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.

Tato práce se zabývá charakterizací topologického izolátoru Bi2Te3, materiálu s nevodivými stavy v objemu, ale jedním vodivým pásem na povrchu. Tento materiál je zkoumán již přes 60 let, ale i přes to není jeho objemová pásová struktura úplně objasněna, obzvláště charakter zakázaného pásu je stále předmětem diskuze. V této práci jsou prezentovány výsledky infračervené spektroskopie na Landauových hladinách v magnetickém poli až do 34 T, doplněné elipsometrickým měřením mimo magnetické pole. Výsledky těchto měření by měli pomoci vyjasnit některé vlastnosti zakázaného pásu. Pozorovaná optická odezva odpovídá polovodiči s přímým zakázaným pásem, ve kterém se nosiče náboje chovají jako Diracovské hmotné fermiony. Šířka zakázaného pásu za nízkých teplot byla určena jako Eg = (175±5) meV a samotný zakázaný pás se nachází mimo trigonální osu, tím pádem se v první Brillouinově zoně vyskytuje 6 krát nebo 12 krát.

Grâce à leur propriétés uniques, les nanofils d'InAs et de Bi1-xSbx sont important pour les domaines de la nanoélectronique et de l'informatique quantique. Alors que la mobilité électronique de l'InAs est intéressante pour les nanoélectroniques; l'aspect isolant topologique du Bi1-xSbx peut être utilisé pour la réalisation de Qubits basés sur les fermions de Majorana. Dans les deux cas, l'amélioration de la qualité du matériau est obligatoire et ceci est l'objectif principal cette thèse ou` nous étudions l'intégration des nanofils InAs sur silicium (compatibles CMOS) et où nous développons un nouvel isolant topologique nanométrique: le Bi1-xSbx. Pour une compatibilité CMOS complète, la croissance d'InAs sur Silicium nécessite d'être auto- catalysée, entièrement verticale et uniforme sans dépasser la limite thermique de 450 ° C. Ces normes CMOS, combineés à la différence de paramètre de maille entre l'InAs et le silicium, ont empêché l'intégration de nanofils InAs pour les dispositifs nanoélectroniques. Dans cette thèse, deux nouvelles préparations de surface du Si ont été étudiées impliquant des traitements Hydrogène in situ et conduisant à la croissance verticale et auto-catalysée de nanofils InAs compatible avec les limitations CMOS. Les différents mécanismes de croissance résultant de ces préparations de surface sont discutés en détail et un passage du mécanisme Vapor-Solid (VS) au mécanisme Vapor- Liquid-Solid (VLS) est rapporté. Les rapports d'aspect très élevé des nanofils d'InAs sont obtenus en condition VLS: jusqu'à 50 nm de diamètre et 3 microns de longueur. D'autre part, le Bi1-xSbx est le premier isolant topologique 3D confirmé expérimentalement. Dans ces nouveaux matériaux, la présence d'états surfacique conducteurs, entourant le coeur isolant, peut héberger les fermions de Majorana utilisés comme Qubits. Cependant, la composition du Bi1-xSbx doit être comprise entre 0,08 et 0,24 pour que le matériau se comporte comme un isolant topologique. Nous rapportons pour la première fois la croissance de nanofils Bi1-xSbx sans défaut et à composition contrôlée sur Si. Différentes morphologies sont obtenues, y compris des nanofils, des nanorubans et des nanoflakes. Leur diamètre peut être de 20 nm pour plus de 10 microns de long, ce qui en fait des candidats idéaux pour des dispositifs quantiques. Le rôle clé du flux Bi, du flux de Sb et de la température de croissance sur la densité, la composition et la géométrie des structures à l'échelle nanométrique est étudié et discuté en détail. / InAs and Bi1-xSbx nanowires with their distinct material properites hold promises for nanoelec- tronics and quantum computing. While the high electron mobility of InAs is interesting for na- noelectronics applications, the 3D topological insulator behaviour of Bi1-xSbx can be used for the realization of Majorana Fermions based qubit devices. In both the cases improving the quality of the nanoscale material is mandatory and is the primary goal of the thesis, where we study CMOS compatible InAs nanowire integration on Silicon and where we develop a new nanoscale topological insulator. For a full CMOS compatiblity, the growth of InAs on Silicon requires to be self-catalyzed, fully vertical and uniform without crossing the thermal budge of 450 °C. These CMOS standards, combined with the high lattice mismatch of InAs with Silicon, prevented the integration of InAs nanowires for nanoelectronics devices. In this thesis, two new surface preparations of the Silicon were studied involving in-situ Hydrogen gas and in-situ Hydrogen plasma treatments and leading to the growth of fully vertical and self-catalyzed InAs nanowires compatible with the CMOS limitations. The different growth mechanisms resulting from these surface preparations are discussed in detail and a switch from Vapor-Solid (VS) to Vapor- Liquid-Solid (VLS) mechanism is reported. Very high aspect ratio InAs nanowires are obtained in VLS condition: upto 50 nm in diameter and 3 microns in length. On the other hand, Bi1-xSbx is the first experimentally confirmed 3D topololgical insulator. In this new material, the presence of robust 2D conducting states, surrounding the 3D insulating bulk can be engineered to host Majorana fermions used as Qubits. However, the compostion of Bi1-xSbx should be in the range of 0.08 to 0.24 for the material to behave as a topological insula- tor. We report growth of defect free and composition controlled Bi1-xSbx nanowires on Si for the first time. Different nanoscale morphologies are obtained including nanowires, nanoribbons and nanoflakes. Their diameter can be 20 nm thick for more than 10 microns in length, making them ideal candidates for quantum devices. The key role of the Bi flux, the Sb flux and the growth tem- perature on the density, the composition and the geometry of nanoscale structures is investigated and discussed in detail.

