Spin Transport Properties In Topological Insulator Nano Device

Topological insulators are a new type of material which discovered in recent years.Since the discovery of topological insulators,they are currently creating a surge of research activities.At present,the researches on topological materials mainly focus on the topological insulators whose time inversion is invariant.Although topological insulators have the same band gaps as ordinary insulators,however,due to the strong spin-orbit coupling,the topological insulators have topology protected edge states(Two dimension)/ surface states(Three dimension)in the bulk energy gap,the edge states/ surface states rely entirely on the bulk of the material's topology,where conduction of the electron is non-dissipative,low-heat,and impervious to defects and impurities,thus make it an ideal conductive material.The edge / surface states of topological insulators are not only symmetrically protected by time inversion and it also show Dirac dispersion relations,which are physically related to Relativistic Dirac fermions,thus they present many novel physical properties.Subsequent studies have found that the doped topological insulator(quantum spin Hall insulator)can cause topological quantum phase transitions without applying magnetic field,and thus evolve into quantum anomalous Hall insulators.In recent years,people have coupled topological insulators to the superconductors and found that it can induce a new material phase,the topological superconducting phase,at the boundary of which a novel Majorana fermion is predicted.In addition,the research of topological insulators is closely connected with the hotspots of research in recent years,such as quantum Hall effect,quantum anomalous Hall effect and quantum spin Hall effect.The basic characteristic is the use of the topological properties of the edge state in the bulk band gap,A variety of novel physical properties are realized.In summary,the study of topological insulator materials have become a hot topic in condensed matter physics.Due to its chirality and helicity,the topological insulator materials have potential applications in spintronics.Therefore,the researches on the design of spin-based nanostructures based on topological insulator materials are booming around the world.In this paper,we introduce the historical background and topological properties of topological insulator materials,at the same time,described the spin dependent transport properties appear in the transport of topological insulator materials.And then introduce several methods to obtain grided Hamiltonian and introduce the lattice Green's function method.We also introduce involved formula in the calculation of quantum transport.Finally,the spin dependent transport properties in three kinds of mesoscopic system constructed by topological materials are studied.1.By using the Green's function method,we have investigated spin Hall conductance(SHC)in a four terminal quantum spin Hall insulator.The results show that the intrinsic spin orbit coupling in a HgTe/CdTe hetero-structure interface naturally leads to separate probability distributions for the two spins in coordinate space,which leads to the spin Hall effect in our proposed device.We also find that the SHC of bulk states exhibits an oscillatory behavior as a function of the device width and persists at a broad device width.In addition,we calculate the effects of disorder on the SHC of the bulk states of non-trivial and trivial topology.The results indicate that the spin up and spin down conductances show different degrees of suppression by disorder;thus the SHC could be significantly enhanced by the disorder.This kind of property has a great value to practical applications.2.Based on the Green's function method and tight-binding model,we have investigated tunneling magnetoresistance(TMR)in two-dimensional ferromagnet/topological superconductor(TSC)/ferromagnet hybrid structure with its chern number N=1 and N=0.It is found that the TMR effect can emerge in our proposed structure.In presence of the chiral gapless Majorana edge state,the 100% TMR ratio is robust to disorder and is independent of the length of TSC.The further calculations show that the TMR effect could be adjusted by spin polarized angle and magnetization strength.In addition,we also calculate the TMR effect in the QAHI/TSC/QAHI hybrid structure with its Chern number N=2 in the central TSC region.We found that our conclusions are still applicable.3.By using the Green's function method and tight-binding model,we have studied the Anderson disorder effect on electronic transport properties in a two-dimensional quantum anomalous Hall insulator(QAHI)/ topological superconductors(TSC)/ QAHI hybrid structure and find that Anderson disorder can induce quantum topological transition in TSC,especially trivial TSC state can be driven into a chiral TSC state.In order to confirm that the topological transition has occurred,we numerically compare our result with the result of the effective-medium theory and find effective-medium theory can explain our calculation results.