Surface superconductivity and $H_{c3}$ in UPt$_3$

TL;DR

This paper investigates surface superconductivity in UPt₃ using Ginzburg-Landau theory, comparing models with different order parameters, calculating $H_{c3}$ for various orientations, and relating findings to experimental data.

Contribution

It provides a detailed theoretical analysis of $H_{c3}$ in UPt₃ for different order parameter models and predicts experimental signatures for future verification.

Findings

$H_{c3}/H_{c2}$ ratio is mostly 1 or 1.695 depending on orientation.

$H_{c3}$ vs. temperature curves differ between models for various geometries.

Results align with some experimental data and suggest new experimental tests.

Abstract

Surface superconductivity is studied within Ginzburg-Landau theory for two classes of models for the order parameter of UPt$_{3}$. The first class assumes two independent one-dimensional order parameters ($AB$ models), while the second assumes a single two-dimensional order parameter ($E$ models). $H_{c3}$ is calculated for all cases where the surface normal and magnetic field lie along high symmetry directions. Assuming specular reflection, it is found that except when ${\bf H}\parallel{\bf\hat c}$, the ratio $H_{c3}/H_{c2}$ is either unity or equals its `s-wave' value 1.695, although the precise $H_{c3}$ vs. $T$ curve predicted by the $AB$ and $E$ models differs for various geometries. The results are compared with recent experiments, and predictions are made for future experiments.