Microscopic Theory of Thermal Conductivity in an Electron-Phonon System

Abstract

Using the Kubo formula and thermal Green function technique, we formulate a microscopic method for calculating the thermal conductivity of an electron-phonon system. First, we derive generalized Ward idetities (GWI) for the heat current vertices, and calculate the Green functions and current vertices in an approximation consistent with the GWI. Thermal conductivity becomes divergent in this calculation in the same sense that electrical conductivity is divergent as was shown by Holstein. The additivity of electron and phonon contributions to thermal conductivity is shown to be approximately valid.