grafeno prístino. Para o estudo destes sistemas, implementamos no código SIESTA a aproximação on-site do acoplamento spin-órbita via o formalismo dos pseudopotenciais relativísticos de norma conservada. Nossa implementação foi testada a partir do estudo de fenômenos já conhecidos: i) o strong spin-splitting gerado no grafeno pela adsorção de Au, ii) o efeito hall quântico de spin no poço quântico de HgTe/CdTe e, iii) a formação de estados topológicos na superfície do Bi2Se3 e as fases magnéticas deste material com átomos de Mn adsorvidos. / In this work, were studied the non-trivial topological phases present in systems formed by deposition of atoms in graphene. We found that when an atom hybridizes strongly with grapheme, has a magnetic moment and a strong spin-orbit it is possible the formation of a hexagonal network of barycentres that effectively generates a structure band characteristic of a quantum anomalous Hall effect. Specifically, we determined that Ru satisfies these characteristics. When this metal is deposited in a triangular configuration in grapheme, peaks occur in the density of localized states in the geometric center (centroid) of the triangles formed by Ru. These peaks are distributed in a hexagonal structure and effectively generates a band structure that near the Fermi level has a spin configuration characteristic of the spin quantum Hall effect anomalous. Additionally, we found that the system composed by the adsorption of Ba or Sr in grapheme, promotes the formation of spin quantum Hall effect. In this system, the spin-orbit coupling (SOC) generates a gap more than 1000 times grater that predicted in pristine praphene. To study these systems, wu implemented in the code SIESTA the on-site approach of the spin-orbit coupling throught the formalism of norm conserved relativistic pseudo potentials. Our implementation was tested from the study of phenomena already known: i) the strong spin-splitting generated in graphene by adsorption of Au, ii) the quantum spin Hall effect in quantum well of HgTe / CdTe and, iii) formation of topological states in the surface of Bi2Se3 and the magnetic of this material with Mn atoms adsorved.

Orientador: Pascoal José Giglio Pagliuso / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-09-02T11:57:27Z (GMT). No. of bitstreams: 1 Souza_JeanCarlo_M.pdf: 4438731 bytes, checksum: aaba7a375b2b45b638619e944111c41b (MD5) Previous issue date: 2017 / Resumo: A ideia de topologia na Física da Matéria da Condensada, apesar de ter surgido com o efeito Hall quântico inteiro, só voltou a ser explorada recentemente na busca de novas fases da matéria depois do surgimento dos Isolantes Topológicos (ITs) 2D. Após a previsão teórica, e a descoberta experimental, foi proposto que esta nova fase poderia ser generalizada para sistemas 3D, em que o volume do material seria isolante com estados metálicos de superfície que possuiriam canais de spin polarizados. Apesar de diversos experimentos e o surgimento de outras fases topológicas da matéria subsequentes, ainda há dúvidas sobre a natureza dos ITs 3D. Os efeitos topológicos mais claros ainda não foram observados de forma inequívoca e reprodutível experimentalmente e ainda seria de extrema valia encontrar técnicas experimentais que possam complementar os mais discutidos experimentos de ARPES. Nesta dissertação foram estudadas duas famílias distintas de materiais propostas como possíveis ITs 3D: os binários Bi2Se3 e Sb2Te3 e o half-Heusler YPdBi. Utilizando a técnica de auto-fluxo e a fusão estequiométrica, os sistemas foram sintetizados dopados com os terras-rara Gd3+, Nd3+ e Er3+ para realizar estudos de ressonância de spin eletrônico (RSE) e do papel dos efeitos de campo cristalino (CEF) - no caso do half-Heusler. Para o ternário YPdBi foram feitos dois estudos. Na família dos half-Heuslers, a ordem topológica surge da relação entre o acoplamento spin-órbita e a hibridização, que está ligada com a mudança do parâmetro de rede, então os efeitos de CEF poderiam estar refletindo a transição entre a trivialidade e a não-trivialidade. A partir das medidas de susceptibilidade magnética em função da temperatura das amostras dopadas com Nd3+ e Er3+ combinadas com os estudos de RSE, foi possível extrair os parâmetros de campo cristalino (CFP) de quarta e sexta ordem. Comparando esses dados com resultados anteriores