Spin Hall effect due to intersubband-induced spin-orbit interaction in symmetric quantum wells

We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity σ xy z is calculated in the ballistic limit within the standard Kubo formalism in the presence of a magnetic field B and is found to remain finite in the B=0 limit, as long as only the lowest subband is occupied. Our calculated σ xy z exhibits a nonmonotonic behavior and can change its sign as the Fermi energy (the carrier areal density n2D) is varied between the subband edges. We determine the magnitude of σ xy z for realistic InSb quantum wells by performing a self-consistent calculation of the intersubband-induced spin-orbit coupling.