Journal
PHYSICAL REVIEW LETTERS
Volume 97, Issue 6, Pages -Publisher
AMERICAN PHYSICAL SOC
DOI: 10.1103/PhysRevLett.97.066601
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We derive the ac spin-Hall conductivity sigma(sH)(omega) of two-dimensional spin-orbit coupled systems interacting with dispersionless phonons of frequency omega(0). For the linear Rashba model, we show that the electron-phonon contribution to the spin-vertex corrections breaks the universality of sigma(sH)(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 sigma(sH)(omega) unaffected by the electron-phonon interaction.
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