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

Abstract

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 $\ensuremath{\alpha}(p)$ and nonparabolic spectrum $ϵ(p)$. 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 $l\ensuremath{\rightarrow}\ensuremath{\infty}$ and in the presence of electron-electron interactions, we derived the universal relation between frequency-dependent spin-Hall conductivity ${\ensuremath{\sigma}}_{\mathrm{sH}}(\ensuremath{\Omega})$ and Pauli susceptibility $\ensuremath{\chi}(\ensuremath{\Omega})$. Electron-electron interaction is shown to modify the ``universal'' value ${\ensuremath{\sigma}}_{\mathrm{sH}}^{(0)}=e∕8\ensuremath{\pi}\ensuremath{\hbar}$ by the corrections of the relative magnitude determined by the standard Coulomb parameter only.