Ballistic quantum spin Hall state of HgTe quantum wells in a strong magnetic field

Recently novel two-dimensional electronic state - quantum spin Hall (QSH) state - has been theoretically proposed and experimentally realized in HgTe quantum wells. It is observed in a zero magnetic field and for this reason is distinct from quantum Hall states. We show theoretically that the QSH state persists in strong quantizing fields, turning into a quantum Hall one if the Fermi level is driven out of the band gap. We find that near such a transition the longitudinal ballistic conductance of edge channels vanishes due to the combined effect of edge-spectrum nonlinearity and channel backscattering. This contrasts the usual behavior of the zero-field conductance which increases as the Fermi level is pushed from the band gap into the metallic-type conduction (or valence) band. The combined effect of the spectral nonlinearity and backscattering is found to cause power-law suppression of the edge conductance with magnetic field, accompanied by spatial redistribution of the QSH channels. Our findings can be used for the detection and characterization of the QSH state in the recently achieved ballistic regime, still remaining largely unexplored.