Orbital upper critical field of type-II superconductors with pair breaking

TL;DR

This paper evaluates the orbital upper critical field in isotropic type-II superconductors considering pair-breaking effects, revealing suppression of $H_{c2}$ and modifications to its temperature dependence due to pair-breaking scattering.

Contribution

It introduces a comprehensive model for the orbital upper critical field incorporating arbitrary transport and pair-breaking scattering rates, including a phenomenological approach for magnetic field-induced pair-breaking.

Findings

Pair-breaking suppresses $H_{c2}$ and lowers the $h^*(0)$ ratio from 0.7 to 0.5.

The model predicts positive curvature of $H_{c2}(T)$ and low-temperature upturns.

Transport scattering enhances $H_{c2}$, contrasting pair-breaking effects.

Abstract

The orbital upper critical field $H_{c2} $ is evaluated for isotropic materials with arbitrary transport and pair-breaking scattering rates. It is shown that unlike transport scattering which enhances $H_{c2} $, the pair breaking suppresses the upper critical field and reduces the dimensionless ratio $h^*(0)=H_{c2}(0)/T_c(dH_{c2}/dT)_{T_c} $ from the Helfand-Werthamer value of $\approx 0.7$ to 0.5 for a strong pair-breaking. $h^*(T)$ is evaluated for arbitrary transport and pair-breaking scattering. A phenomenological model for the pair-breaking suppression by magnetic fields is introduced. It shows qualitative features such as a positive curvature of $H_{c2}(T) $ and the low temperature upturn usually associated with multi-band superconductivity.