Theoretical Researches On Topological Properties And Transport Properties In Topological Materials

Recently,the discovery and research of the integer quantum Hall effect has brought the concept of topological state into condensed matter physics.Later on,the quantum spin Hall effect has been predicted and discovered as a new generation of topological state.The quantum spin Hall state,which is also called the two-dimensional topological insulator,has a insulating bulk band and gapless edge states traversing the energy gap.Furthermore,there is an interlocking between the spin and the momentum of the edge state and the edge states are called as helical edge states.The quantum spin Hall effect relies on spin orbit coupling,and it is protected by the time reversal symme-try and the bulk band topology.The nontrivial topological properties of the quantum spin Hall effect can be depicted by Z2 topological invariant or the spin Chem number.Afterwards,the discovery of three dimensional topological insulators has drawn much attention.For the thin film of the three dimensional topological insulators,however,the hybridization of the surface states on the two surfaces results in energy gap opening.The discovery of topological insulators has inspired the researches on a lot of interest-ing physical phenomena including the topological spin pumps,such as the Z2 pump and the spin Chern pump.Also,due to the strong spin orbit coupling,the topological insulators has been considered as a useful platform to observe the spin orbit torque.The spin Chern pump,which is a topological spin pump independent of any sym-metries protected by the band topology alone,has been proposed recently.However,previous researches on the spin Chern pumps are confined to a single spin pump or a series of spin pumps without interaction.In Chapter two,two spin Chern pumps are coupled by a magnetic impurity potential.We study the influence of the coupling ef-fect on the pumping process,also,the time reversal symmetry is broken.Through the Green's function and Born approximation,along with the scattering matrix formula,we calculate the spin pumped per cycle.It is found that the influence of the magnet-ic impurity on the amount of spin pumped is just perturbative.In the circumstances where both,either or neither of the two pumps are topological nontrivial,we discover that the spin pumped per cycle stays near the quantized value determined by the total spin Chem number of the system Cspin = 4,2 and 0 in the unit of h/2,respectively.It is concluded that spin Chem pumps can be classified by different total spin Chern number of the system,which is independent of any symmetry.The spin orbit toque,which provides a mechanism of switching the magnetiza-tion direction by using the spin orbit coupling of materials,has been a hotspot lately.Apart from heavy metal materials,topological insulators has also been used as popu-lar materials to study spin orbit torques because of their comparably strong spin orbit coupling.In Chapter three,by using a semiclassical Boltzmann equation with proper boundary conditions,we investigate the spin orbit torque in a thin film of the topo-logical insulator Bi2Se3 from the ballistic regime to the diffusive regime.Because of the spin-momentum interlocking of the surface states,the magnitude of the field-like torque is linearly proportional to the longitudinal electrical current.It is discovered that for fixed electric field,the spin orbit torque is proportional to the sample length in the ballistic limit,and saturates to a constant in the diffusive limit.We also obtain a simple analytical expression for the spin orbit torque when the magnetization direction is perpendicular to the sample plane.We also investigate the influence of the exchange coupling strength on the spin orbit torque.When the exchange coupling strength in-creases,the magnitude of the spin orbit toque field shows a non-monotonic behavior.It first increases,and then decreases.This phenomenon is attributed to the competition between the exchange coupling strength and the radius of the Fermi surface.Variation of the magnitude of the spin orbit toque on the magnetization direction is also studied.We found that the magnitude of the spin torque is independent of the polar angle,and is maximal when the azimuthal angle is ?/2.The last chapter contains a summary of this dissertation and an outlook for future investigation.