Are quantum spin Hall edge modes more resilient to disorder, sample geometry and inelastic scattering than quantum Hall edge modes?

TL;DR

This paper compares the robustness of quantum spin Hall (QSH) and quantum Hall (QH) edge modes against disorder, geometry, and inelastic scattering, revealing that QSH modes are more susceptible to certain perturbations than QH modes.

Contribution

The study provides a detailed analysis showing that QSH edge modes are less resilient to disorder and inelastic scattering than QH modes, challenging previous assumptions about their robustness.

Findings

QSH edge modes are more affected by disorder and inelastic scattering than QH modes.

Single disordered contact induces a finite charge Hall current in QSH but not in QH.

Sample asymmetry negatively impacts QSH modes but not QH modes.

Abstract

On the surface of 2D Topological insulators occur 1D quantum spin Hall(QSH) edge modes with Dirac like dispersion. Unlike quantum Hall(QH) edge modes which occur at high magnetic fields in 2DEGs, the occurrence of QSH edge modes is because of 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 larger decoherence and relaxation time than charge- in view of this its 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 to QSH edge modes when subjected to 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. Further, while a single disordered contact has no effect on QH edge modes it leads to a finite charge Hall current in case of quantum spin Hall edge modes and thus vanishing of pure quantum spin Hall effect. For more than a single disordered contact while quantum Hall states continue to remain immune to disorder, quantum spin Hall edge modes become more susceptible- the Hall resistance for quantum spin Hall effect changes sign with increasing disorder. In case of many disordered contacts with inelastic scattering included while quantization of Hall edge modes holds, for quantum spin Hall edge modes- a finite charge Hall current still flows. For quantum spin Hall 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 on quantum spin Hall case it has no impact in quantum Hall case.