para o material, supostamente, não-trivial YPtBi, observou-se uma mudança sistemática no sinal dos CFP. Resultados prévios para as amostras de YPtBi dopadas com Nd3+ mostram uma evolução não usual para uma forma de linha difusiva com a potência de micro-onda. Neste trabalho também foi realizado um estudo da forma de linha em função da potência. Apenas a ressonância do Nd3+ para os monocristais de 10% de Nd em YPdBi mostrou uma forma de linha difusiva que evolui com a potência da micro-onda. No caso dos binários Bi2Se3 e Sb2Te3, o objetivo era otimizar a rampa de tratamento térmico para obter monocristais melhores que poderiam permitir a observação de um espectro totalmente resolvido do Gd3+. Após mudanças no crescimento dos monocristais, o espectro totalmente resolvido foi obtido para as amostras de Bi2Se3. No caso do Sb2Te3 apenas uma linha central com a estrutura fina colapsada foi observada. Acompanhando o deslocamento g e a evolução da largura de linha dH da RSE do Gd3+ com a temperatura, o comportamento negativo do deslocamento g para toda a faixa de temperatura indica que elétrons do tipo p são os grandes responsáveis pela formação da superfície de Fermi residual destes sistemas. Um aumento no coeficiente angular de dH em função da temperatura, a taxa Korringa b, foi observado em baixas temperaturas, logo diferentes concentrações de Gd3+ foram utilizadas para estudar este comportamento. Novamente observou-se um comportamento anômalo em baixas temperaturas, o que poderia estar relacionado com a evolução dos CFP com a temperatura. Todos esses resultados foram discutidos levando-se em conta a possibilidade de existência de topologia não-trivial na estrutura eletrônica desses materiais, com foco particular na relação da interação spin-órbita e os efeitos de campo cristalino com a manifestação da topologia não trivial nesses sistemas / Abstract: The idea of topological systems in Condensed Matter Physics, although already explored in the Quantum Hall Effect, has recently become a topic of intense scientific investigation. In particular, great efforts have been dedicated to the search for new quantum phases since the proposal of the Topological Insulators (TIs) in 2D. After the theoretical prediction and the experimental discovery of the TIs in the 2D case, the existence of the Quantum Hall Spin Effect in 3D, 3D TIs, was proposed, where an insulator bulk and metallic surface states with spin polarized channels could be experimentally realized. Although many experiments have been performed, and some groups claimed the direct observation of such new topological phases, there is still a lot of controversy about the nature of the 3D TIs and about the actual microscopic origin of the metallic states on the surface of the studied materials. Other signatures of the topological phases have not been unambiguously and repeatedly measured yet and there is an obvious lack of a supplementary lab technique to be compared to the most used technique to probe these states, which is ARPES. In this work we have studied two different classes of 3D TIs: the binaries Bi2Se3 and Sb2Te3 and the half-Heusler YPdBi. We have been able to grow single crystals of these materials pure and rare-earth doped with Gd3+, Nd3+ and Er3+ using the self-flux technique and the stoichiometric melting. The aim was to use these crystals to study Electron Spin Resonance (ESR) as a potential probe to investigate the existence of the metallic surface states and to explore the possible of the crystalline electrical field (CEF) effects on the formation of the non-trivial electronic structure of these materials. Regarding the YPdBi, our ESR and magnetization studies have revealed that, in the half-Heusler family, the topological order emerges from the interplay between spin-orbit coupling and the hybridization, which is connected with the changes on the lattice parameter. Thus, the CEF effects could reflect the transition from trivial to nontrivial topology. From the magnetic susceptibility data as a function of temperature from the Nd3+ and Er3+ doped samples combined with the ESR studies, it was possible to extract the fourth and sixth order crystal field parameters (CFP). Comparing our data with the previous results from YPtBi, which is a putative non-trivial material, a systematic change in the sign of the CFP was observed. Previous