Study Of Bulk Extended States In2D Topological Insulators

In recent years, topological insulators is one of the hottest topics in physics, both theoretical studies and experiment realizations experience a fast development. From the bulk properties, topological insulators belong to the insulators which have energy gap and do not conduct electricity, but there exist robust conducting edge states (for2D topological insulators) or surface states (for3D topological insulators) at the system's boundaries, which indicates the nontrivial topological properties of system. As a novel state of quantum matter, just as the quantum Hall state, it can not be described by Lan-dau's theory of spontaneous symmetry breaking, but by the notion of topological order which distinguish it from the normal insulators. However, different from the quantum Hall state and Chern insulators characterized by the Chern number of occupied valence bands, topological insulators is characterized by new class of invariants, including Z2index and spin Chern numbers. As we all know, dimensionality, symmetry and the pres-ence of topological terms in the Lagrangian determines the properties of bulk extended states in disordered systems. As a matter state which has novel topological properties, the properties of bulk extended states in2D topological insulators (also called Quan-tum Spin Hall state) attract people's interest. On the one hand, nontrivial topological properties indicates the existence of the extended states and will affect the localization of electron wave functions obviously; on the other hand, the existence and ways of an-nihilation of delocalized states also support the conclusion that system is topologically nontrivial. According the concept of universal classes, different disorder systems can be classified into different universal classes, which does not rely on the details of model. The classification of the2D topological insulators is also what we concern. Its study will present us more aspects of the topological insulators. The dissertation consists of five chapters:In chapter one, we give an introduction for the related experimental and theoretical background, theoretical methods and a brief outline of some fundamental conceptions.In chapter two, we demonstrate the existence of robust bulk extended states in the disordered Kane-Mele model with vertical and horizontal Zeeman fields, which are protected by the topological invariant, namely the spin Chern numbers C±. C±are protected by the finite energy and spin gaps. The phase diagrams are mapped out by us-ing level statistics analysis and computations of the localization length and spin-Chern numbers C±. For arbitrarily large vertical Zeeman fields the spin gap stays open, and the extended states from valence and conduction band annihilate each other in the band gap through the mechanism of "pair-annihilation". For relative large horizontal Zee-man fields, at moderate disorder the spin gap will close, leading to the annihilation of the spin Chern numbers, so the extended states also disappear without pair-annihilation in the band gap.In chapter three, the disorder-driven metal-insulator transition in the quantum spin Hall systems is studied by scaling analysis of the Thouless conductance g. Below a critical disorder strength, the conductance is independent of the sample size M, an indication of critically delocalized electron states. The calculated beta function β=dlng/dln M indicates that the metal-insulator transition is Kosterlitz-Thouless (KT) type, characterized by bounding and unbounding of vortex-antivortex pairs of the local currents. The beta functions for the QSH systems with and without the time-reversal symmetry are close to each other on the metallic side, but somewhat different on the insulating side, the latter being attributed to the fact that they belong to different symmetry classes.In chapter four, a honeycomb lattice model exhibiting quantum spin-Hall effect is proposed, where the low-energy properties of the electrons are mainly determined by the energy spectrum in the vicinity of the г point, for suitable parameters. Through the calculation of Chern number, we present the phase diagram of model. Also, by calcu- lation of berry curvature distribution and edge state spectrum, different characters of quantum spin Hall state and the insulator are revealed. We further show that in the con-tinuum limit, the model Hamiltonian is equivalent to the effective model for the surface states in thin films of three-dimensional topological insulator. As a consequence, this lattice model provides a useful tool for numerical simulation of the physical properties of the surface states.In chapter five, we study the magnetotransport of the interacting QD system in a magnetic field using the numerical method of embedded-cluster approximation (ECA). The spin-resolved conductances display different magnetic field dependences for dif-ferent transport regimes. Through comparison of conductance polarization, the mixed-valence regime shows the largest polarization. The spin-resolved conductance as a function of the ratio between the magnetic field and Kondo temperature H/TK is found to exhibit an approximate universal behavior in the Kondo regime. We also investigate conductance dependence on interaction strength and find interesting inversion of sign of polarization in some cases.