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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 |B| at small B. The observed behavior is in qualitative agreement with the cusp-like features observed in recent magnetotransport measurements on HgTe quantum wells. We propose a dimensional crossover scenario as a function of W, in which for weak disorder W < E_g the edge liquid is analogous to a disordered spinless 1D quantum wire, while for strong disorder W > E_g, the disorder causes frequent virtual transitions to the 2D bulk, where the originally 1D edge electrons can undergo 2D diffusive motion and 2D antilocalization.