results with the YPtBi Nd-doped samples show an unusual evolution of the Nd3+ ESR line to a diusive-like line shape as a function of the microwave power. In this work we have performed a similar study of the Nd3+ ESR line shape as a function of the microwave power. Only for the single crystal of 10% Nd in YPdBi resonance shows a diffusive-like line shape that evolves with the microwave power. In the case of the binaries Bi2Se3 e Sb2Te3, the aim of this work was to optimize the heat treatment used in previous works of our group to obtain better single crystals that could allow the observation of the full resolved spectra from Gd3+. After many changes in the single crystal growth method, we were able to observe fully resolved Gd3+ ESR spectra in the Bi2Se3 samples. Regarding the Sb2Te3 single crystals, only a single Gd3+ Dysonian ESR line was observed. Following the Gd3+ ESR dg and dH as a function of temperature, the observed negative behavior of dg, in the whole temperature range studied, indicates that p-type electrons are the main source for the formation of the small the Fermi surface of these materials. An increase of the angular coefficient of dH as a function of temperature, the Korringa rate b, at low temperatures was observed and different concentrations of Gd3+ were required to investigate this anomaly. Again this anomalous behavior at low temperatures was observed for the all Gd-doped samples, which could be related to an evolution of CFP with temperature. We discuss our results taking into account the existence of non-trivial topological states in our samples and the role of spin-orbit and CEF effects might have in the formation of such states / Mestrado / Física / Mestre em Física / 132653/2015-0 / CNPQ / CAPES / FAPESP

Le tellurure de mercure et de cadmium (HgCdTe ou MCT) est un matériau reconnu pour la physique de la matière condensée, dont l'histoire, datant aujourd'hui de plus de cinquante ans, constitue un excellent exemple des progrès remarquables réalisés dans la recherche sur les semi-conducteurs et les semi-métaux. Notre travail est principalement motivé par l’intérêt fondamental que suscitent ces systèmes, mais notre recherche peut également avoir un impact pratique (indirect) sur la médecine, la surveillance ou la détection de l’environnement ainsi que sur les systèmes de sécurité. Cela peut aider à améliorer les performances des photodétecteurs dans la limite des grandes longueurs d'onde ou à faciliter la fabrication de dispositifs émettant de la lumière.La présente thèse de doctorat vise principalement à combler certaines des lacunes de notre compréhension de la structure de bande électronique des hétérostructures 2D et quasi-2D basées sur les matériaux HgTe/HgCdTe et InAs/InSb, qui peuvent être transformés en phase topologiquement isolante à l'aide des paramètres de croissance. Pour explorer leurs propriétés, la technique expérimentale de base, la magnéto-spectroscopie infrarouge et THz fonctionnant dans un large éventail de champs magnétiques, est combinée à des mesures complémentaires de magnéto-transport. Cette combinaison de méthodes expérimentales nous permet d’obtenir de précieuses informations sur les états électroniques non seulement à l’énergie de Fermi, mais également dans son voisinage relativement large. Diverses hétérostructures ont été étudiées avec des caractéristiques globales et/ou spécifiques déterminées principalement par les paramètres de croissance.La réponse magnéto-optique observée, due aux excitations intra-bande (résonance cyclotron) et interbandes (entre les niveaux de Landau) peut être interprétée dans le contexte d'études antérieures sur des échantillons 3D, des puits quantiques et des super-réseaux, mais également en rapport aux attentes théoriques. Ici, nous visons à obtenir une explication quantitative des données expérimentales recueillies, mais également à développer un modèle théorique fiable. Ce dernier comprend le réglage précis des paramètres de structure de bande présents dans le modèle établi de Kane, mais surtout, l'identification de termes supplémentaires pertinents (d'ordre élevé) nécessaires pour parvenir à un accord quantitatif avec nos expériences. On peut s’attendre à ce que les corrections dues à ces termes supplémentaires affectent davantage les sous-bandes de valence, généralement caractérisées par des masses effectives