# Metastability and bifurcation in superconducting nanorings

## TL;DR

This paper introduces a numerical approach to analyze metastability and bifurcation phenomena in superconducting nanorings, providing insights into critical currents, activation energies, and their dependence on temperature and current.

## Contribution

It presents a novel numerical method based on the Usadel equation to study stationary points, metastability, and bifurcation in superconducting nanorings, including a correction to Bardeen's formula.

## Key findings

- Computed critical current as a function of temperature.
- Mapped activation energy landscape for nanorings.
- Identified discrepancies with experimental data at high currents.

## Abstract

We describe an approach, based on direct numerical solution of the Usadel equation, to finding stationary points of the free energy of superconducting nanorings. We consider both uniform (equilibrium) solutions and the critical droplets that mediate activated transitions between them. For the uniform solutions, we compute the critical current as a function of the temperature, thus obtaining a correction factor to Bardeen's 1962 interpolation formula. For the droplets, we present a metastability chart that shows the activation energy as a function of the temperature and current. A comparison of the activation energy for a ring to experimental results for a wire connected to superconducting leads reveals a discrepancy at large currents. We discuss possible reasons for it. We also discuss the nature of the bifurcation point at which the droplet merges with the uniform solution.