Non--Adiabatic Contributions to the Free Energy from the Electron--Phonon Interaction for Na, K, Al, and Pb

TL;DR

This paper calculates the non-adiabatic electron-phonon contributions to the free energy of Na, K, Al, and Pb metals at intermediate temperatures, including the zero-temperature value and low-temperature behavior.

Contribution

It provides the first calculation of the zero-temperature non-adiabatic free energy contribution for these metals and analyzes its temperature dependence.

Findings

Zero-temperature non-adiabatic free energy contribution calculated for the first time.

Temperature dependence of the non-adiabatic contribution analyzed.

Results applicable to nearly free electron metals in the intermediate temperature range.

Abstract

We calculate the non--adiabatic contributions to the free energy of metals due to the electron--phonon interaction at intermediate temperatures, $0 \leqslant k_{B} T < \epsilon_{F}$ for four different nearly free electron metals, Na, K, Al, and Pb. We calculate its value for $T = 0$ which has not been calculated before and we study its low--temperature behavior.