Electron–hole symmetry and spin–orbit splitting in IV–VI asymmetric quantum wells

It is shown that, due to the electron–hole symmetry of the fundamental gap of the lead–salts (PbTe, PbSe and PbS), the Rashba spin splitting in their flat band asymmetric quantum wells is much reduced with the usual equal conduction and valence band-offsets. Different from the III–V case, we find that the important structure inversion asymmetry for the Rashba splitting in IV–VI quantum wells with different left and right barriers is not a material property (i.e., barrier height, effective mass or band gap) but results from the band alignment. This is shown by specific envelope function calculations of the spin-dependent subband structure of Pb_1−xEu_xTe/PbTe/Pb_1−yEu_yTe asymmetric quantum wells (x≠y), based on a simple but accurate four-band kp model for the bulk band structure near the gap, which takes into account band anisotropy, nonparabolicity and multi-valley effects.