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Local Transport Properties and Complex Band Structure of Topological Insulators
One of the great achievements of modern condensed matter physics is the discovery of topological insulators. Their unique properties, such symmetry protected edge and surface states, are interesting both from the fundamental point of view as well as from the point of view of potential applications in nanoelectronics as perfectly conducting channels and functional elements of novel devices and circuits. This dissertation is focused on the theoretical studies of the electronic structure and local transport properties of topological insulators. Using a tight-binding description of the electronic structure within a model Hamiltonian approach, we analyze electronic properties intrinsic to the two-dimensional (2D) topological insulators. We utilize a concept of the complex band structure to describe the decay of the topologically protected states from the edge to the bulk and the formation of the energy gap in the spectrum of the edge states. By employing the Landauer-Büttiker approach within the Green’s function formalism, we explore the effect of impurities on the local conductance of the 2D topological insulators. We predict a number of relevant phenomena, such as an oscillatory decay of the local conductance with distance from the edge, vortex currents of certain chirality, and Friedel oscillations. We find that resonant scattering driven by an impurity state in the interior of the topological insulator can produce antiresonances in conductance. We show that the transmission of the edge states can be controlled by the ferromagnetic gate which may have important implications in spintronics. Finally, we expand the concept of the complex band structure to real 3D topological insulator Bi2Se3, and show the presence of the oscillatory component in the evanescent states, which in particular leads to a non-monotonous decrease of the band gap in Bi2Se 3 slabs of finite thickness.
Physics|Condensed matter physics
Dang, Xiaoqian, "Local Transport Properties and Complex Band Structure of Topological Insulators" (2017). ETD collection for University of Nebraska - Lincoln. AAI10602524.