The spin Hall effect can be induced by both extrinsic impurity scattering and intrinsic spin-orbit coupling in the electronic structure. The $\mathrm{HgTe}/\mathrm{CdTe}$ quantum well has a quantum phase transition where the electronic structure changes from normal to inverted. We show that the intrinsic spin Hall effect of the conduction band vanishes on the normal side, while it is finite on the inverted side. By tuning the Cd content, the well width, or the bias electric field across the quantum well, the intrinsic spin Hall effect can be switched on or off and tuned into resonance under experimentally accessible conditions.

• Received 22 October 2007

DOI:https://doi.org/10.1103/PhysRevLett.100.056602