Vortex nucleation barrier in superconductors beyond the Bean-Livingston approximation: A numerical approach for the sphaleron problem in a gauge theory

TL;DR

This paper introduces a numerical method to calculate vortex nucleation barriers in superconductors, accounting for complex effects like geometry and pinning, which are vital for optimizing superconductor applications.

Contribution

It generalizes the string method to gauge field theories, enabling the exploration of energy barriers and saddle points in superconductor vortex nucleation.

Findings

Successfully computes vortex nucleation barriers considering nonlinearity and geometry.

Analyzes effects of surface roughness and pinning on nucleation barriers.

Provides a new tool for studying energy landscapes in superconductors.

Abstract

The knowledge of vortex nucleation barriers is crucial for applications of superconductors, such as single-photon detectors and superconductor-based qubits. Contrarily to the problem of finding energy minima and critical fields, there are no controllable methods to explore the energy landscape, identify saddle points, and compute associated barriers. Similar problems exist in high-energy physics where the saddle-point configurations are called sphalerons. Here, we present a generalization of the string method to gauge field theories, which allows the calculation of energy barriers in superconductors. We solve the problem of vortex nucleation, assessing the effects of the nonlinearity of the model, complicated geometry, surface roughness, and pinning.