Superconductivity in Pb, H under extreme pressure and CaBeSi, in the framework of the density functional theory for superconductors, is discussed. A detailed analysis on how the electron-phonon and electron-electron interactions combine together to determine the superconducting gap and critical temperature of these systems is presented. Pb, H under pressure and CaBeSi are multigap superconductors. We will address the question under which conditions does a system exhibits this phenomenon. The presented results contribute to the understanding of multiband and anisotropic superconductivity, which has received a lot of attention since the discovery of MgB2, and show how it is possible to describe the superconducting properties of real materials on a fully {\it ab-initio} basis.
@article{arxiv.0902.1952,
title = {Multiband superconductivity in Pb, H under pressure and CaBeSi from {\it ab-initio} calculations},
author = {C. Bersier and A. Floris and P. Cudazzo and G. Profeta and A. Sanna and F. Bernardini and M. Monni and S. Pittalis and S. Sharma and H. Glawe and A. Continenza and S. Massidda and E. K. U. Gross},
journal= {arXiv preprint arXiv:0902.1952},
year = {2009}
}