Spin-Hall conductivity in electron-phonon coupled systems.
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.
Grimaldi
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LPM, Ecole Polytechnique Fédérale de Lausanne, Station 17, CH-1015 Lausanne, Switzerland.
Cappelluti
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Marsiglio
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F