relativement importantes et, par conséquent, par une grande densité d’états ou, lorsque le champ magnétique est appliqué, par un espacement assez étroit (et mélange important) des niveaux de Landau. / Mercury cadmium telluride (HgCdTe or MCT) is a time-honored material for condensed matter physics, whose history  nowadays more than fifty years long  may serve as an excellent example of remarkable progress made in research on semiconductors and semimetals. The ternary compound HgCdTe implies two important aspects, which largely contributed to its undoubted success in solid-states physics.The present PhD thesis primarily aims at filling some of existing gaps in our understanding of the electronic band structure in 2D and quasi-2D heterostructures based on HgTe/HgCdTe and InAs/InSb materials, which both may be tuned into topologically insulating phase using particular structural parameter. To explore their properties, the primal experimental technique, infrared and THz magneto-spectroscopy operating in a broad of magnetic fields, is combined with complementary magneto-transport measurements. This combination of experimental methods allows us to get valuable insights into electronic states not only at the Fermi energy, but also in relatively broad vicinity.The observed magneto-optical response - due to intraband (cyclotron resonance) and interband inter-Landau level excitations - may be interpreted in the context of previous studies performed on bulk samples , quantum wells and superlattices, but also compared with theoretical expectations. Here we aim at achieving the quantitative explanation of the collected experimental data, but also further developing a reliable theoretical model. The latter includes the fine-tuning of the band structure parameters present in the established Kane model, but even more importantly, identifying additional relevant (high-order) terms and finding their particular strengths, needed to achieve quantitative agreement with our experiments. One may expect that corrections due to these additional terms will more affect the valence subbands, which are in general characterized by relatively large effective masses. Consequently, valence subbands have larger density of states compared to conduction band or, when the magnetic field is applied, rather narrow spacing (and possibly large mixing) of Landau levels.

Dans le cadre de ce travail de doctorat, nous avons mis au point un nouveau microscope à balayage à transistor à électron unique (SET) qui fonctionne à très basse température (T = 50 mK) et à champs magnétiques intenses (18 T). Un SET se compose d'un petit îlot métallique relié aux électrodes de source et de drain par deux jonctions tunnel. En régime de blocage de Coulomb à basse température (T < 5 K), un champ électrique externe règle le courant circulant dans le SET. De plus, de petites variations du champ électrique entraînent de grandes variations du courant SET, ce qui fait de l'appareil un détecteur de charge très sensible, capable de détecter des charges inférieures à 0,01e. Ainsi, lorsque le SET scanne au-dessus d'une surface, il cartographie les propriétés électrostatiques de l'échantillon. Cependant, la mise en œuvre d'un microscope à balayage SET est extrêmement difficile car il combine la microscopie à sonde à balayage, les basses températures et les dispositifs nanoscopiques très sensibles. Pour cette raison, seuls quelques groupes ont réussi sa réalisation. Nos choix technologiques pour construire le microscope améliorent certains aspects par rapport aux instruments déjà existants.La percée est que nous fabriquons la sonde SET en utilisant des techniques lithographiques standard sur des plaquettes commerciales de silicium. C'est pourquoi il est possible de fabriquer des sondes SET par lots. De plus, grâce à une combinaison de techniques de découpage et de gravure, le SET est conçu très près du bord du substrat de Si (< 1 micromètre ). De cette façon, le SET peut être approché à quelques nanomètres de la surface de l'échantillon au moyen d'un contrôle de distance de force atomique. De plus, une électrode de grille fabriquée sur la sonde à proximité de l'îlot peut être utilisée pour régler le point de fonctionnement du SET. Une nouveauté de notre instrument est qu'avec cet électrode de grille et une boucle de rétroaction, nous avons cartographié