Topological insulators: theory and electronic transport calculations

In this thesis we investigate quantum transport properties of topological insulator (TI) Bi2 Se3 from atomistic point of view. TI is a material having an energy gap in its bulk but supporting gapless helical states on its boundary. The helical states have Dirac-like linear energy dispersion continuously crossing the bulk band gap with a spin texture in which the electron spin is locked perpendicular to the electron momentum. The peculiar electronic structure of TI material Bi2 Se3 is due to a strong spin-orbit interaction and is protected by the time reversal symmetry. The thesis consists of two main parts. The first reviews the theory of TI and the second presents our atomistic calculations of electron transport in the Bi2 Se3 material. In the theoretical review of the physics of TI, I follow the literature and attempt to present it in a reasonably accessible manner. The theory of TI is explained in terms of well known physical phenomena including classical and quantum Hall effects, spin-orbit coupling, spin current, and spin-Hall effect. The concept of Berry's phase is then introduced to link with the formal conventionalclassification of TI by the topological Z2 invariants. The entire discussion is within the well known Bloch band theory. In the second part of this thesis, numerical studies of transport properties of Bi2 Se3 are presented. After a brief discussion of the relevant quantum transport theory and the tight binding atomistic model, we present our calculated quantum transport results of Bi2 Se3 films having a trench in the middle. Such a large defect, if on normal conductors, would cause significant back scattering of the carriers. Here, by topological protection of the helical states, back scattering is forbidden due to the spin-momentum locking. Nevertheless, large trenches in the film may cause the helical states on the surface to mix inside the trench, thereby affecting the transmission.%%%%Dans cette these, nous etudions le transport quantique dans l'isolant topologique (TI) Bi2Se3 a partir d'un modele d'echelle atomique. Un TI est un materiau ayant une structure de bande de type isolant bien qu'on y retrouve des etats helicodaux en surface. Ces etats helicoidaux ont une relation de dispersion lineaire, dite dispersion de Dirac, qui traverse la bande interdite du cristal. Ces electrons voyageant selon les relations de Dirac sont contraints a se mouvoir perpendiculairement a leur spin. La structure electronique particuliere de l'isolant topologique Bi2Se3 est due a une forte interaction spin-orbite et est protegee par une symetrie par renversement du temps. Cette thse comporte deux grands segments. Dans un premier temps, nous presentons une synthese de la theorie generale des isolants topologiques. Nous presentons ensuite les resultats de nossimulation de transport quantique dans le materiau Bi2Se3. Dans notre resume de la theorie des TI, nous presentons une revue de litterature et decrivons conceptuellement, dans la mesure du possible, le comportement des TI de…