Magnetoconductance of the quantum spin Hall state

We study numerically the edge magnetoconductance of a quantum spin Hall insulator in the presence of quenched nonmagnetic disorder. For a finite magnetic field B and disorder strength W on the order of the bulk gap E(g), the conductance deviates from its quantized value in a manner which appears to be linear in vertical bar B vertical bar at small B. The observed behavior is in qualitative agreement with the cusplike features observed in recent magneto-transport measurements on HgTe quantum wells. We propose a dimensional crossover scenario as a function of W, in which for weak disorder WE(g), the disorder causes frequent virtual transitions to the two-dimensional (2D) bulk, where the originally 1D edge electrons can undergo 2D diffusive motion and 2D antilocalization.