Electronic Structure And Transport In Q1D Systems Based On Topological Insulator Surface

The topological insulator (TI), a new phase of quantum matter, is very dif-ferent from the traditional metal and insulator. These materials are electrically insulating in the bulk but have current-carrying gapless Dirac surface/edge states, whose gaplessness is protected by time-reversal symmetry. This occurs as a result of the electron spin-orbit coupling (SOC) which leads to the band-invert for the materials. Due to the unique properties, the TI has been a hot topic in condensed matter physics community in recent years. In this thesis, the electronic structure and spin-related properties of the surface states of topological insulators, which modulated by electric field and ferromagnetic exchange field, have been theoreti-cally investigated by the transfer matrix method. The purpose of this study is for providing physical basis for the design of nano-electronical devices and low-energy consumption spintronics devices in the future.The thesis is divided into six chapters. In the first chapter, we briefly introduce Quantum Spin Hall Effect and TIs, as well as the fabrication techniques of quasi-one-dimensional (QlD) system of TIs. In the second chapter, we provide a detailed introduction to the transfer matrix and non-equilibrium Green function method which are often used in the study of mesoscopic quantum transport.In the third chapter, based on the Dirac equation we study the electronic structure and spin polarization of the surface states of a three-dimensional topo-logical insulator (3D TI) thin film modulated by an electrical potential well. It is demonstrated that, there exist confined surface states in the potential well, in which the electron density is almost localized inside the well and exponentially decays outside in real space. The subbands of confined states are quasilinear with respect to the propagating wavevector. Importantly, a large proportion of electrons with ky>0occupy the top surface of the thin film, while for ky<0, most elec-trons occupy the bottom surface of the film in the Q1D quantum well region; The top and bottom surface confined states with the same density distribution have opposite spin polarizations due to the hybridization between the two surfaces.In the fourth chapter, by using a numerical method, we study the effect of an electric square-well potential on the Landau level (LL) spectrum for surface states of a3D TI. The results show that the energy spectrum as a function of both the magnetic field and the wavevector in certain range. It is demonstrated that the conduction and valence bands are no longer symmetric with respect to the lowest subband, and the valence branch is suppressed when the center of electron cyclotron orbit is inside the well. However, the energy bands trend to flat when the cyclotron orbit center is not too close to the well boundaries (corners). Interestingly, we find that the confining potential not only shifts LLs but also creates propagating interface states near boundaries. Moreover, the probability densities and spin polarization distributions of interface states in conduction band oscillate mainly inside the well and decay outside, while those in valence band oscillate outside and decay inside the well.In the fifth chapter, by using the transfer matrix method and Landaur-Buttiker formula, we theoretically study the spin and valley transport properties of Dirac electrons in a channel created by the local exchange field and local per-pendicular electric field on silicene sheet. The multiple total internal reflections at the interfaces result in the bound states in the channel, which behaves like an electronic waveguide. The different effects of local electric and exchange fields on both conduction and valence bands for bound states are identified by spin and valley indices. Interestingly, the electron transmitting along the channel can be both spin-and valley-polarized, and its degree of polarization can be tuned by electric and/or exchange fields. And, in particular, the condition for fully spin-and valley-polarization is obtained. Our findings may provide a scheme for efec-tively manipulating spin and valley degrees of freedom in this magnetic waveguide structure on a silicene sheet.In chapter six, a summary of the work and a outlook of the transport prop-erties of quasi-1D TI under the electric field and ferromagnetic modulation are given.