directement le champ électrique local. Nous démontrons cette nouvelle méthode de balayage par rétroaction en imaginant un réseau interdigité d'électrodes à l'échelle nanométrique. De plus, le SET est un outil idéal pour l'étude de la localisation d'états électroniques. À l'avenir, notre microscope sera utilisé pour l'étude des systèmes d'électrons bidimensionnels en régime de l'effet Hall quantique, des isolants topologiques et de la transition métal-isolant. / In this doctoral work, we have developed a new scanning single electron transistor (SET) microscope that works at very low temperatures (T = 50 mK) and high magnetic fields (B = 18 T). A SET consists of a small metallic island connected to source and drain electrodes through two tunnel junctions. In the Coulomb blockade regime at low temperature regime (T 5 K), an external electric field tunes the current circulating through the SET. In addition,small electric field variations lead to large SET current changes that makes the device a highly sensitive charge detector, able to detect charges smaller than 0.01 e. Thus, when the SET scans above a surface, it maps the electrostatic properties of the sample. However, the implementation of a scanning SET microscope is extremely challenging since it combines scanning probe microscopy, low temperatures and sensitive nanoscopic devices. For thisreason, only a few groups have succeeded its realization. Our technological choices to build the microscope improve certain aspects with respect to the already existing instruments. The breakthrough is that we fabricate the SET probe using standard lithographic techniques on commercial silicon wafers.For that reason, batch fabrication of SET probes is possible. Furthermore, by a combination of dicing and etching techniques, the SET is engineered extremely close to the edge of the Si chip (< 1 micrometer). In this way, the SET can be approached to a few nanometer from the sample surface by means of a atomic force distance control. Additionally, an on-probe gate electrode fabricated close to the island can be used to tune the operating point of the SET. Anovelty of our instrument is that with this on-probe gate and a feedback loop we have been able to map directly the local electric field. We demonstrate this new feedback scanning method by imaging an interdigitated array of nanometer scale electrodes. Moreover, the SET is an ideal tool for the study of the localization of electronic states. In the future, our scanning SET will be used for the study of two-dimensional electron systems in the quantum Hall regime, topological insulators and the metal insulator transition.

We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.

We discuss the appearance of quantum orders in the Hubbard model for interacting electrons, at half-filling. Such phases do not have local order parameters and need to be characterized by the quantum mechanical properties of their ground state. On one hand, we study the Mott transition from a metal to a spin liquid insulator in two dimensions, of potential relevance to some layered organic compounds. The correlation-driven transition occurs at fixed filling and involves fractionalization of the electron: upon entering the insulator, a Fermi surface of neutral spinons coupled to an internal gauge field emerges. We focus on the transport properties near the quantum critical point and find that the emergent gauge fluctuations play a key role in determining the universal scaling. Second, motivated by a class of three-dimensional transition metal oxides, the pyrochlore iridates, we study the interplay of non-trivial band topology and correlations. Building on the strong spin orbit coupling in these compounds, we construct a general microscopic Hubbard model and determine its mean-field phase diagram, which contains topological insulators, Weyl semimetals, axion insulators and various antiferromagnets. We also discuss the effects many-body correlations on theses phases. We close by examining a fractionalized topological insulator that combines the two main themes of the thesis: fractionalization and non-trivial band topology. Specifically, we study how the two-dimensional protected surface states of a topological Mott insulator interact with a three-dimensional emergent gauge field. Various correlation effects on observables are identified.