The layered honeycomb lattice iridate Na2IrO3 is a novel candidate material for either a topological insulator or spin liquid. These states of matter are one possible starting point for the future realization of scalable quantum computation, but may also find application in magnetic memory or low-power electronic devices. This thesis reports on the pulsed laser deposition of high-quality heteroepitaxial (001)-oriented Na2IrO3 thin films with well-defined in-plane epitaxial relationship on 5-by-5 and 10-by-10 square millimeter single-crystalline sapphire, YAlO3 and zinc oxide substrates. Three-dimensional Mott variable range hopping is the dominant conduction mechanism between 40 and 300 K. Moreover, a signature of the proposed topological insulator phase is found in magnetoresistance by observation of the weak antilocalization effect that is associated with topological surafce states. Compared to single crystals, a smaller, 200-meV optical gap in Na2IrO3 thin films is found by Fourier-transform infrared transmission spectroscopy.

Dirac fermions provide a prototypical description of topological insulators and their gapless boundary states, which are predicted by the bulk-boundary correspondence. Motivated by the unusual physical properties of these states, we study them in two different Hermitian quantum systems. In non-Hermitian systems, we investigate the failure of the bulk-boundary correspondence and show that non-Hermitian topological invariants impact a system’s bulk response. First, we study electronic topological insulators in three dimensions with time-reversal symmetry. These can be characterized by a quantized magnetoelectric coefficient in the bulk, which, however, does not yield an experimentally observable response. We show that the signature response of a time-reversal-invariant topological insulator is a nonlinear magnetoelectric effect, which in the presence of a small electric field leads to the appearance of half-integer charges bound to a magnetic flux quantum. Next, we consider topological superconducting nanowires. These feature Majorana zero modes at their ends, which combine nonlocally into a single electronic state. An electron tunneling through such a state will be transmitted phase-coherently from one end of the wire to the other. We compute the transmission phase for nanowires with broken time-reversal symmetry and confirm that it is independent of the wire length. Turning to non-Hermitian systems, we consider planar optical microcavities with an anisotropic cavity material, which may feature topological degeneracies known as excep- tional points in their complex frequency spectrum. We present a quantitative method to extract an effective non-Hermitian Hamiltonian for the eigenmodes, and describe how a pair of exceptional points arises from a Dirac point due to the cavity loss. Finally, we investigate generalized topological invariants that can be defined for non- Hermitian systems, but which have no counterpart (i.e. vanish) in Hermitian systems, for example the so-called non-Hermitian winding number in one dimension. Contrary to Hermitian systems, the bulk-boundary correspondence breaks down: Comparing Green functions for periodic and open boundary conditions, we find that in general there is no correspondence between topological invariants computed for periodic boundary con- ditions, and boundary eigenstates observed for open boundary conditions. Instead, we prove that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function, which we define as the response of a gapped system to an external perturbation on timescales where the induced excitations have not propagated to the boundary yet. Since periodic systems cannot accommodate such spatial growth, they differ from open ones.

