Impurity influence in quantum spin Hall transport

Abstract

Influences of impurities on the electron density and transmission of a finite HgTe/CdTe quantum well sample are studied numerically in the framework of the Landauer-B\uttiker formula. In a geometry of a slab with finite width, electrons in helical edge states protected by the time-reversal symmetry can tunnel through nonmagnetic impurities at two resonant energy levels. Electrons of one side can tunnel to the other side and the quantized conductance can be broken down. For a small sample with impurity, the transmission coefficient can even drop to zero for the crosswalk between the helical edge states at two sample sides. The distance between helical edge states is critical for the suppression of the transmission. The $s$ orbital and $p$ orbital of pseudospins affect the quantized spin Hall current in a different way for their different energies.