The Study Of Spin Hall Effect In Semiconductors And 1D Zero-line Mode In Graphene Systems

The spin Hall effect(SHE)refers to a transverse spin transport phenomenon in-duced by longitudinal electrical current.As an important concept and method in the field of spintronics,the spin Hall effect provides the possibility to manipulate the spin degree of freedom by pure electrical ways.Spin-orbit(SO)interactions give a spin-dependent correction rSO to the position operator,referred to as the anomalous position operator.We study the contributions of rSO to the spin Hall effect in quasi-two-dimensional(2D)semiconductor quantum wells with strong band-structure SO interactions that cause spin precession.The skew scattering and side-jump scattering terms in the SHE vanish,but we identify two additional terms in the SHE,due to rSO,which have not been consid-ered in the literature so far.One term reflects the modification of spin precession due to the action of the external electric field(the field drives the current in the quantum well),which produces,via rSO,an effective magnetic field perpendicular to the plane of the quantum well.The other term reflects a similar modification of spin precession due to the action of the electric field created by random impurities,and appears in a careful formulation of the Born approximation.We refer to these two effects collectively as anomalous spin precession and we note that they contribute to the SHE to the first order in the SO coupling constant even though they formally appear to be of second order.In electron systems with weak momentum scattering,the contribution of the anoma-lous spin precession due to the external electric field equals 1/2 the usual side-jump SHE,while the additional impurity-dependent contribution depends on the form of the band-structure SO coupling.For band-structure SO coupling linear in wave vector,the two anomalous spin precession contributions cancel.For band-structure SO coupling cubic in wave vector,however,they do not cancel,and the anomalous spin precession contribution to the SHE can be detected in a high-mobility 2D electron gas with strong SO coupling.In 2D hole systems,both anomalous spin precession contributions vanish identically.Finally,we predict the experimental observation of the signal of anomalous spin precession in InSb based 2D quantum well.Compared to conventional semiconductors,graphene,a two-dimensional hexag-onal structure of carbon,is intrinsically a zero-gap semimetal and possess linear dis-persion relation in low energies.Various novel quantum states have been proposed in graphene systems including(quantum)spin Hall effect,(quantum)anomalous Hall ef-fect and(quantum)valley Hall effect.Its internal binary degrees of freedom such as the valleys,sublattices,and top/bottom layers in multilayers lead to a two-dimensional elec-tron gas with valley selective chirality of the electrons near the Fermi energy.Breaking inversion symmetry in chiral graphene systems,e.g.,by applying a perpendicular elec-tric field in chirally stacked rhombohedral multilayer graphene or by introducing stag-gered sublattice potentials in monolayer graphene,opens up a bulk band gap that harbors a quantum valley-Hall state.When the gap size is allowed to vary and changes sign in space,a topologically confined one-dimensional(1D)zero-line mode(ZLM)is formed along the zero lines of the local gap.Here,we show that gapless ZLM with distinguish-able valley degrees of freedom K and K' exist for every propagation angle except for the armchair direction that exactly superpose the valleys.We further analyze the role of different geometries of top-bottom gated device setups that can be realized in experi-ments,discuss the effects of their edge misalignment,and analyze three common forms of topological defects that could influence the 1D ZLM transport properties in actual de-vices.Our findings will provide some useful insights into the experimental realisation of 1D ZLM.