Cette thèse traite de la manipulation de l'énergie dans trois systèmes quantiques ouverts différents dans la limite de couplage faible système-environnement, et leurs dynamiques respectives sont décrites par une équation maîtresse quantique markovienne. Dans le premier chapitre, le calcul d'une telle équation est réalisé pour un système particulier, et diverses notions de thermodynamique quantique sont introduites. Pour le premier système physique, on analyse le transport d'énergie le long de chaînes atomiques (entre 2 et 7 atomes) soumises à un rayonnement de corps noir proche de la température ambiante. Il est montré que l'efficacité du transport peut atteindre des valeurs remarquables, surpassant 100% et atteignant jusqu'à 1400% dans certaines configurations. De plus, lorsque l'efficacité est amplifiée, la portée du transport est également considérablement augmentée. Le chapitre suivante traite aussi du transport d'énergie dans des chaînes atomiques. Le système quantique est placé à l'interface d'un isolant topologique photonique (ITP), qui supporte un plasmon polariton de surface (PPS) insensible à la réflexion. Le PPS se propage le long de la chaîne atomique et assiste le transport d'énergie. La comparaison est faite entre PPSs réciproque et unidirectionnel en termes d'efficacité du transport, et il est démontré que ce dernier produit une meilleure efficacité, de plus d'un ordre de grandeur. De surcroît, divers aspects pratiques dus aux propriétés des ITPs sont mis en avant, notamment la robustesse du transport d'énergie en présence de défauts sur le parcours du PPS. Enfin, un système quantique immergé dans un champ électromagnétique hors équilibre thermique est étudié. Il est composé d'un système à trois niveaux d'énergie, jouant le rôle de machine thermique quantique à absorption, ainsi que de N atomes à deux niveaux ("qubits") qui sont affectés par l'action de la machine. Il est montré que la machine est capable de délivrer des tâches thermiques d'intensité significative sur les qubits, y compris lorsque leur nombre augmente. De plus, il est mis en évidence qu'en raison d'interactions qubit-qubit, les tâches réalisées par la machine sont distribuées parmi l'ensemble du système des qubits en interaction, de sorte que dans certains cas, même les qubits complètement découplés de la machine subissent une modification de température considérable. Ce mécanisme de distribution des tâches est analysé à travers les corrélations entre différentes partitions du système quantique. Par ailleurs, le contrôle des tâches thermiques est également discuté. / This thesis deals with energy management in open quantum systems. Three different systems are under study in the limit of weak system-environment coupling, and their dynamics is described by Markovian quantum master equations. In the first chapter, the complete derivation of such equation is performed in a specific case, and several notions of quantum thermodynamics are introduced. In the first system, energy transport is investigated along atomic chains (between 2 and 7 atoms) embedded in blackbody radiation around room temperature. It is shown that the transport efficiency can reach remarkable values, exceeding 100% and reaching 1400% in some configurations. Moreover, when the efficiency is amplified, the transport range is also considerably increased. The following chapter also deals with energy transport in atomic chains. The quantum system is located at the interface of a photonic topological insulator (PTI), supporting a unidirectional surface-plasmon-polariton (SPP) immune to backscattering. The SPP propagates along the chain and assists energy transport. Comparison is made between reciprocal and unidirectional SPPs in terms of transport efficiency, and it is shown that the latter can yield an efficiency larger by one order of magnitude. In addition, several practical aspects stemming from PTIs are highlighted, including the robustness of energy transport in the presence of defects on the SPP path. In the last chapter, a quantum system embedded in an out-of-thermal-equilibrium electromagnetic field is investigated. It is composed of a three-level atom playing the role of an absorption quantum thermal machine, as well as N two-level atoms ('qubits'), with N=1,...,6, which are the target bodies. It is demonstrated that the machine is able to perform significant thermal tasks on the qubits, even when their number is increased. Moreover, it is pointed out that due to qubit-qubit interactions, the tasks delivered by the machine are distributed throughout the system of interacting qubits, such that in some cases the temperature of the qubits which are completely decoupled from the machine can still be considerably affected by it. This task-distribution mechanism is investigated by means of the correlations between different subparts of the system. In addition, the tuning of thermal tasks is discussed.

