Monolayers and heterostructures of two-dimensional (2D) electronic materials with spin-orbit interactions offer the promise of observing many novel physical effects. While theoretical predictions of 2D layered materials based on density functional theory (DFT) are many, the DFT approach is limited to small simulation sizes (several nanometers), and thus inhomogeneous strain and boundary effects that are often observed experimentally cannot be simulated within a reasonable time. The aim of this thesis is (i) to study effects of strain on 2D materials beyond graphene using first-principles and tight-binding methods and (ii) to investigate the effects of cuts--"kirigami"-- on 2D materials using molecular dynamics and machine learning approach. The first half of this thesis focuses on the effects of strain on manipulating spin and valley degrees of freedom for two classes of 2D materials--monochalcogenide and lead chalcogenide monolayers--using DFT. A tight-binding (TB) approach is developed to describe the electronic changes in lead chalcogenide monolayers due to strains that often persist in real devices. The strain-dependent TB model allows one to establish a relationship between the Rashba field and the out-of-plane strain or electric polarization from a microscopic view, a connection that is not well understood in the ferroelectric Rashba materials. This framework connecting strain fields and electronic changes is important to overcome the size and computational limitations associated with DFT. The second part of the thesis focuses on defect engineering and design of 2D materials via the "kirigami" technique of introducing different patterns of cuts. A machine learning (ML) approach is presented to provide physical insights and an effective model to describe the physical system. We demonstrate that a machine learning model based on a convolutional neural network is able to find the optimal design from a training data set that is much smaller than the design space.

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abstract: This dissertation aims to study and understand relevant issues related to the electronic, spin and valley transport in two-dimensional Dirac systems for different given physical settings. In summary, four key findings are achieved. First, studying persistent currents in confined chaotic Dirac fermion systems with a ring geometry and an applied Aharonov-Bohm flux, unusual whispering-gallery modes with edge-dependent currents and spin polarization are identified. They can survive for highly asymmetric rings that host fully developed classical chaos. By sustaining robust persistent currents, these modes can be utilized to form a robust relativistic quantum two-level system. Second, the quantized topological edge states in confined massive Dirac fermion systems exhibiting a remarkable reverse Stark effect in response to an applied electric field, and an electrically or optically controllable spin switching behavior are uncovered. Third, novel wave scattering and transport in Dirac-like pseudospin-1 systems are reported. (a), for small scatterer size, a surprising revival resonant scattering with a peculiar boundary trapping by forming unusual vortices is uncovered. Intriguingly, it can persist in arbitrarily weak scatterer strength regime, which underlies a superscattering behavior beyond the conventional scenario. (b), for larger size, a perfect caustic phenomenon arises as a manifestation of the super-Klein tunneling effect. (c), in the far-field, an unexpected isotropic transport emerges at low energies. Fourth, a geometric valley Hall effect (gVHE) originated from fractional singular Berry flux is revealed. It is shown that gVHE possesses a nonlinear dependence on the Berry flux with asymmetrical resonance features and can be considerably enhanced by electrically controllable resonant valley skew scattering. With the gVHE, efficient valley filtering can arise and these phenomena are robust against thermal fluctuations and disorder averaging. / Dissertation/Thesis / Doctoral Dissertation Electrical Engineering 2017

La possibilité de créer des monocouches de dichalcogenures à métaux de transition (MoS2, WSe2,MoSe2 pour ceux étudiés dans ce manuscrit) a été démontrée récemment (2005) et a ouvert la voie à l’étude de ces matériaux sous leur forme 2D. Il apparaît depuis que les propriétés de ces semi-conducteurs sous leur forme monocouche offrent des perspectives intéressantes à la fois du point de vue de la physique fondamentale et des potentielles applications qui peuvent en découler ; en plus de bénéficier d’un fort couplage avec la lumière, l’existence d’un gap important (situé dans le visible, 1.7-1.8 eV) permet entre autres de réaliser des transistors d’épaisseur mono-atomique. Par ailleurs, la physique de ces matériaux est prometteuse pour les applications dans le domaine de l’optoélectronique. En effet, lorsque le matériau est affiné jusqu’à la monocouche atomique, son gap optique devient direct et la brisure de symétrie d’inversion associée au fort couplage spin-orbite provoque l’apparition de règles de sélection optique originales qui relient directement la polarisation de la lumière émise ou absorbée à une des deux vallées non-équivalentes de l’espace réciproque. Cela ouvre la possibilité d’explorer une nouvelle physique, basée sur l’indice de vallée et intitulée en conséquence vallée-tronique, avec comme perspectives futures la manipulation de l’indice de vallée et l’exploitation d’effetsliés à cette relation originale entre propriétés optiques et électroniques (effet vallée-Hall par exemple). Cemanuscrit de thèse regroupe une série d’expériences réalisées dans le but de comprendre et caractériser les propriétés optoélectroniques de ces matériaux. Un premier chapitre introductif présente le contexte scientifique de ces travaux de recherche et démontre l’origine des propriétés électroniques et optiques de ces matériaux via un modèle théorique simple. Le second chapitre présente en détails les échantillons étudiés ainsi que le dispositif expérimental utilisé lors des mesures. Enfin les chapitres 3 à 6 détaillent les expériences menées et les résultats obtenus ; le lecteur y trouvera des mesures de photoluminescence apportant la démonstration expérimentale des règles de sélection optique, l’identification des différents raies spectrales d’émission pour les différentstypes d’échantillons mentionnés plus haut ainsi que des mesures de photoluminescence résolues en temps permettant d’extraire la dynamique des propriétés des porteurs photo-générés. Une part importante de ce manuscrit est consacrée à l’étude expérimentale des propriétés excitoniques de ces matériaux dont la structure de bande électronique est finalement sondée via des études de magnéto-spectroscopie. / The possibility of isolating transition metal dichalcogenide monolayers by simple experimental means has been demonstrated in 2005, by the same technique used for graphene. This has sparked extremely diverse and active research by material scientists, physicists and chemists on these perfectly two-dimensional (2D) materials. Their physical properties inmonolayer formare appealing both fromthe point of view of fundamental science and for potential applications. Transition metal dichalcogenidemonolayers such asMoS2 have a direct optical bandgap in the visible and show strong absorption of the order of 10% per monolayer. For transistors based on single atomic layers, the presence of a gap allows to obtain high on/off ratios.In addition to potential applications in electronics and opto-electronics these 2D materials allow manipulating a new degree of freedom of electrons, in addition to the spin and the charge : Inversion symmetry breaking in addition to the strong spin-orbit coupling result in very original optical selection rules. The direct bandgap is situated at two non-equivalent valleys in k-space, K+ and K−. Using a specific laser polarization, carriers can be initialized either in the K+ or K− valley, allowing manipulating the valley index of the electronic states. This opens up an emerging research field termed "valleytronics". The present manuscript contains a set of experiments allowing understanding and characterizing the optoelectronic properties of these new materials. The first chapter is dedicated to the presentation of the scientific context. The original optical and electronic properties of monolayer transition metal dichalcogenides are demonstrated using a simple theoreticalmodel. The second chapter presents details of the samples and the experimental setup. Chapters 3 to 6 present details of the experiments carried out and the results obtained. We verify experimentally the optical selection rules. We identify the different emission peaks in the monolayer materials MoS2, WSe2 and MoSe2. In time resolved photoluminescence measurements we study the dynamics of photo-generated carriersand their polarization. An important part of this study is dedicated to experimental investigations of the properties of excitons, Coulomb bound electron-hole pairs. In the final experimental chapter, magneto-Photoluminescence allows us to probe the electronic band structure and to lift the valley degeneracy.

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