Study Of Topological Phase Quantum Transitions And Transport Properties In Topological Materials

Topological insulators are novel states of matter, which have a bulk gap as an or-dinary insulator but have gapless boundary states on the sample boundary owning to the topological nontrivial band structures. Topological insulators are characterized by topological invariants:the Z2 index or spin Chern numbers. The boundary states are protected from impurity scattering by nontrivial bulk band topology and time-reversal symmetry. Due to the spin-momentum locking in the boundary states, the topological insulators have potential application in the field of spintronics. Soon after the theo-retical prediction, the topological insulators were observed experimentally, and were extended to three dimensions. The rapid development of topological insulators have been attracting a great deal of interest. Inspired by the discovery of topological insula-tors, the classification of band structures has been extended to a different direction-to include crystal point group symmetries. The topological insulators protected by crystal symmetry are called "topological crystal insulator". Some theoretical work predicted that a topological crystal insulator state can be realized in authentic materials, which has been confirmed experimentally. Besides the charge and spin degrees of freedom, there exists the valley degree of freedom in honeycomb lattices, based on which var-ious valley-dependent topological phases have been proposed and a lot of interesting devices have been designed.In chapter two, we have investigated topological properties of the surface states of the topological crystalline insulator in the presence of a Zeeman field. It is found that changing the direction of the Zeeman field can achieve valley-dependent topological phase transitions. By symmetry analysis and using the pseudospin Chern numbers to characterize the topological quantum phase, we obtain a phase sphere with radius B, consisting of a quantum anomalous Hall phase with Chern number C=2, a quantum anomalous Hall phase with Chern number C=1, a quantum pseudospin Hall phase, and an unusual insulator phase. In the C=1 quantum anomalous Hall phase and the insulator phase, the two valleys are in different topological phases. The valley-dependent topological phases provide a platform to design low-power electronics and advance the application of topological crystalline insulator based valleytronics.Topological insulators are characterized by topological invariants:the Z2 index or spin Chern numbers. However, unlike the first Chern number underlying the quan-tum Hall effect, at present these topological invariants have not been measured and utilized directly, though several schemes have been proposed to observe them. There-fore, a simpler and more practicable method to measure the topological invariants is highly desirable. In chapter three, we propose a scheme to realize adiabatic topological pumping in silicene to by applying an in-plane ac electric field with amplitude Ey and a vertical electric field consisting of an electrostatic component and an ac component with amplitudes Ez0 and Ez1. By using the spin-valley Chern numbers, it is shown that the system can be in the pure valley pumping regime, mixed spin and valley pumping regime, or trivial pumping regime, depending on the strengths Ez0 and Ez1 of the per-pendicular electric field. The total amount of valley or spin quanta pumped per cycle, calculated from the scattering matrix formula, is fully consistent with the spin-valley Chern number description. It is proportional to the cross-section of the sample, and insensitive to the material parameters, a clear evidence that the pumping is a bulk topo-logical effect, irrelevant to the edge states.The spin Hall effect refers to the phenomenon that a charge current induces a pure transverse spin current through the spin-orbit coupling. This effect provides an electri-cal method to generate spin currents. Based on the same physical mechanism, a pure spin current can also generate a transverse charge current or a measurable voltage differ-ence, which is call inverse spin Hall effect. In chapter four, we have developed a theory to describe the inverse spin Hall effect of the surface states in a thin film of Bi2Se3 con- nected to a reservoir with applied spin bias. The spin bias drives the electron transport through its projection on the subspace spanned by the allowable channel eigenstates. We demonstrated that the topological surface states provide an ideal platform for the inverse spin Hall effect, where a spin bias is converted into a measurable transverse voltage without generating any longitudinal spin current in the topological insulator due to the spin-momentum locking. Our theory explains the very large spin Hall an-gle experimentally observed in the topological insulator. Besides, the inverse Edelstein effect with complete spin-to-charge conversion can happen in the surface states.The last chapter presents a summary of this dissertation, and then gives some outlook for the investigation.