AC response of spin-pseudospin current in a double quantum well

Abstract

The spin Hall effect due to the skew scattering is studied using the Boltzmann equation in a double quantum well when the inplane electric field with angular frequency ω is applied. The two wells have opposite signs of impurity potential so that the skew-scattering spin Hall current is antiparallel and carries a pseudospin, which is formed by ∣L〉 and ∣R〉, the ground states of the two wells. The pseudospin precession is induced by the interwell tunneling in the strength of ℏ ω SAS, the energy difference between the symmetric and antisymmetric states. It is found that the dynamics of the spin-pseudospin current, described by the pseudospin analogue of the Bloch equation, is equivalent in form to the classical cyclotron resonance. Consequently, the antiparallel spin Hall current exhibits the resonance peak at ω ∼ ω SAS. Such spin-pseudospin coupling is expected to be useful in controlling the spin polarization in many electronic systems.