Spin Hall Effect in Symmetric Wells with Two Subbands
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We investigate the spin Hall conductivity σ xy z of a clean 2D electron gas formed in a two-subband well. We determine σ xy z as arising from the inter-subband induced spin–orbit (SO) coupling η (Calsaverini et al., Phys. Rev. B 78:155313, 2008) via a linear-response approach due to Rashba. By self-consistently calculating η for realistic wells, we find that σ xy z presents a non-monotonic (and non-universal) behavior and a sign change as the Fermi energy varies between the subband edges. Although our σ xy z is very small (i.e., ≪`` e/4π″), it is non-zero as opposed to linear-in-k SO models.