Abstract

We propose a practical alternative to Eliashberg equations for the abinitio 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.

Highlights

  • We propose a practical alternative to Eliashberg equations for the ab initio calculation of superconducting transition temperatures and gap functions

  • 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

  • In SCDFT, both the normal density nðrÞ and the superconducting order parameter χðr; r0Þ of the system are reproduced by a noninteracting Kohn-Sham (KS) system, where the exchangecorrelation effects on superconductivity are included via the pairing potential Δsðr; r0Þ1⁄2n; χŠ

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Summary

Introduction

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.

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