Thermodynamic properties of a metal near a Fermi surface topological transition: the anomalous electron-phonon interaction contribution

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Abstract
A compression induced Fermi surface topological transition leads to volume dependent anomalies of the phonon spectrum which may affect the metal thermodynamic behavior. The free energy F is calculated by the thermal Green function formalism. The calculation is perturbative and valid in intermediate temperature range. The result includes the anomalous purely electronic Lifshitz contribution and a non-analytical electron-phonon interaction contribution. The effect on a possible first order isostructural transition is studied: the electron-phonon interaction is found to always favour such a transition.