Spin-Hall Conductivity and Pauli Susceptibility in the Presence of Electron-Electron Interactions

We found the universal relationship between frequency-dependent spin-Hall conductivity and magnetic susceptibility in clean 2D electron systems with Rashba coupling: $\sigma_{sH}(\Omega)= \frac{e}{(g\mu_B)^2m_b}\chi_\parallel(\Omega)$ in the presence of an arbitrary two-particle spin-conserving interaction. We show that the Coulomb interaction renormalizes the spin-Hall constant. The magnitude of the relative correction to $\sigma_{sH}$ is proportional to the Coulomb interaction parameter $e^2/\epsilon v_F\hbar$ and does not depend on the strength of the Rashba coupling $\alpha$.