Renormalization Group Approach to Strong-Coupled Superconductors

TL;DR

This paper introduces an exact renormalization group method to analyze strongly coupled superconductors, unifying electron interactions and predicting the critical temperature with a new numerical approach.

Contribution

It develops an unbiased RG framework that treats electron-electron and electron-phonon interactions equally, connecting high-temperature instabilities to Eliashberg theory.

Findings

Identifies the temperature T* where Fermi liquid becomes unstable.

Shows T* equals the Eliashberg critical temperature Tc.

Provides a new numerical method to compute Tc from microscopic parameters.

Abstract

We develop an asymptotically exact renormalization group (RG) approach that treats electron-electron and electron-phonon interactions on equal footing. The approach allows an unbiased study of the instabilities of Fermi liquids without the assumption of a broken symmetry. We apply our method to the problem of strongly coupled superconductors and find the temperature T* below which the high-temperature Fermi liquid state becomes unstable towards Cooper pairing. We show that T* is the same as the critical temperature Tc obtained in Eliashberg's strong coupling theory starting from the low-temperature superconducting phase. We also show that Migdal's theorem is implicit in our approach. Finally, our results lead to a novel way to calculate numerically, from microscopic parameters, the transition temperature of superconductors.