Cette thèse présente une étude sur les hétérostructures à base de mercure, cadmium et tellure (HgCdTe ou MCT) pour l'émission et la détection de radiations Térahertz (THz). En raison de leurs propriétés physiques spécifiques, les hétérostructures à base de HgCdTe devraient en effet jouer un rôle important dans les futurs dispositifs Térahertz. Parmi les autres propriétés remarquables de ces structures, les puits quantiques de HgTe/CdTe à l'épaisseur critique (environ 6,3 nm) présentent un état sans gap caractérisé par la relation de dispersion linéaire propre aux fermions Dirac sans masse. Lorsque la largeur du puits quantique dépasse la valeur critique, la structure de la bande s’inverse. Dans ce cas, ces puits deviennent des isolants topologiques bidimensionnels qui passionnent la communauté scientifique depuis une décennie. Cette inversion de bande peut être brisée en variant plusieurs paramètres physiques tels que le champ magnétique ou la température. Ces transitions de phases topologiques pourraient être très intéressantes en vue d’applications à l’électronique haute fréquence et à basse consommation d'énergie.Dans ce travail, l’accent est mis sur des dispositifs munis de grilles et présentant une structure de bande inversée. Premièrement, nous mettons en évidence la possibilité de détecter la lumière incidente Térahertz à des températures cryogéniques. Nous rapportons également une amélioration de la détection Térahertz au voisinage de la transition de phase topologique induite par le champ magnétique et proche du point de neutralité de charge. Deuxièmement, nous observons sans ambiguïté la transition de phase induite par la température entre l'état isolant topologique et l'état isolant de l’effet Hall quantique, par des expériences de magnéto-transport. Ensuite, en utilisant la technique de détection Térahertz non résonnante, nous avons retracé avec succès les niveaux de Landau du puits et défini précisément le champ magnétique critique correspondant à la transition de phase quantique. Nous avons constaté que cette technique Térahertz peut être utilisée dans chaque échantillon avec grille sans besoin de quatre contacts de mesure ni de traitement de données mathématiques.En ce qui concerne les émetteurs Térahertz, nous présentons ici nos résultats sur l'émission stimulée d'hétérostructures de HgCdTe dans leur état semi-conducteur conventionnel à des fréquences supérieures à 30 THz. Nous discutons des mécanismes physiques impliqués et des voies prometteuses vers le domaine de fréquence entre 5 et 15 THz. Malgré le fait que les principaux matériaux pour les lasers solides à grandes longueurs d'ondes sont des hétérostructures basées sur les semi-conducteurs III-V, leurs bandes Reststrahlen rendent cette gamme de fréquences inaccessible pour les lasers à base de III-V (y compris les lasers à cascade quantique) même à des températures cryogéniques. Étant donné que la bande d'absorption du réseau cristallin dans les hétérostructures à base de Hg1-xCdxTe est décalée vers des longueurs d'onde plus grandes, ces composés (avec x <0,21) semblent être très prometteurs en tant que lasers solides Térahertz. / This thesis presents an investigation of mercury-cadmium-telluride (HgCdTe or MCT) based heterostructures for emission and detection of Terahertz (THz) radiations. Due to their specific physical properties, HgCdTe-based heterostructures are indeed expected to play an important role in future terahertz systems. Among other remarkable properties, HgTe/CdTe-based quantum wells (QWs) at the critical thickness (about 6.3 nm), exhibit a gapless state characterized by the linear energy-momentum law of massless Dirac fermions. When the QW width exceeds this critical value, the energy band structure becomes inverted. In this case, these QWs are shown to be two-dimensional topological insulators that attract since the last decade a great fundamental interest. This band inversion can be broken by varying several external physical parameters as magnetic field or temperature. These so-called topological phase transitions could be of high interest for future low-energy consumption and high frequency electronics.Here, focusing on gated devices presenting inverted band ordering, we first evidence the possibility to detect THz incident light at cryogenic temperatures. We also report on an enhancement of the terahertz photoconductive response in the vicinity of the magnetic field driven topological phase transition and close to the charge neutrality point. Secondly, we observed unambiguously the temperature driven phase transition between the topological insulator state and the usual quantum Hall insulator state by magneto-transport experiments. Then, using the non-resonant THz detection technique, we successfully imaged the QWs Landau levels and defined precisely the critical magnetic field corresponding to the quantum phase transition. We found that this THz technique can be used in every gated sample without need neither for four contacts devices nor mathematical data processing.Regarding terahertz emitters, we present here our results on stimulated emission of HgCdTe heterostructures in their conventional semiconductor state above 30 THz, discussing the physical mechanisms involved and promising routes towards the 5–15 THz frequency domain. Despite the fact that the leading materials for long wavelength solid-state lasers are heterostructures based on III-V semiconductors, their Reststrahlen bands makes this frequency range inaccessible for III-V-based lasers (including quantum cascade lasers) even at cryogenic temperatures. Since the lattice absorption band in Hg1-xCdxTe-based heterostructures is shifted to longer wavelengths, these compounds with (x<0.21) seem to be very promising as interband solid-state THz lasers.

