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.

Apresentamos neste trabalho algumas propriedades do transporte de cargas de heteroestruturas contendo pontos-quânticos. Três tópicos foram explorados: no primeiro, observamos um comportamento anômalo nos platôs do efeito Hall quântico, que atribuímos à existência de estados de borda contra-rotativos; no segundo, determinamos o tempo de decoerência do sistema bidimensional de elétrons em função do estágio evolutivo de pontos-quânticos de InAs autoformados nas suas proximidades. Concluímos que a tensão mecânica acumulada durante o crescimento epitaxial \"congela\" os elétrons, reduzindo a taxa de decoerência; finalmente, testamos algumas das possíveis configurações de heteroestruturas visando a construção de fotodetectores baseados em pontos-quânticos. Observamos que a repetição da região-ativa pode ser utilizada como um parâmetro no controle das mobilidades quânticas e, por conseguinte, das propriedades de operação desses detectores. / In this work we present transport properties of heterostructures with quantum-dots. Three subjects were exploited: on the first one, we observed anomalous quantum Hall plateaus, for wich we attributed to the existence of counter-rotating edge-states; on the second subject, we determined the decoherence time of the bidimensional electron system as a function of the evolutionary stage of nearby self-assembled quantum-dots. We concluded the mechanical stress accumulated during the epitaxial growth \"freezes\" the electrons, reducing the decoherence rate; finally, we tested some base-heterostructures of infrared photodetectors. We observed the stacking of active-regions can be used as a parameter to control quantum-mobilities and, as a consequence, the operation properties of such detectors.

Cette thèse est dédiée à l'analyse de signaux électriques quantiques dans les canaux de bords de l'effet Hall quantique. En particulier, j'ai utilisé l'analogue électronique de l'interféromètre de Hong, Ou et Mandel pour réaliser des expériences d'interférométrie à deux particules. En entrée de l'interféromètre sont placées des sources d'électrons uniques qui permettent l'injection contrôlée d'excitation ne contenant qu'une seule particule. Les canaux de bords guident ces excitations jusqu'à l'interféromètre. Il s'agit d'un contact ponctuel quantique qui agit comme une lame semi-réfléchissante pour les électrons. On mesure en sortie les fluctuations basse fréquence du courant. Cela nous permet de mesurer le recouvrement entre les fonctions d'onde à un électron émises à chaque entrée. Grâce à cette mesure de recouvrement, j'ai pu caractériser à des échelles de temps sub-nanoseconde, le rôle des interactions Coulombienne sur la propagation de l'électron unique. J'ai pu montrer que ces interactions étaient la source principale de la décohérence du paquet d'onde mono-électronique et qu'elles décomposent l'électron sur des modes collectifs. C'est une manifestation de la fractionalisation de l'électron qui apparaît dans les systèmes uni-dimensionnel en interactions. Grâce à cet interféromètre, j'ai pu aussi implémenter un protocole de tomographie qui permet de reconstruire toute les informations à une particule de n'importe quel signal émis dans le canal de bord. / This thesis is dedicated to processing of quantum electronic signals in the edge channels of the integer quantum Hall effect. In particular, I used the electronic analogue of the Hong, Ou and Mandel interferometer to realize two particle interference measurements. The interferometer consists of a quantum point contact (QPC) that acts as an electronic beam-splitter. The inputs are fed by single electron sources whose single particle excitations are guided toward the QPC by quantum Hall edge channels. We measure low frequency current noise in one of the output to measure overlaps of first order coherence functions. With this interferometer I could characterize on short time scales the role of Coulomb interactions on single electron propagation. I could show that interactions are the main source of decoherence of the single particle wave packet and that the electron decomposes into collective modes. This is due to fractionalisation which is a hallmark of interacting unidimensional systems. Thanks to this interferometer I could also implement a universal tomography protocol to dissect all single particle information of any arbitrary current. This enables the study of non-classical propagating state.

