Dirac fermions in semiconductors

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Two dimensional (2D) topological insulators form a new state of matter where insulating properties of the bulk are accompanied by edge states. These helical edge states are formed by Kramers partners in materials with strong spin-orbit interactions where time reversal symmetry is conserved. Similarly, three dimensional (3D) topological insulators are characterized by metallic surface states while the bulk of the material is gapped. Typical 2D and 3D topological insulators are various narrow gap semiconductors in which the usual band ordering is inverted. In this project, we will explore theoretically transport properties of topological insulators when the Fermi level probes the helical edge states (quantum spin-Hall state) or surface states, and when the Fermi energy lies deep in the conduction band or valence band (doped topological insulators). In particular, we will investigate interfaces between quantum spin Hall state and doped topological insulator and the response of the quantum spin Hall state to perturbations breaking time-reversal symmetry like magnetic impurities and magnetic fields. Further we will study weak antilocalization and universal conductance fluctuations in doped topological insulators to better understand these materials. We will use diagrammatic techniques accompanied by numerical calculations within the Landauer-Büttiker-Keldysh formalism. The complete characterization of the transport in topological insulators should allow us to evaluate the importance and consequences of the existence of Dirac fermions in these materials.