We propose a practical alternative to Eliashberg equations for the ab initio calculation of superconducting transition temperatures and gap functions. Within the recent density functional theory for superconductors, we develop an exchange-correlation functional that retains the accuracy of Migdal's approximation to the many-body electron-phonon self-energy, while having a simple analytic form. Our functional is based on a parametrization of the Eliashberg self-energy for a superconductor with a single Einstein frequency, and enables density functional calculations of experimental excitation gaps. By merging electronic structure methods and Eliashberg theory, the present approach sets a new standard in quality and computational feasibility for the prediction of superconducting properties.
Bibliographical noteFunding Information:
A. S. acknowledges useful discussions with S. Pittalis, A. Linscheid, and J. K. Dewhurst. E. K. U. G. acknowledges financial support by the European Research Council Advanced Grant FACT (No. ERC-2017-AdG-788890).
© 2020 authors. Published by the American Physical Society. Open access publication funded by the Max Planck Society.