Combined effect of thermal and quantum fluctuations in superconducting nanostructures: a path integral approach

TL;DR

This paper develops a path integral method to analyze the combined effects of thermal and quantum fluctuations in zero-dimensional superconductors, providing new expressions valid across all temperatures.

Contribution

It introduces a novel path integral approach that includes both thermal and quantum fluctuations in superconducting nanostructures, avoiding divergences at low temperatures.

Findings

Derived new expressions for the partition function and order parameter

Results agree with RPA and SPA in respective temperature limits

Avoided divergences at low temperatures through non-perturbative treatment

Abstract

We study the combined effect of thermal and quantum fluctuations in a zero dimensional superconductor. By using path integral techniques, we obtain novel expressions for the partition function and the superconducting order parameter which include both types of fluctuations. Our results are valid for any temperature and to leading order in \delta/\Delta_{0} where \delta is the mean level spacing and \Delta_{0} is the bulk energy gap. We avoid divergences at low temperatures, previously reported in the literature, by identifying and treating non-perturbatively a low-energy collective mode. In the low and high temperature limit our results agrees with those from the random phase (RPA) and the static path approximation (SPA) respectively.