Kohn anomalies and enhanced superconductivity in simple systems under pressure: Insights from the nearly free electron model

The phonon spectrum of sodium is studied using ab initio methods and a simple nearly free electron model in the pressure range where the fcc phase is stable. It is found that the phonon softening previously reported consist of simple Kohn anomalies, the amplitudes of which are increased under pressure; their relative amplitudes and positions are easily understood in terms of the nearly free electron model. Furthermore, it is shown that superconductivity should be enhanced by pressure because of the increased contribution to the Eliashberg function associated to transverse phonon modes.