Renormalization group approach to anisotropic superconductivity

TL;DR

This paper uses a renormalization-group approach to analyze anisotropic superconductivity, deriving generalized Eliashberg equations and exploring how different electron-boson couplings influence superconducting instabilities.

Contribution

It introduces a renormalization-group method that incorporates retardation effects to study anisotropic electron-boson couplings and derives generalized Eliashberg equations for complex momentum dependencies.

Findings

Superconducting instabilities depend on anisotropic electron-boson couplings.

Competition exists between different symmetry order parameters.

Frequency dependence of vertices varies with coupling strength.

Abstract

The superconducting instability of the Fermi liquid state is investigated by considering anisotropic electron-boson couplings. Both electron-electron interactions and anisotropic electron-boson couplings are treated with a renormalization-group method that takes into account retardation effects. Considering a non-interacting circular Fermi surface, we find analytical solutions for the flow equations and derive a set of generalized Eliashberg equations. Electron-boson couplings with different momentum dependences are studied, and we find superconducting instabilities of the metallic state with competition between order parameters of different symmetries. Numerical solutions for some couplings are given to illustrate the frequency dependence of the vertices at different coupling regimes.