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.
Highlights
The knowledge of vortex nucleation barriers is crucial for applications of superconductors, such as singlephoton detectors and superconductor-based qubits
The Meissner state can survive as a metastable state, causing the phenomenon known as magnetic superheating [1]
The problem of a vortex entry barrier consists of finding the sphaleron, i.e., the saddle point which separates two stable states in a gauge theory [18,19,20,21,22]
Summary
Vortex nucleation barrier in superconductors beyond the Bean-Livingston approximation: A numerical approach for the sphaleron problem in a gauge theory. We solve the problem of vortex nucleation, assessing the effects of the nonlinearity of the model, complicated geometry, surface roughness, and pinning. While a microscopically derived Ginzburg-Landau model applies only close to the critical temperature, many aspects of low-temperature vortex physics may under certain conditions be fittable by effective Ginzburg-Landau-type models [30] In this Rapid Communication, we generalize to gauge theories the simplified string method [31]. This allows us to perform surface barrier calculations in type-II superconductors for vortex nucleation ( Fn) and escape ( Fe), by computing the minimum energy path of the transition in the Ginzburg-Landau
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