On the accuracy of conductance quantization in spin-Hall insulators

In contrast to the case of ordinary quantum Hall effect, the resistance of ballistic helical edge channels in typical quantum spin-Hall experiments is non-vanishing, additive and poorly quantized. Here we present a simple argument connecting this qualitative difference with a spin relaxation in the current/voltage leads in an experimentally relevant multi-terminal bar geometry. Both the finite lead resistance and the spin relaxation contribute to a non-vanishing four-terminal edge resistance, explaining poor quantization quality. We show that corrections to the four-terminal and two-terminal resistances in the limit of strong spin relaxation are opposite in sign, making a measurement of the spin relaxation resistance feasible, and estimate the magnitude of the effect in HgTe-based quantum wells.