Quantum Waveguide On Surface Of Three Dimensional Topological Insulator And Its Transport Properties

Topological insulators (TIs) are new quantum state of matter, possessing unusual phases of quantum matter simultaneously with insulating bulk and con-ducting edge or surface states, have been extensively studied in recent years due to its potential application in spintronics. In this master degree thesis, we investigate the electronic structure of the quantum waveguide and its transport properties on the surface of topological insulator. There are five chapters in this thesis.This first chapter is an introduction about this thesis. We describe, respec-tively, the basic concept of TI, spin-orbit interaction, quantum spin Hall effect, the three dimensional TI and its surface states birefly. The second chapter intro-duces some basic conceptions, such as the well-known Landauer-Buttiker formula in quantum transport and the most usually used method, the transform matrix method, with which one can obtain the transmission spectrum of a system.In the third chapter, we study the spatial distribution of electron spin polar-ization for a gate-controlled T-shapedchannel on the surface of a three-dimensional topological insulator (3D TI). We demonstratethat an energy gap depending on channel geometry parameters is definitely opened due to the spatial confinement. Spin surface locking in momentum space for a uniform wide channel with Hamil-tonian linearity in the wavevector is still kept, but it is broken with Hamiltonian nonlinearity in the wavevector, like that for two-dimensional surface states widely studied in the literature. However, the spin surface locking for a T-shaped chan-nel is broken even with Hamiltonian linearity in the wavevector. Interestingly, the magnitude and direction of the in-plane spin polarization are spatially depen-dent in all regions due to the breaking of translational symmetry of the T-shaped channel system. These interesting findings for an electrically controlled nanostruc- ture based on the3D TI surface may be testable with the present experimental technique, and may provide further understanding the nature of3D TI surface states.In the forth chapter, we study the electronic structure and transport for a quasi-one-dimensional channel constructed via two ferromagnetic (FM) stripes on the surface of a three-dimensional (3D) topological insulator (TI) in parallel (P) or antiparallel (AP) magnetization configuration along the vertical z-direction. We demonstrate that the confined states which are localized inside the channel always exist due to the magnetic potential confinement. Interestingly, the channel is metallic because of the existence of a topologically protected gapless chiral edge mode in the case of AP configuration. The asymmetric spatial-distribution of both electron probability density and in-plane spin polarization for the confined states implies that in the case of P con-figuration there exists a chiral state near the channel edge owing to the Hamiltonian inversion symmetry broken in real space, while the distributions in AP case are always symmetry for the inversion symmetry is still kept. Furthermore, the transmission probability and the spatial-dependent distributions of charge and spin along a narrow-wide-narrow channel on the surface with P configuration confinement are also calcu-lated, from which a fully in-plane spin-polarized electron output is achieved. Along with the mathematical analysis we provide an intuitive, topological understanding of these effects.In chapter five, a summary of the work is given.