In this thesis, we investigate the emergence of kinetic processes in finite quantum systems. We first generalize the Redfield theory to describe the dynamics of a small quantum system weakly interacting with an environment of finite heat capacity. We then study in detail the spin-GORM model, a model made of a two-level system interacting with a random matrix environment. By doing this, we verify our new theory and find a critical size of the environment over which kinetic processes occur. We finally study the emergence of a diffusive transport process, on a finite tight-binding subsystem interacting with a fast environment, when the size of subsystem exceeds a critical value.

Electron transport at low temperatures in two-dimensional electron systems is governed by two quantum corrections to the conductivity: weak localisation and electron-electron interaction in the presence of disorder. We present the first experimental observation of these quantum corrections in graphene, a single layer of carbon atoms, over a temperature range 0.02 - 200 K. Due to the peculiar properties of graphene, weak localisation is sensitive not only to inelastic, phase-breaking scattering events, but also to elastic scattering mechanisms. The latter includes scattering within and between the two valleys (intra- and inter-valley scattering, respectively). These specifics make it possible, for example, to observe a transition from weak localisation to antilocalisation. Our work reveals a number of surprising features. First of all the transition occurs not only as the carrier density is varied, but also as the temperature is tuned. The latter has never been observed in any other system studied before. Second, due to weak electron-phonon interaction in graphene, quantum interference of electrons survives at very high temperatures, up to 200 K. For comparison, in other two-dimensional (2D) systems the weak localisation effect is only seen below 50 K. The electron-electron interaction correction is also affected by elastic scattering. In a two-valley system, there are two temperature regimes of the interaction correction that depend on the strength of inter-valley scattering. In both regimes the correction has its own expression. We show that because of the intra-valley scattering, a third regime is possible in graphene, where the expression for the correction takes a new form. The study of weak localisation demonstrates that the third regime is realised in our experiments. We use the new expression to determine the Fermiliquid parameter, which turns out to be smaller than in other 2D systems due to the chirality of charge carriers. At very low temperatures (below 100 mK) we observe a saturation of the electron dephasing length. We study different mechanisms that could be responsible for the saturation and discuss in detail one of them – spin-orbit interaction. We determine the spin coherence length from studies of weak localisation and the temperature dependence of the conductivity and found good agreement between the two types of experiments. We also show the way to tune the spin coherence length by an order of magnitude by controlling the level of disorder. However, experiment shows contradictions with theory both in values of the spin coherence length and the type of spin relaxation. We speculate about another spin-related mechanism, spin flip by vacancies, which to some extent could also explain our observations. We also present electron transport in graphene irradiated by gallium ions. Depending on the dosage of irradiation the behavior of electrons changes. Namely, electron localisation can be tuned from weak to strong. At low dosages we observe the weak localisation regime, where the mentioned quantum corrections to the conductivity dominate at low temperatures. We found the electron scattering between the valleys to be enhanced, attributing it to atomically sharp defects (kicked out carbon atoms) produced by ion irradiation. We also speculate that gallium ions can be embedded in the substrate or trapped between silica and graphene. We draw this conclusion after investigation of the spin-orbit interaction in irradiated samples. At high dosages electrons become strongly localised and their transport occurs via variable-range hopping.

