Gaussian fluctuation corrections to the BCS mean field gap amplitude at zero temperature

TL;DR

This paper calculates the Gaussian fluctuation correction to the BCS superconducting gap at zero temperature, finding it small due to cancellations at high energies and momenta, refining the mean-field approximation.

Contribution

It provides a detailed computation of fluctuation corrections to the BCS gap, highlighting the dominant high-energy contributions and their cancellation effects.

Findings

Correction is smaller by the weak-coupling factor gN_0

High energies and momenta dominate the correction

Cancellation reduces the fluctuation impact at high energies

Abstract

The leading (Gaussian) fluctuation correction to the weak coupling zero temperature BCS superconducting gap equation is computed. We find that the dominant contribution comes from the high energies and momenta (compared to the gap) and gives a correction smaller by the weak-coupling factor $gN_0$ than the mean-field terms. This correction is small due to cancellation of singular contributions from the amplitude and phase mode at high energies and momenta.