Parametrization of Nambu vertex in a singlet superconductor

TL;DR

This paper studies the properties and flow of the Nambu two-particle vertex in a spin-singlet superconductor, revealing how to efficiently parametrize singularities in its momentum and energy dependence.

Contribution

It introduces a simplified, spin-rotation invariant form of the Nambu vertex and demonstrates a method to isolate and parametrize singularities in the vertex's momentum and energy dependencies.

Findings

Exact flow solution for a mean-field model with BCS and forward scattering

Identification of singularities in the vertex at the critical energy scale

Efficient parametrization of momentum and energy dependences

Abstract

We analyze general properties of the effective Nambu two-particle vertex and its renormalization group flow in a spin-singlet superconductor. In a fully spin-rotation invariant form the Nambu vertex can be expressed by only three distinct components. Solving exactly the flow of a mean-field model with reduced BCS and forward scattering interactions, we gain insight into the singularities in the momentum and energy dependences of the vertex at and below the critical energy scale for superconductivity. Using a decomposition of the vertex in various interaction channels, we manage to isolate singular momentum and energy dependences in only one momentum and energy variable for each term, such that the singularities can be efficiently parametrized.