The first and main part of this thesis concerns the quantization of the transverse transport in diverse periodic quantum systems. From a theoretical point of view, the Hall conductivity's quantization may be understood at the single-particle level in terms of topological invariants. In periodic media such as crystals, the single-particle energy spectrum depicts a specific band structure. A modern approach, based on topology and differential geometry, consists in assigning an abstract mathematical object, a fibre bundle, to each energy band. The fibre bundle's topology is measured by a topological invariant, called the Chern number, which only takes integral values. Surprisingly, the transverse conductivity can be expressed as a sum of Chern numbers. In this work, one provides a rigorous derivation of this fact and one presents several methods which allow the numerical and analytical computation of the Chern numbers for diverse systems. The first original study concerns the physics of ultracold atoms trapped in optical lattices. These very popular experimental setups, which are currently designed in several laboratories worldwide, allow for the exploration of fundamental problems encountered in modern physics. In particular atoms trapped in optical lattices reproduce with a very high accuracy the physics of the Hubbard-type models which describe a huge variety of condensed matter phenomena, such as high-Tc superconductivity and the Mott quantum phase transition. Particularly interesting is the possibility to create artificial magnetic fields in optical lattices. Generated by complex laser configurations or by rotation of the trap, these artificial fields allow the simulation of electronic systems subjected to intense magnetic fields. In this thesis, one explores the possibility of a quantum Hall-like effect for neutral particles in such arrangements. In particular one focuses on the exotic situation in which non-Abelian gauge potentials are generated in the system. In these interesting arrangements, the atomic hoppings are assisted by external lasers and are described by non-commutating translation operators. The non-Abelian fields which are generated in these systems are well known in high-energy physics, where they play a key role in modern theories of fundamental interactions. Thereafter, our study of the IQHE in periodic systems concerns quantum graphs. These models which describe the propagation of a quantum wave within an arbitrary complex object are extremely versatile and hence allow the study of various interesting quantum phenomena. Quantum graphs appear in diverse fields such as solid state physics, quantum chemistry, quantum chaology and wave physics. On the other hand, in the context of quantum chaology, graphs have been the vehicle to confirm important conjectures about chaos signatures. In this thesis, one studies the spectral and chaological properties of infinite rectangular quantum graphs in the presence of a magnetic field. One then establishes the quantization of the Hall transverse conductivity for these systems. The second part of the thesis is devoted to the physics of interacting atoms trapped in optical lattices and subjected to artificial gauge potentials. One explores the Mott quantum phase transition in both bosonic and fermionic optical lattices subjected to such fields. The optical lattices are described through the Hubbard model in which the dynamics is ruled by two competing parameters: the interaction strength U and the tunneling amplitude t. The Mott phase is characterized by a commensurate filling of the lattice and is reached by increasing the ration U/t, which can be easily achieved experimentally by varying the depth of the optical potential. In this thesis one studies how this quantum phase transition is modified when the optical lattice is subjected to diverse artificial gauge potentials. Moreover, one shows that vortices are created in bosonic optical lattices in the vicinity of the Mott regime. The vortices are topological defects in the macroscopic wave function that describes the superfluid. One comments on the vortex patterns that are observed for several configurations of the gauge potential. %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%% La physique statistique quantique prédit l’émergence de propriétés remarquables lorsque la matière est soumise à des conditions extrêmes de basses températures. Aujourd’hui ces nouvelles phases de la matière jouent un rôle fondamental pour les technologies actuelles et ainsi méritent d’être étudiées sur le plan théorique. Dans le cadre de ma thèse, j’ai étudié l’effet Hall quantique qui se manifeste dans des systèmes bidimensionnels ultra froids et soumis à des champs magnétiques intenses. Cet effet remarquable se manifeste par la quantification parfaite d’un coefficient de transport appelé conductivité de Hall. Cette grandeur physique évolue alors sur divers plateaux qui correspondent à des valeurs entières d’une constante fondamentale de la nature. D’un point de vue théorique, cette quantification peut être approchée par la théorie des espaces fibrés qui permet d’exprimer la conductivité de Hall en termes d’invariants topologiques. Nous explorons l'effet Hall quantique pour différents systèmes en nous appuyant sur l’interprétation topologique de la quantification de la conductivité de Hall. Nous démontrons ainsi que l’effet Hall quantique se manifeste aussi bien dans les métaux que dans les graphes quantiques et les réseaux optiques. Les graphes quantiques sont des modèles permettant l’étude du transport dans des circuits fins, alors que les réseaux optiques sont des dispositifs actuellement réalisés en laboratoire qui piègent des atomes froids de façon périodique. Considérant différents champs magnétiques externes et variant la géométrie des systèmes, nous montrons que cet effet subit des modifications remarquables. Notamment, l’effet Hall quantique est représenté par des diagrammes des phases impressionnants : les multiples phases correspondant à la valeur entière de la conductivité de Hall se répartissent alors dans des structures fractales. De plus, ces diagrammes des phases se révèlent caractéristiques des différents systèmes étudiés. D’autre part, nous étudions la transition quantique de Mott dans les réseaux optiques. En augmentant l’interaction entre les particules, le système devient isolant et se caractérise par le remplissage homogène du réseau. Nous étudions également l’apparition de tourbillons quantiques lorsque le système est soumis à un champ magnétique au voisinage de la phase isolante.

