Renormalization-group approach to superconductivity: from weak to strong electron-phonon coupling

TL;DR

This paper applies a renormalization group approach to analyze superconductivity driven by electron-electron and electron-phonon interactions, covering the entire coupling spectrum from weak to strong, and offers insights into the instability of Fermi liquids.

Contribution

It introduces a numerical solution to RG equations for superconductivity, capturing the crossover from weak to strong coupling and providing an analytical ansatz for these regimes.

Findings

RG flow of couplings analyzed with retardation effects

Crossover from weak to strong coupling characterized

Numerical results suggest an analytical solution in asymptotic limits

Abstract

We present the numerical solution of the renormalization group (RG) equations derived in Ref. [1], for the problem of superconductivity in the presence of both electron-electron and electron-phonon coupling at zero temperature. We study the instability of a Fermi liquid to a superconductor and the RG flow of the couplings in presence of retardation effects and the crossover from weak to strong coupling. We show that our numerical results provide an ansatz for the analytic solution of the problem in the asymptotic limits of weak and strong coupling.