Eliashberg equations derived from the functional renormalization group

TL;DR

This paper demonstrates how the fermionic functional renormalization group can be extended to derive the Eliashberg equations for superconductivity, providing a unified framework across all temperatures including the symmetry-broken phase.

Contribution

It introduces a method to derive Eliashberg equations from the fRG flow, bridging a gap between renormalization group techniques and superconducting theory.

Findings

Reproduces Eliashberg equations from fRG flow

Applicable across all temperatures including the superconducting phase

Potential for including vertex corrections in future extensions

Abstract

We describe how the fermionic functional renormalization group (fRG) flow of a Cooper+forward scattering problem can be continued into the superconducting state. This allows us to reproduce from the fRG flow the fundamental equations of the Eliashberg theory for superconductivity at all temperatures including the symmetry-broken phase. We discuss possible extensions of this approach like the inclusion of vertex corrections.