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Abstract
We implement the Bogoliubov-de Gennes (BdG) equation in a screened Korringa-Kohn-Rostoker (KKR) method for solving, self-consistently, the superconducting state for 3d crystals. This method combines the full complexity of the underlying electronic structure and Fermi surface geometry with a simple phenomenological parametrisation for the superconductivity. We apply this theoretical framework to the known s-wave superconductors Nb, Pb, and MgB$_2$. In these materials multiple distinct peaks at the gap in the density of states were observed, showing significant gap anisotropy which is in good agreement with experiment. Qualitatively, the results can be explained in terms of the k-dependent Fermi velocities on the Fermi surface sheets exploiting concepts from BCS theory.
Highlights
The structure of the superconducting gap in s-wave phonon-mediated superconductors may show a surprisingly complex structure
It was limited to the weakcoupling regime, which later was rectified by the Eliashberg theory [16,17] and, more recently, by full density functional theory (DFT) approaches to electron-phonon-coupling-driven superconductivity [18,19]
Gap anisotropy analysis is present in such codes, much of the DFT-based ab initio work focused on other aspects
Summary
The structure of the superconducting gap in s-wave phonon-mediated superconductors may show a surprisingly complex structure Can it show a large degree of anisotropy on the Fermi surface of a given material, but several known examples exhibit clear signatures of two superconducting gaps. Gap anisotropy analysis is present in such codes, much of the DFT-based ab initio work focused on other aspects These aspects are expanding the description of s-wave superconductivity with emphasis on the correct description of the driving mechanism [20,21,22,23,24] or on the extension to unconventional pairing pushing the boundaries in our treatment of iron-based [25], spin [26], and magnetic effects [27,28]
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