Spin-Hall conductivity in a two-dimensional Rashba electron gas

Spin-Hall conductivity and Pauli susceptibility of 2D electron gas with Rashba spin-orbital interaction is studied theoretically in the semiclassical limit k(F)l >> 1. Static spin-Hall conductivity is shown to be zero for any nonvanishing disorder strength in the general case of the momentum-dependent Rashba velocity alpha(p) and nonparabolic spectrum epsilon(p). This result is derived both by an explicit diagrammatic calculation for the model of noninteracting electrons in a disorder potential, and via the analysis of general operator commutation relations, that are valid also for the case of interacting electrons. For the clean limit l ->infinity and in the presence of electron-electron interactions, we derived the universal relation between frequency-dependent spin-Hall conductivity sigma(sH)(Omega) and Pauli susceptibility chi(Omega). Electron-electron interaction is shown to modify the universal value sigma((0))(sH)=e/8 pi h by the corrections of the relative magnitude determined by the standard Coulomb parameter only.