Magneto-transport study on high mobility electron systems in both 2D- and 3D- case has attracted intense attention in past decades. This thesis focuses on the magnetoresistance behavior in 3D topological insulator Bi2Te3 and GaAs/AlGaAs 2D electron system at low magnetic field range 0.4T the first drop at T~3.4K to tndium superconductor and considered the second drop at lower temperature as the proximity effect that occurred near the interface between these two materials. On the other hand, GaAs/AlGaAs heterostructure, as a III-V semiconductor family, has been extensively studied for exploring many interesting phenomena due to the extremely high electron mobility up to 10^7 cm^2/Vs. In this thesis, two interesting phenomena are present and discussed in a GaAs/AlGaAs system, which are the electron heating induced tunable giant magnetoresistance study and phase inversion in Shubnikov-de Haas oscillation study, respectively. By applying elevated supplementary dc current bias, we found a tunable giant magnetoresistance phenomenon which is progressively changed from positive to giant negative magnetoresistance. The observed giant magnetoresistance is successfully simulated with a two-term Drude model at all different dc biases, I_{dc}, and temperature, T. In addition, as increasing the dc current bias, a phase inversion behavior was observed in Shubnikov-de Haas oscillation, which was further demonstrated by the simulation with an exponential damped cosine function. This thesis also presents an ongoing project, which is the observation and fabrication of 2D layered materials. The studied 2D layered materials includes graphene, biron nitride, Molybdenum disulfide, etc. At the end, a future work about fabrication of the 2D layered materials devices as well as the suggestion about the measurement are discussed.

Strong quantum correlations between many particles in low dimensions lead to emergence of interesting phases of matter. These phases are often studied through the properties of the many-body eigenstates of an interacting quantum many-body system. The folklore example of topological order in the ground states is the fractional quantum Hall (FQH) effect. With the current developments in the field of ultracold atoms in optical lattices, realizing FQH physics on a lattice and being able to create and braid anyons is much awaited from the view point of fault tolerant quantum computing. This thesis contributes to the field of FQH effect and anyons in a lattice setting. Conformal field theory has been useful to build interesting lattice FQH models which are few-body and non-local. We provide a general scheme of truncation to arrive at tractable local models whose ground states have the desired topological properties. FQH models are known to host anyons, but, it is a hard task when it comes to braiding them on small sized lattices with edges. To get around this problem, we demonstrate that one can squeeze the anyons and braid them successfully within a smaller area by crawling them like snakes on modest sized open lattices. As a numerically cheap approach to detect topological quantum phase transitions, we again resort to anyons that are only well defined in a topological phase. We create defects and study a simple quantity such as the charge of the defect to test whether the phase supports anyons or not. On the other hand, with the advent of many-body localization (MBL) and quantum many-body scars, interesting eigenstate phases which were otherwise only known to occur in ground states have been identified even at finite energy densities in the many-body spectra of generic systems. This thesis also contributes to the field of non-equilibrium physics by portraying models that display interesting non-ergodic phases and also quantum many-body scars. For instance, we show that an emergent symmetry in a disordered model can be used as a tool to escape MBL in a single eigenstate while not preventing the rest of the states from localizing. This can lead to an interesting situation of weakly broken MBL phase where a non-MBL state lives in the spectrum of MBL like states. We also demonstrate the emergence of a non-ergodic, but also a non-mbl phase in a non-local model with SU(2) symmetry. We provide two constructions of rather different models with quantum many-body scars with chiral and non-chiral topological order.

<div>Over the last decade, Dirac matter has become one of the most prominent fields of research in contemporary material science due to the incredibly rich physics of the Dirac equation. Notable examples are the Dirac cones in graphene, Weyl points in TaAs, and gapless edge states in Bi₂Te₃. These unique phases of matter are intimately related to the topological structure of Dirac fermions. However, it remains an open question if the topological structure of Maxwell's equations predicts yet new phases of matter. This thesis will conclusively answer this question.</div><div><br></div><div>Topological electrodynamics is concerned with the geometry of electromagnetic waves in condensed matter. At the microscopic level, photons couple to the dipole-carrying excitations of a material, such as plasmons and excitons, which hybridize to form new normal modes of the system. The interaction between these bosonic oscillators is the origin of temporal and spatial dispersion in optical response functions like the conductivity tensor. Our main achievement is motivating a global interpretation of these response functions, over all frequencies and wavevectors. This theory led us to the conclusion that there are topological invariants associated with the conductivity tensor itself. In this thesis, we show exactly how to calculate these electromagnetic invariants, in both continuum and lattice theories, to identify unique Maxwellian phases of matter. Magnetohydrodynamic electron fluids in strongly-correlated 2D materials like graphene are the first candidates of this new class of topological phase. The fundamental physical mechanism that gives rise to a topological electromagnetic classification is Hall viscosity which adds a nonlocal component to the Hall conductivity. To study the topological electrodynamics, we propose viscous Maxwell-Chern-Simons theory -- a Lagrangian framework that naturally generates the equations of motion, nonlocal Hall response and the boundary conditions. We demonstrate that nonlocal Hall conductivity is the spin-1 photonic equivalent of dispersive mass and induces precession of bulk photonic skyrmions. Nontrivial photonic skyrmions are associated with Dirac monopoles in the bulk momentum space and a singular Berry gauge. A singular gauge occurs when the photonic mass changes sign. Remarkably, the boundary of this medium supports gapless chiral edge states that are spin-1 helically-quantized and satisfy open boundary conditions.</div>

