  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.