As devise sizes approach the nanoscale, novel device geometries and materials are considered, and new types of essential physics becomes important and new physical switching mechanism are considered, and as our intuitive understanding of device behavior is stretched accordingly, increasing first-principles simulation is required to understand and predict device behavior. To this end, initially I worked to capture the richness of the confinement and transport physics in quantum-wire devices. I developed an efficient fully three dimensional atomistic quantum transport simulator within a nearest-neighbor atomistic tight-binding framework. However, I soon adapted this work to the study of transport in graphene mono-layer and bilayer nano-ribbons. Motivated by proposals for use of nano-ribbons to create band gaps in otherwise gapless graphene monolayers, I studied the effects of edge disorder in such graphene nano-ribbon FETs. I found that ribbon widths sufficiently narrow to produce useful bandgaps, would also lead to an extreme sensitivity to ribbon-edge roughness and associated performance degradation and device-to-device variability. Going beyond conventional switching but staying with the graphene material system, to model electron-hole condensation in two graphene monolayers separated by a tunnel dielectric potentially beyond room temperature, I developed a self-consistent atomistic tight-binding treatment of the required interlayer exchange interaction within non-local Hartree-Fock mean-field theory. Such condensation, associated many-body enhanced interlayer current flow, and gate-control thereof is the basis for the beyond-CMOS Bilayer-pseudoSpin Field Effect Transistor (BiSFET) proposed by colleagues. I studied the effect of various system parameters and on interlayer charge imbalance on the strength of the condensate state. I also modeled the critical current, the maximum interlayer current that can be supported by the condensate, its detailed dependence on the nature and strength of the required interlayer bare tunneling and on charge imbalance. The results presented here are expected to be used to refine devices models of the BiSFET, and may serve as guides to experiments to observe such a condensate state. / text

We employ a four-band continuum model to study the transport and confinement in an n-p-n junction in bilayer chiral borophene for both the identical- and oppositechirality configurations. The conditions for transport and confinement are elucidated in terms of the pseudospin. We study the transmission and reflection probabilities, conductances, and bound states. We demonstrate the existence of topological states in a domain wall between domains of opposite-chirality bilayer chiral borophene with reversed layer stacking. We find that changing the interlayer bias modifies the conductance of the identical-chirality configuration but not that of the opposite-chirality configuration, and that it induces a layer localization of the bound and topological states. Our findings suggest paths towards utilization of the layer degree of freedom in bilayer chiral borophene in future electronic devices.

In this work, we expand the scope of the present implications of the tight-binding microcanonical picture of electron transport, which is proposed by Di Ventra and co-workers as an alternative to the Landauer’s static scattering approach. We investigate the structure dependence of current flow in electrode-conductor-electrode systems and calculate the local occupation functions and time-dependent conductor current for various conductor lengths and electrode configurations. We also explore fundamental physical limits to the encoding of information in the nanoscale conductor by application of electrode bias in a model system. Using the microcanonical description of a nanoconductor, composed of linear chain of atoms, bridging two electrodes, we obtain upper bounds on the accessible information in the conductor as a function of electrode bias, when the current flow is governed by the conductance quantum.

