Hedin Equations for Superconductors

TL;DR

This paper extends Hedin equations to superconducting systems with electron-phonon interactions, providing a framework to include fluctuations beyond standard approximations for better understanding of superconductivity.

Contribution

The authors derive generalized Hedin equations for superconductors coupled with phonons, incorporating vertex corrections and non-local interactions for advanced fluctuation descriptions.

Findings

Derived continuity equation with superconducting condensate

Formulated vertex corrections as non-local effective interactions

Framework applicable to spin and phase fluctuations in superconductors

Abstract

We generalize Hedin equations to a system of superconducting electrons coupled with a system of phonons. The electrons are described by an electronic Pauli Hamiltonian which includes the Coulomb interaction among electrons and an external vector and scalar potential. We derive the continuity equation in the presence of the superconducting condensate and point out how to cast vertex corrections in the form of a non-local effective interaction that can be used to describe both fluctuations of spin and superconducting phase beyond the screened Coulomb self-energy diagram.