Ab Initio Theory of Superconductivity in a Magnetic Field I. : Spin Density Functional Theory For Superconductors and Eliashberg Equations

TL;DR

This paper introduces a first-principles density functional theory called SpinSCDFT to describe the interplay of magnetism and superconductivity, along with Eliashberg equations for such systems.

Contribution

It extends the Hohenberg-Kohn theorem to magnetic superconductors and derives an exchange-correlation functional based on Eliashberg theory.

Findings

Development of SpinSCDFT framework

Derivation of exchange-correlation functional from Eliashberg theory

Formulation of reference Eliashberg equations with magnetism

Abstract

We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory: SpinSCDFT, by extending the Hohenberg-Kohn theorem and constructing the non-interacting Kohn- Sham system. An exchange-correlation functional for SpinSCDFT is derived from the Sham Schl\"uter connection between the SpinSCDFT Kohn-Sham and a self-energy in Eliashberg approximation. The reference Eliashberg equations for superconductors in the presence of magnetism are also derived and discussed.