Finite-temperature contributions to the specific heat of the electron-phonon system

Abstract

We calculate the $T^3$lnT contribution to the specific heat of metals due to the electron-phonon interaction and show that it may be regarded either as a Bose contribution or as a Fermi one. We find that the magnitude of the coefficient of the $T^3$lnT term is (12/7 times larger than that calculated by previous authors and demonstrate that the difference between the results is due to our inclusion of the temperature dependence of the quasiparticle spectrum. We discuss renormalization effects due to the electron-phonon interaction and, by using experimentally determined values of the relevant parameters in our expressions, show that for ordinary metals one would not expect to be able to isolate this $T^3$lnT contribution in measurements of the specific heat.