Restoring gauge invariance in conventional fluctuation corrections to a superconductor

TL;DR

This paper derives the complete set of fluctuation correction diagrams for ultraclean superconductors, identifying an essential additional diagram that restores gauge invariance and correct electromagnetic response.

Contribution

It introduces an additional diagram necessary for gauge invariance in fluctuation corrections, resolving a key issue in the conventional formalism.

Findings

Standard diagrams are insufficient for gauge invariance

An additional diagram is essential for correct electromagnetic response

All microscopic diagrams are encompassed within a Gaussian-level effective action

Abstract

The complete set of diagrams for conventional fluctuation corrections to the normal state of an ultraclean superconductor is derived using the functional-integral approach. The standard diagrams which characterize the fluctuation phase of a superconductor, namely, Aslamazov-Larkin, Maki-Thompson, and Density of States, are obtained and proved to be insufficient to produce a gauge-invariant electromagnetic response. An additional diagram is derived, and it is found to be essential for resolving a problematic and underappreciated aspect of the conventional fluctuation formalism. It is only with the inclusion of this additional diagram that the theory is now rendered gauge invariant and does not display a normal-state Meissner effect. It is shown that not only the Aslamazov-Larkin term but all of the microscopic diagrams are encapsulated within a Gaussian-level treatment of the effective action.