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Spin-Hall Conductivity in Electron-Phonon Coupled Systems

C. Grimaldi·E. Cappelluti·F. Marsiglio
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Abstract

We derive the ac spin-Hall conductivity $σ_{\rm sH}(ω)$ of two-dimensional spin-orbit coupled systems interacting with dispersionless phonons of frequency $ω_0$. For the linear Rashba model we show that the electron-phonon contribution to the spin-vertex corrections breaks the universality of $σ_{\rm sH}(ω)$ at low-frequencies and provides a non-trivial 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 $σ_{\rm sH}(ω)$ unaffected by the electron-phonon interaction.

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C. Grimaldi, E. Cappelluti, F. Marsiglio. 2006-08-08. Spin-Hall Conductivity in Electron-Phonon Coupled Systems. https://doi.org/10.1103/physrevlett.97.066601

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