We discuss the effect of elastic deformations on the electronic properties of atomically thin materials, with a focus on bilayer graphene and MoS2 membranes. In these materials distortions of the lattice translate into fictitious gauge fields in the electronic Dirac Hamiltonian that are explicitly derived here for arbitrary elastic deformations, including in-plane as well as flexural (out-of-plane) distortions. We consider bilayer graphene, where a constant fictitious gauge field causes a dramatic reconstruction of the low energy trigonally warped electronic spectrum inducing topological transitions in the Fermi surface. We then present results of ballistic transport in trigonally warped bilayer graphene with and without strain, with particular focus on noise and the Fano factor. With the inclusion of trigonal warping the Fano factor at the Dirac point is still F = 1/3, but the range of energies which show pseudo diffusive transport increases by orders of magnitude compared to the results stemming out of a parabolic spectrum and the applied strain acts to increase this energy range further. We also consider arbitrary deformations of another two-dimensional membrane, MoS2. Distortions of this lattice also lead to a fictitious gauge field arising within the Dirac Hamiltonian, but with a distinct structure than seen in graphene. We present the full form of the fictitious gauge fields that arise in MoS2. Using the fictitious gauge fields we study the coupling between electronic and mechanical degrees of freedom, in particular the coupling between electrons and excited vibrational modes, or vibrons. To understand whether these effects may have a strong influence on electronic transport in MoS2 we calculate the dimensionless electron-vibron coupling constant for all vibron modes relevant for electronic transport. We find that electron-vibron coupling constant is highly sample specific and that the longitudinal stretching mode is the vibron with the dominant coupling. This however reaches maximum values which are lower than those observed in carbon nanostructures.

Le graphène est un matériau constitué d'une seule couche atomique de carbone et représente un sujet majeur de la physique de la matière condensée. Le graphène possède de nombreuses propriétés remarquables : structure électronique décrite par une equation de Dirac sans masse, forte mobilité électronique, effet Hall quantique anormal, résistance ,rigidité et conductivité thermique élevée. Cette these concerne la structure électronique et le transport dans le graphène. Nous considérons en particulier le cas des bicouches tournées de graphène. Ces systèmes ont été découverts en particulier dans le graphène produit sur le carbure de silicium et présentent des propriétés originales par rapport aux bicouches dans l' empilement AB qui existe par exemple dans le graphite. Nous analysons au moyen d'une théorie perturbative et aussi par des approches numériques la densité d'états dans ces systèmes.Nous montrons que la densité d'états présente des oscillations avec la même période que celle du Moiré produit par ces bicouches. Nous analysons aussi le rôle des défauts sur les propriétés de transport en particulier dans le cas ou les défauts sont répartis uniquement sur une des deux couches. Ici aussi notre approche combine théorie perturbative du couplage interplans et approches purement numérique en liaisons fortes. Nous considérons aussi le role joué par les adatomes comme l'hydrogène par exemple. Nous analysons la modification de la densité d'états induite autour de l'adatome et les variations correspondantes de densité de charge et de potentiel électrostatique. Ces systèmes tendent à produire des états resonants près de l'énergie de Dirac qui dependent beaucoup aussi de la position top ou hollow de l' adsorbat. Pour des orbitales de type “s” la resonance est plus marquée si l'adatome est en position hollow. Nous montrons que l'image par experience STM (microscopie à effet tunnel) depend beaucoup de la distance entre l'adsorbat et la pointe du STM. Dans un régime de champ proche la résonance de l'adsorbat peut même apparaître comme un creux dans le signal dI/dV du STM. / Graphene, a material made of a one-atom-thick carbon layer, is a major topic of modern condensed-matter research. Graphene exhibits exciting properties such as massless Dirac electronic structure, high mobility anomalous quantum Hall effects, strength, stiffness and extraordinary high thermal conductivity. This thesis deals with electronic structure and transport properties of graphene. We consider in particular the case of twisted bilayers of graphene. These systems have been discovered especially in graphene produced on Silicon Carbide and present original properties when compared with standard AB bilayers that occur for example in graphite. We analyze by perturbative theory and by numerical methods the density of states. We show that the electronic density of states presents periodic oscillations with the period of the geometric Moiré produced by these systems. We analyze also the role of defects on transport properties and in particular we consider the case where the defects are on one layer only : the layer exposed to the air. We show how defects on this layer affects the conductivity of the bilayer. Here also we use simple analytical models and numerical approaches. We consider also the role played by atomic impurities like Hydrogen adatom on the graphene plane. We analyze the modification of density of states induced around the adatom and the corresponding modifications of charge density and electrostatic potential. These systems tend to produce a resonant state close to the Dirac energy which depends much on whether the adatom is in a top or hollow position. For hydrogen like orbital (s orbital) the resonance is stronger in the hollow position. We show that the image obtained through STM experiments for these resonant state depends very much on the distance of the STM tip to the adatom. In a near field regime the resonance can even appear as a dip in the STM signal dI/dV.