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<p dir="ltr">Since the discovery of graphene in 2004, numerous other materials with intriguing electronic, optical, and magnetic properties have been found to be layered and exfoliatable down to atomic thickness. Owing to their weak interlayer coupling, mediated only by van der Waals forces, this new class of 2-dimensional materials, also known as van der Waals (vdW) materials, allows layer-by-layer stacking, overcoming some of the limitations of growth techniques. In particular, the growing inventory of vdW materials has expanded to include magnetic materials, further broadening the possibilities of novel devices based on stacked heterostructures. These magnetic heterostructures can find applications in spintronics and memory devices and may be combined with other vdW materials with optical properties for applications in optoelectronics. In this thesis, we assembled heterostructures via mechanical transfer or growth to modify the magnetism in these vdW materials. We used various optical and electrical techniques to probe the modified magnetism or its effects on the novel heterostructure. Thus, we observed the emergence of the magnetic proximity effect on the topological insulator BiSbTeSe₂ after dry transferring a thin flake of Cr₂Ge₂Te₆ on top, taking steps towards the observation of novel topological phases, such as the quantum Hall insulator. Additionally, we demonstrated an increased Curie temperature and magnetic anisotropy, effectively enhancing the magnetism, in thin flakes of Cr₂Ge₂Te₆ and Cr₂Si₂Te₆ after sputtering NiO or MgO. Finally, noting that the effect of modified magnetism in Cr2Ge2Te6 after sputtering NiO or MgO is induced due to wrinkle formation and strain, we further reproduce similar wrinkle formation on other 2D materials such as hBN, graphite, and 2D antiferromagnets (XPS₃, (X= Mn, Fe, Ni), CrSBr, RuCl₃). We used polarized Raman spectroscopy to characterize the induced biaxial strain in hBN and showed that such wrinkle formation can lead to moderately (up to 1.4% strain) spatially inhomogeneous and anisotropic strain profiles. These efforts demonstrate the versatility of tailoring the properties of these vdW materials.</p>

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<p>In this overview I describe the simplest models for the quantum Hall and quantum spin Hall effects, and give some general indications as to the description of topological insulators. As a background to the theoretical models I will first trace the development leading up to the description of topological insulators . Then I will present Laughlin's original model for the quantum Hall effect and briefly discuss its limitations. After that I will describe the Kane and Mele model for the quantum spin Hall effect in graphene and discuss its relation to a general quantum spin Hall system. I will conclude by giving a conceptual description of topological insulators and mention some potential applications of such states.</p>

In this overview I describe the simplest models for the quantum Hall and quantum spin Hall effects, and give some general indications as to the description of topological insulators. As a background to the theoretical models I will first trace the development leading up to the description of topological insulators . Then I will present Laughlin's original model for the quantum Hall effect and briefly discuss its limitations. After that I will describe the Kane and Mele model for the quantum spin Hall effect in graphene and discuss its relation to a general quantum spin Hall system. I will conclude by giving a conceptual description of topological insulators and mention some potential applications of such states.