Spin Hall conductivity based on the Drude model

Abstract

We reexamine the work of Chudnovsky on extending the Drude model to incorporate the spin-orbit interaction [Phys. Rev. Lett. 99, 206601 (2007)]. Here we determine the extension of the Drude model by using the WKB approximation in the low energy limit of the Dirac equation. Different from Chudnovsky's treatment, our model does not depend on the special assumption ∂2Φ∂ri∂rj=Aδij. Because a rigid treatment is introduced, we obtain a general formula for the spin Hall conductivity, which holds in the extensive regime of magnetic fields. By contrast, Chudnovsky's model is only an approximation of our model in the regime of the weak magnetic field. Regarding the metal aluminum, our theoretical result for the spin Hall conductivity is in agreement with the experimental measure value; however, our model shows that the Drude model may be inappropriate for describing heavy metals and many strong-correlation systems. Furthermore, our model predicts a negative spin Hall conductivity in the regime of the asymptotically strong magnetic field.