Grâce aux progrès techniques récents, les sources d'électrons uniques sontpassées de la théorie au laboratoire. Des expériencesconceptuellement nouvelles où l'on sonde directement la dynamique quantiqueinterne des systèmes sont désormais possibles. Dans cette thèse nousdéveloppons les outils analytiques et numériques pour analyser et comprendre cesproblèmes. Les simulations requièrent une résolution spatiale appropriée pourles systèmes, et des temps simulés suffisament longs pour sonder leurs tempscaractéristiques. Jusqu'à présent l'approche théorique standard utilisée pour traiter de tels problèmes numériquement---connue sous les dénominations de formalisme Keldysh ou NEGF (Fonctions de Green Hors Equilibre)---n'a pas été très fructueuse, principalement à cause du coût en temps de calcul prohibitif. Nous proposons une reformulation decette technique sous la forme des fonctions d'onde électroniques du système dansune représentation énergie--temps. Le coût de calcul de notre algorithmenumérique est maintenant linéaire avec le temps simulé et le volume du système,rendant possible la simulation de système contenant $10^5-10^6$ atomes/sites.Nous utilisons cet outil pour proposer de nouveaux effets intrigants ainsi quedes expériences. Nous introduisons la modification dynamique du motifd'interférence d'un système quantique. Nous montrons, par exemple, que la montéed'une tension DC $V$ sur un interféromètre électronique produit un régimetransitoire où le courant oscille comme $cos(eVt/hbar)$. Nous prévoyons unegrande variété d'effets nouveaux lorsque les circuits de nanoélectronique sontsondés très rapidement. Les outils et concepts développés dans cette thèseauront un rôle clé dans l'analyse et les propositions des expériences à venir. / With the recent technical progress, single electron sources have moved fromtheory to the lab. Conceptually new types of experiments where one probesdirectly the internal quantum dynamics of the devices are within grasp. In thisthesis we develop the analytical and numerical tools for handling suchsituations. The simulations require appropriate spatial resolution for thesystems, and simulated times long enough so that one can probe their internalcharacteristic times. So far the standard theoretical approach used to treatsuch problems numerically---known as Keldysh or NEGF (Non Equilibrium Green'sFunctions) formalism---has not been very successful mainly because of aprohibitive computational cost. We propose a reformulation of the NEGFtechnique in terms of the electronic wave functions of the system in anenergy--time representation. The numerical algorithm we obtain scales nowlinearly with the simulated time and the volume of the system, and makessimulation of systems with $10^5-10^6$ atoms/sites feasible. We leverage thistool to propose new intriguing effects and experiments. In particular weintroduce the concept of dynamical modification of interference pattern of aquantum system. For instance, we show that when raising a DC voltage $V$ to anelectronic interferometer, the transient current responseoscillates as $cos(eVt/hbar)$. We expect a wealth of new effects whennanoelectronic circuits are probed fast enough. The tools and conceptsdeveloped in this work shall play a key role in the analysis and proposal ofupcoming experiments.

