Rigorous results for the electrical conductivity due to electron-phonon scattering

Abstract

We present a rigorous solution of the Boltzmann equation for the electron-phonon scattering problem in three spatial dimensions in the limit of low temperatures. The different temperature scaling of the various scattering rates turns the temperature into a control parameter that is not available in classical kinetic theory and allows for a rigorous proof of Bloch's $T^5$ law. The relation between the Boltzmann equation and the Kubo formula is also discussed, as well as implications for the scattering of electrons by excitations other than phonons.

arXiv comment16pp

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Cited by in corpus (1)

• Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime