The thermodynamics and the inverse isotope effect of superconducting palladium hydride compounds under pressure

We present in this paper a general method to calculate the thermodynamics and the isotope effect under pressure within the Migdal-Eliashberg theory. We apply this method to Palladium hydrides. We have considered the crystal lattice to be zincblende taking into account the experimental evidence for both PdH and PdD at temperatures below 55 K. We have studied, in particular, the changes induced by pressure in the critical temperature, Tc, in the specific heat jump at Tc, in the energy gap at T=0K and in the deviation function D(t). Replacement of hydrogen by deuterium in palladium hydride results in a higher superconducting temperature and in an anomalous isotope effect coefficient, α. The behaviour under pressure of the isotope effect coefficient can be explained taking into account the change in Tc due to the change in both, the electron-phonon and the electron-electron interactions. We get a very good agreement with experiment where the data exist. This method represents a basis on which the thermodynamics of other hydrides under pressure can be studied.