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

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

2005-09-12

arxiv.org/abs/cond-mat/0509305v2

Physics

Condensed Matter

Other Condensed Matter

Updated version

Scientific paper

10.1103/PhysRevB.73.075114

We calculate the adiabatic contributions to the free energy due to the electron--phonon interaction at intermediate temperatures, $0 \leqslant k_{B} T < \epsilon_{F}$ for the elemental metals Na, K, Al, and Pb. Using our previously published results for the nonadiabatic contributions we show that the adiabatic contribution, which is proportional to $T^{2}$ at low temperatures and goes as $T^{3}$ at high temperatures, dominates the nonadiabatic contribution for temperatures above a cross--over temperature, $T_{c}$, which is between 0.5 and 0.8 $T_{m}$, where $T_{m}$ is the melting temperature of the metal. The nonadiabatic contribution falls as $T^{-1}$ for temperatures roughly above the average phonon frequency.

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