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The quantum spin Hall (QSH) state, observed in a zero magnetic field in HgTequantum wells, respects the time-reversal symmetry and is distinct from quantumHall (QH) states. We show that the QSH state persists in strong quantizingfields and is identified by counter-propagating (helical) edge channels withnonlinear dispersion inside the band gap. If the Fermi level is shifted intothe Landau-quantized conduction or valence band, we find a transition betweenthe QSH and QH regimes. Near the transition the longitudinal conductance of thehelical channels is strongly suppressed due to the combined effect of thespectrum nonlinearity and enhanced backscattering. It shows a power-law decay1/B^2N with magnetic field B, determined by the number of backscatterers on theedge, N. This suggests a rather simple and practical way to probe the qualityof recently realized quasiballistic QSH devices using magnetoresistancemeasurements.

Ballistic quantum spin Hall state and enhanced edge backscattering in strong magnetic fields