title: Spin-Hall conductivity in electron-phonon coupled systems.
abstract: We derive the ac spin-Hall conductivity sigmasH(omega) of two-dimensional spin-orbit coupled systems interacting with dispersionless phonons of frequency omega0. For the linear Rashba model, we show that the electron-phonon contribution to the spin-vertex corrections breaks the universality of sigmasH(omega) at low frequencies and provides a nontrivial renormalization of the interband resonance. On the contrary, in a generalized Rashba model for which the spin-vertex contributions are absent, the coupling to the phonons enters only through the self-energy, leaving the low-frequency behavior of sigmasH(omega) unaffected by the electron-phonon interaction.
authors.affiliation: LPM, Ecole Polytechnique Fédérale de Lausanne, Station 17, CH-1015 Lausanne, Switzerland.
authors.forename: C
authors.initials: C
authors.lastname: Grimaldi
authors.forename: E
authors.initials: E
authors.lastname: Cappelluti
authors.forename: F
authors.initials: F
authors.lastname: Marsiglio