<p dir="ltr"><b>Tellurium (Te) stands out as an elemental narrow-bandgap semiconductor characterized by its distinctive chiral crystal structure. The interplay between fundamental symmetries and the topological properties of electrons has garnered significant attention in the scientific community. With its unique chiral crystal structure featuring three Tellurium atoms spiraling within a single unit cell, Tellurium offers a singular material system. This system provides an exceptional opportunity to explore the novel quantum and topological transport properties of electrons. Hydrothermally grown two-dimensional (2D) Te with a thickness of several nanometers gives us an opportunity to precisely control the carrier density and the carrier type in Te using gate voltage. In this dissertation, the spin-orbit coupling (SOC) of Te is quantitatively analyzed using the weak anti-localization effect. The strong SOC also gives rise to the Weyl point at the band edge of the conduction band. The topological nontrivial band structure of Te is characterized by a π phase shift in the Shubnikov-de Haas (SdH) oscillations. Due to the high mobility, the quantum Hall effect is measured with low spin and valley Landau levels controlled by an electric and magnetic field. Bilayer charge transferable quantum Hall states of Weyl fermions is observed in a wide Te quantum well. The topological phase transition from a semiconductor to Weyl semimetal under high pressure is studied up to 2.47 GPa. The chirality of 2D Te is separated by the hot sulfuric acid etching technique. The spin configuration and topological charge of the Weyl node exhibit a reversal in different chiralities, leading to an inverse in nonlinear responses, encompassing both electrical (nonreciprocal transport in the longitudinal direction and nonlinear planar Hall effect in the transvers direction) and optical phenomena (circular photogalvanic effect and circular photovoltaic effect). Our results unveil the topological nature of the Tellurium (Te) band structures, offering a promising avenue for controlling charge and spin transport within the chiral degree of freedom.</b></p>

Cette thèse décrit deux expériences mettant en lumière l'existence d'un degré de liberté fermionique dans l'effet Josephson: le doublet d'Andreev. Elles sont toutes les deux réalisées sur l'élément Josephson le plus élémentaire qui soit, un contact atomique entre deux électrodes supraconductrices. Dans la première, nous avons observé la disparition du supercourant, qui traduit le piégeage spontané d'une quasiparticule dans l'un des deux états liés d'Andreev. Dans la seconde, nous avons réalisé la spectroscopie photonique de ce système à deux niveaux, en utilisant une jonction Josephson à la fois en tant qu'émetteur et détecteur microonde. On peut bien rendre compte des spectres observés avec un modèle spin-boson incluant le doublet d'Andreev et un mode électromagnétique de l'environnement.

