Practically universal representation of the Helfand-Werthamer upper critical field for any transport scattering rate

TL;DR

This paper presents a simple, accurate approximation for the temperature dependence of the upper critical magnetic field in isotropic superconductors, valid across all transport scattering rates, aiding experimental data analysis.

Contribution

It introduces a universal scaling formula for the upper critical field applicable to any transport scattering rate in isotropic superconductors.

Findings

Provides a simple approximation valid across the entire temperature range

Accurately models the upper critical field for any transport scattering rate

Facilitates experimental data analysis with a universal formula

Abstract

The simplified scaling of the orbital upper critical field, $H_{c2}(T)$, for the isotropic case is discussed. To facilitate the analysis of the experimental data, we suggest a simple but accurate approximation in the entire temperature range of the scaled upper critical field valid for any transport scattering rate $H_{c2}/H_{c2}(0) \approx (1-t^2)/(1+0.42 \,t^{1.47})$.