The Thermodynamics and the Inverse Isotope Effect of superconducting PdH and PdD under pressure

We present in this paper the thermodynamics of superconducting PdH and PdD under pressure. We make use of a general method to calculate the thermodynamics under pressure within the Migdal-Eliashberg theory. 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, $T_c$, in the specific heat jump at $T_c$, in the energy gap at $T=0K$, in the deviation function $D(t)$ and in the isotope effect coefficient, $\alpha$. We get a very good agreement with experiment where this data exist. This method represents a basis on which the thermodynamics of other hydrides under pressure can be calculated.