Ginzburg-Landau theory of the superheating field anisotropy of layered superconductors

TL;DR

This paper analyzes how material anisotropy affects the superheating field in layered superconductors, providing theoretical insights and quantitative estimates relevant for superconducting applications.

Contribution

It develops a Ginzburg-Landau based framework to quantify superheating field anisotropy and maps the phase diagram across different material parameters.

Findings

High anisotropy near zero temperature suggested for MgB2.

Significant anisotropy occurs only with large crystal anisotropy and small .

Small anisotropies are expected near the critical temperature for typical superconductors.

Abstract

We investigate the effects of material anisotropy on the superheating field of layered superconductors. We provide an intuitive argument both for the existence of a superheating field, and its dependence on anisotropy, for $\kappa = \lambda / \xi$ (the ratio of magnetic to superconducting healing lengths) both large and small. On the one hand, the combination of our estimates with published results using a two-gap model for MgB${}_2$ suggests high anisotropy of the superheating field near zero temperature. On the other hand, within Ginzburg-Landau theory for a single gap, we see that the superheating field shows significant anisotropy only when the crystal anisotropy is large and the Ginzburg-Landau parameter $\kappa$ is small. We then conclude that only small anisotropies in the superheating field are expected for typical unconventional superconductors near the critical temperature. Using a generalized form of Ginzburg Landau theory, we do a quantitative calculation for the anisotropic superheating field by mapping the problem to the isotropic case, and present a phase diagram in terms of anisotropy and $\kappa$, showing type I, type II, or mixed behavior (within Ginzburg-Landau theory), and regions where each asymptotic solution is expected. We estimate anisotropies for a number of different materials, and discuss the importance of these results for radio-frequency cavities for particle accelerators.