On the Calculation of the Inverse Isotope Effect in PdH(D): A Migdal-Eliashberg Theory Approach

Replacement of hydrogen by deuterium in palladium hydride results in higher superconducting temperatures and an anomalous isotope effect that has not been yet fully explained. In this work, we try a new approach to the explanation of the inverse isotope effect in PdH(D). Our approach introduces two new aspects. First, we took into account the experimental evidence that at temperatures below 50 K, the crystal structure of PdH and of PdD is zincblende. Second, we take into account not only the influence of the electron-phonon interaction but also the electron-electron interaction contribution to the isotope coeffiecient due tothe replacement of deuterium in the place of hydrogen. We used the Migdal-Eliashberg theory to perform our ab initio calculations. We found in this picture that the electron-electron interaction is considerably reduced by the isotope substitution and is the most important factor to explain the inverse isotope effect. We found $\Delta T_c^{total}=2.224\:K$ and $\alpha= -0.3134$ in excellent agreement with the values found experimentally.