Fragility of non-local edge mode transport in the quantum spin Hall state

Non-local currents and voltages are better able at withstanding the deleterious effects of dephasing than local currents and voltages in nanoscale systems. This hypothesis is known to be true in quantum Hall set-ups. We test this hypothesis in a four terminal quantum spin Hall set up wherein we compare the local resistance measurement with the non-local one. In addition to inelastic scattering induced dephasing we also test resilience of the resistance measurements in the aforesaid set-ups to disorder and spin-flip scattering. We find the axiom that non-local resistance is less affected by the detrimental effects of disorder and dephasing to be in general untrue for quantum spin Hall case. This has important consequences since it has been widely communicated that non-local transport through edge channels in topological insulators will have potential applications in low power information processing.