Mani Arjun, Benjamin Colin
National Institute of Science Education & Research, Bhubaneswar 751005, India.
J Phys Condens Matter. 2016 Apr 13;28(14):145303. doi: 10.1088/0953-8984/28/14/145303. Epub 2016 Mar 11.
On the surface of 2D topological insulators, 1D quantum spin Hall (QSH) edge modes occur with Dirac-like dispersion. Unlike quantum Hall (QH) edge modes, which occur at high magnetic fields in 2D electron gases, the occurrence of QSH edge modes is due to spin-orbit scattering in the bulk of the material. These QSH edge modes are spin-dependent, and chiral-opposite spins move in opposing directions. Electronic spin has a larger decoherence and relaxation time than charge. In view of this, it is expected that QSH edge modes will be more robust to disorder and inelastic scattering than QH edge modes, which are charge-dependent and spin-unpolarized. However, we notice no such advantage accrues in QSH edge modes when subjected to the same degree of contact disorder and/or inelastic scattering in similar setups as QH edge modes. In fact we observe that QSH edge modes are more susceptible to inelastic scattering and contact disorder than QH edge modes. Furthermore, while a single disordered contact has no effect on QH edge modes, it leads to a finite charge Hall current in the case of QSH edge modes, and thus a vanishing of the pure QSH effect. For more than a single disordered contact while QH states continue to remain immune to disorder, QSH edge modes become more susceptible--the Hall resistance for the QSH effect changes sign with increasing disorder. In the case of many disordered contacts with inelastic scattering included, while quantization of Hall edge modes holds, for QSH edge modes a finite charge Hall current still flows. For QSH edge modes in the inelastic scattering regime we distinguish between two cases: with spin-flip and without spin-flip scattering. Finally, while asymmetry in sample geometry can have a deleterious effect in the QSH case, it has no impact in the QH case.
在二维拓扑绝缘体表面，会出现具有类狄拉克色散的一维量子自旋霍尔（QSH）边缘模式。与二维电子气在高磁场下出现的量子霍尔（QH）边缘模式不同，QSH边缘模式的出现是由于材料体相中自旋轨道散射所致。这些QSH边缘模式与自旋相关，手性相反的自旋沿相反方向移动。电子自旋比电荷具有更大的退相干和弛豫时间。鉴于此，预计QSH边缘模式相对于依赖电荷且自旋非极化的QH边缘模式，对无序和非弹性散射将更具鲁棒性。然而，当在与QH边缘模式类似的设置中受到相同程度的接触无序和/或非弹性散射时，我们并未发现QSH边缘模式具有这样的优势。事实上，我们观察到QSH边缘模式比QH边缘模式更容易受到非弹性散射和接触无序的影响。此外，单个无序接触对QH边缘模式没有影响，但在QSH边缘模式的情况下会导致有限的电荷霍尔电流，从而使纯QSH效应消失。对于多个无序接触，当QH态继续对无序免疫时，QSH边缘模式变得更易受影响——QSH效应的霍尔电阻随无序增加而改变符号。在包含非弹性散射的多个无序接触的情况下，虽然霍尔边缘模式的量子化仍然成立，但对于QSH边缘模式仍有有限的电荷霍尔电流流动。对于处于非弹性散射 regime 的QSH边缘模式，我们区分两种情况：有自旋翻转和无自旋翻转散射。最后，虽然样品几何形状的不对称在QSH情况下可能产生有害影响，但在QH情况下没有影响。