Un conducteur est bien caractérisé par sa conductance donnée par la formule de Landauer. Toutefois, le bruit contient davantage d'informations. Il mesure les fluctuations temporelles du courant autour de sa valeur moyenne. De plus, le signe des corrélations croisées est lié à la statistique des porteurs de charge. Cette thèse aborde deux principaux thèmes à savoir le transport dans les liquides de Luttinger et dans les structures hybrides. Dans la première partie, nous commençons par donner une vision détaillée des liquides de Luttinger et des systèmes qu'ils modélisent. Nous parlons également du formalisme de Keldysh permettant de traiter des problèmes hors équilibre. Puis, nous rentrons dans le vif du sujet en étudiant l'effet de la largeur d'un contact ponctuel quantique sur le courant de rétrodiffusion entre les deux états de bords de l'effet Hall quantique. L'augmentation de la largeur du contact ponctuel quantique entraîne une forte diminution du courant de rétrodiffusion. Dans un autre chapitre, nous développons une technique permettant l'utilisation d'un circuit RLC couplé inductivement au circuit mésoscopique pour détecter les corrélations de courant en régime photo-assisté. La mesure de ces corrélations s'effectue à travers la charge aux bornes du condensateur. Dans une deuxième partie, nous consacrons notre étude au transport non-local dans les structures hybrides supraconductrices. L'étude de la réflexion d'Andreev croisée y est détaillée. Finalement, nous étudions une structure en double point quantique reliée à deux électrodes en métal normal et une supraconductrice. Nous mettons en avant la séparation des paires de Cooper en mesurant simultanément les courants de branchement et les corrélations croisées. Nous démontrons que dans le régime antisymétrique, c'est-à-dire lorsque les deux points quantiques ont des niveaux d'énergie opposés par rapport au potentiel chimique du supraconducteur, la réflexion d'Andreev croisée est optimisée. / The conductance is the most natural quantity to characterize a quantum conductor. It is given by the Landauer Formula. However, noise contains more information. It measures the current fluctuations around its average value. Moreover, the sign of the crossed correlations is related to the statistics of carriers. This thesis broaches two main topics which are the transport in the quantum Hall effect and in hybrid circuits.First, we start by introducing the Luttinger liquid and the systems which are modelized by them. Also, we discuss the Keldysh formalism in order to treat nonequilibrium problems. Then, we study the effect of the width of a quantum point contact on the backscattering current between two edge states of the quantum Hall effect. By increasing the width of the quantum point contact, we show that the backscattering current is strongly reduced. In another chapter, we develop a technique to use a RLC circuit inductively coupled to a mesoscopic circuit in order to measure the current correlations in the photo-assisted regime. The measurement of these correlations is performed through the charge on the capacitor plates.Secondly, we present the non-local transport in hybrid structures. The mechanism of Crossed Andreev Reflection is explained. Finally, we study a double quantum dot connected to two normal leads and a superconducting lead. We introduce the separation of the Cooper pair by measuring together the branching currents and the crossed correlations. We demonstrate that in the anti-symmetric regime (the energy level of the two quantum dots have opposite values with respect to the chemical potential of the superconducting lead), crossed Andreev reflection is optimized.

Les propriétés d'un gaz électronique bidimensionnel soumis à champs magnétiques intenses et à bas champs magnétiques sont étudiés par la spectroscopie optique: l'effet Hall quantique fractionnaire (FQHE) par photoluminescence et diffusion inélastique de la lumière, puis un nouvel effet oscillatoire de la résistance induit par micro-ondes (MIROs) par transport et absorption des micro-ondes. Les effets des interactions entre électrons du 2DEG sont à l'origine de FQHE. Jusqu'à maintenant, les expériences d'optiques n'ont pas permis les études des interactions entre électrons sur toute la gamme de fractions. Les fractions 1/3, 2/5, 3/7, 3/5, 2/3 et 1 sont clairement observées dans les spectres non traités et montrent une symétrie autour du facteur de remplissage 1/2. La symétrie des fermions composites ets observée dans les spectres. A bas champ magnétique, sous irradiation micro-onde, les propriétés de transport s'écartent nettement des oscillations bien connues de Shubnikov - de Haas pour évoluer vers une série d'états de résistance zéro. Les résultats des mesures d'absorption des micro-ondes sont présentés pour deux échantillons. L'échantillon de basse mobilité montre seulement une absorption autour de la résonance cyclotron (CR). L' échantillon de haute mobilité montre aussi des signaux d'absorption aux harmoniques de la CR. Les mesures ont permis d'inférer l'existence de deux processus d'absorption différents et séparés. L'absorption non résonante est mieux visible en transport et observée comme MIROs, et l'absorption résonante, mieux observée dans les mesures d'absorption, suit probablement les règles de polarisation de résonance cyclotron.