Ab-initio theory of superconductivity - I: Density functional formalism and approximate functionals

TL;DR

This paper develops a comprehensive ab-initio density functional theory framework for superconductors, incorporating electron, superconducting, and nuclear densities, with approximations derived from many-body perturbation theory, enabling parameter-free predictions.

Contribution

It introduces a formally exact density functional formalism for superconductors, coupling electron, superconducting, and nuclear densities with new exchange-correlation functionals derived from diagrammatic techniques.

Findings

Formulation of coupled Kohn-Sham and Schroedinger equations for superconductors.

Derivation of exchange-correlation functionals using many-body perturbation theory.

Achieves a parameter-free, ab-initio description of superconducting materials.

Abstract

A novel approach to the description of superconductors in thermal equilibrium is developed within a formally exact density-functional framework. The theory is formulated in terms of three ``densities'': the ordinary electron density, the superconducting order parameter, and the diagonal of the nuclear N-body density matrix. The electron density and the order parameter are determined by Kohn-Sham equations that resemble the Bogoliubov-de Gennes equations. The nuclear density matrix follows from a Schroedinger equation with an effective N-body interaction. These equations are coupled to each other via exchange-correlation potentials which are universal functionals of the three densities. Approximations of these exchange-correlation functionals are derived using the diagrammatic techniques of many-body perturbation theory. The bare Coulomb repulsion between the electrons and the electron-phonon interaction enter this perturbative treatment on the same footing. In this way, a truly ab-initio description is achieved which does not contain any empirical parameters.