L'industrie du semiconducteur, dans son effort visant à réduire la taille des nanocomposants, éprouve le besoin de prédire les propriétés physiques des composants futures. Alors que la taille de tels composants se réduit, les modèles semi-classiques en vigueur perdent de leur validité, puisque des effets quantiques, qui sont d'ordinaire invisibles dans des dispositifs en silicium plus grands, prévalent dans des dispositifs plus petits ou à base de matériaux semiconducteurs III-V. Par conséquent, les outils de simulation et de modélisation devraient décrire adéquatement les options technologiques en faveur qui sont aujourd'hui étudiées. Par conséquent, des simulations quantiques sont nécessaires au développement de transistors à effet de champ modernes.Le but de cette thèse de doctorat est de développer les outils appropriés à ces simulations et les utiliser pour étudier certaines des options de conception les plus importantes dans la technologie du transistor.C'est pourquoi nous avons utilisé le formalisme des fonctions de Green hors équilibre pour simuler le transport des porteurs de charge and étudier les transistors à effet de champ.Les structures de bande des semiconducteurs ont été calculées dans le cadre du formalisme k.p, mais nous avons aussi développé une méthode par pseudopotentiel atomique effectif pour effectuer des simulations pleine bande avec une variété d'ingrédients comme une orientation cristalline arbitraire, de la rugosité de surface, une composition d'alliage arbitraire dans le canal du transistor, et ainsi de suite. Cette méthode par pseudopotentiel donne des résultats précis pour un large ensemble de configurations avec un effort de paramétrage inférieur au formalisme k.p.Nous avons utilisé ces outils de simulation pour évaluer les propriétés de transport de FinFETs à base de silicium et d'InAs, en nous concentrant sur l'adaptabilité de la tension d'alimentation de dispositifs à base de III-V comparés à leurs équivalents en silicium. En particulier, nous discutons de la faisabilité de l'obtention d'un fort courant on dans les dispositifs III-V.Ensuite, nous appliquons ce formalisme à des nanofils gate-all-around (GAA) tunnel-FETs (TFETs) à base de III-V. Les tunnel-FETs sont une architecture prometteuse pour les transistors futurs, qui rencontre des problématiques d'optimisation et de performance. Nous avons pour but de faire une évaluation de l'effet de boosters technologiques sur les performances des TFETs, en particulier l'utilisation de contraintes mécaniques, et d'une hétérojonction III-V. Nous avons montré que ces boosters permettent aux TFETs de surpasser en théorie la technologie MOSFET standard, mais que la contraint induit des effets indésirables.Pour concevoir des TFETs à haute performance sans l'utilisation de la contrainte, nous avons enfin introduit un choix de conception qui exploite une gradation de la fraction molaire d'un alliage ternaire, ou alternativement un puits quantique dans la source. Ces configurations augmentent de manière dramatique la densité d'états dans le TFET à la jonction source/canal et sont donc capable d'améliorer les performances électriques des TFETs par rapport aux MOSFET conventionnels. / The semiconductor industry, in its continued effort to scale down nanoscale components further, needs to predict the physical properties of future components. As the size of such devices shrinks down, the currently prevalent semi-classical models start to fall apart, as quantum effects that are usually invisible in larger silicon devices gain in relevance in smaller and/or III-V based semiconductor devices. Therefore, modeling and simulation tools should describe adequately the favorite technological options that are currently under investigation. Consequently, full quantum simulations are necessary to the development of modern field effect transistors.The purpose of this PhD thesis is to develop the tools suitable for those simulations and use them to look into some of the most relevant design options for transistor technology.Hence, we used the Non Equilibrium Green's Functions formalism to simulate charge carriers transport and investigate field effect transistors.The semiconductor band structures were calculated within a continuous kp formalism, but we also developed an atomistic effective pseudopotential method to perform full-band simulations with a variety of ingredients like arbitrary crystal orientation, surface roughness, arbitrary alloy composition in the transistor channel, and so on. This pseudopotential method provides accurate results for a wider array of configurations with a smaller parametrization effort than the k.p formalism.We used these simulation tools to evaluate the transport properties of silicon and InAs based FinFETs, focusing on the supply-voltage scalability of III-V based devices compared to silicon counterparts. In particular, the feasibility of obtaining large on-current values in III-V devices is discussed.Then, we applied that formalism to III-V based gate all-around (GAA) nanowire tunnel-FETs (TFETs). Tunnel-FETs are a promising architecture for future transistors, facing optimization and performance challenges. We aimed at benchmarking the effect of technological boosters on the performances of TFETs, namely the use of strain engineering and of III-V heterojunctions. We've shown that these boosters allow TFETs to theoretically outperform standard MOSFET technology, but that strain engineering induces undesirable drawbacks.In order to design high performance TFETs without the use of strain, we finally introduced novel design options by exploiting a molar fraction grading of a ternary alloy or alternatively a quantum well in the source region. These device configurations dramatically change the density of state of the TFET at the source/channel junction and are therefore able to improve the electrical performance of TFETs with respect to conventional MOSFETs.