Ab-Initio Theory of Superconductivity
E.K.U. Gross
A novel density-functional-type approach to the description of phonon-mediated superconductivity is presented. The goal of this approach is to provide a theory with predictive power, allowing the calculation of material-specific properties such as the critical temperature. To this end, the electron-phonon interaction and the electron-electron repulsion are treated on the same footing. There are no adjustable parameters such as the ${\mu}^*$ of Eliashberg theory. Numerical results for the critical temperature, the isotope effect, the gap function and the jump of the specific heat will be presented for simple metals, for MgB$_2$, and for Li, Al and K under pressure. In particular, for MgB$_2$, the two gaps and the specific heat as function of temperature are in very good agreement with experimental data. For Li and Al under pressure, the calculations explain why these two metals behave very differently, leading to a strong enhancement of superconductivity for Li and to a clear suppression for Al with increasing pressure. For K we predict a behavior similar to Li, i.e. a strong increase of T$_c$ with increasing pressure. Furthermore, the peculiar features of the superconducting phase of calcium intercalated graphite (CaC$_6$) will be analyzed. Finally, results for hydrogen under extreme pressure will be presented. It turns out that hydrogen is a three-gap superconductor whose critical temperature increases with increasing pressure until about 100K (at 500 GPa).