Neste trabalho foram estudadas as fases topológicas não triviais presentes em sistemas formados pela deposição de átomos de grafeno. Encontramos que quando um átomo hibridiza fortemente com o grafeno, apresenta um momento magnético e um forte spin-órbirta é possível a formação de uma rede hexagonal de baricentros que efetivamente gera uma estrutura de bandas característica de um efeito hall quântico anômalo. Especificamente, determinamos que o Ru satisfaz estas características. Quando este metal é depositado em uma configuração triangular no grafeno ocorrem picos na densidade de estados localizados no centro geométrico (baricentro) dos triângulos formados pelos Ru. Estes picos estão distribuídos de forma hexagonal e efetivamente geram uma estrutura de bandas que nas proximidades do nível de Fermi apresenta uma configuração de spin característica do efeito Hall quântico anômalo. Adicionalmente, encontramos que o sistema composto pela absorção de Ba ou Sr no grafeno favorece a formação do efeito Hall quântico de spin. Neste sistema, o acoplamento spin-órbita (SOC) gera um gap mais de 1000 vezes maior ao período no grafeno prístino. Para o estudo destes sistemas, implementamos no código SIESTA a aproximação on-site do acoplamento spin-órbita via o formalismo dos pseudopotenciais relativísticos de norma conservada. Nossa implementação foi testada a partir do estudo de fenômenos já conhecidos: i) o strong spin-splitting gerado no grafeno pela adsorção de Au, ii) o efeito hall quântico de spin no poço quântico de HgTe/CdTe e, iii) a formação de estados topológicos na superfície do Bi2Se3 e as fases magnéticas deste material com átomos de Mn adsorvidos. / In this work, were studied the non-trivial topological phases present in systems formed by deposition of atoms in graphene. We found that when an atom hybridizes strongly with grapheme, has a magnetic moment and a strong spin-orbit it is possible the formation of a hexagonal network of barycentres that effectively generates a structure band characteristic of a quantum anomalous Hall effect. Specifically, we determined that Ru satisfies these characteristics. When this metal is deposited in a triangular configuration in grapheme, peaks occur in the density of localized states in the geometric center (centroid) of the triangles formed by Ru. These peaks are distributed in a hexagonal structure and effectively generates a band structure that near the Fermi level has a spin configuration characteristic of the spin quantum Hall effect anomalous. Additionally, we found that the system composed by the adsorption of Ba or Sr in grapheme, promotes the formation of spin quantum Hall effect. In this system, the spin-orbit coupling (SOC) generates a gap more than 1000 times grater that predicted in pristine praphene. To study these systems, wu implemented in the code SIESTA the on-site approach of the spin-orbit coupling throught the formalism of norm conserved relativistic pseudo potentials. Our implementation was tested from the study of phenomena already known: i) the strong spin-splitting generated in graphene by adsorption of Au, ii) the quantum spin Hall effect in quantum well of HgTe / CdTe and, iii) formation of topological states in the surface of Bi2Se3 and the magnetic of this material with Mn atoms adsorved.