The Upper Critical Field for Unconventional Superconducting Film: a Kink due to the Boundary Conditions

TL;DR

This paper investigates how boundary conditions influence the upper critical field in unconventional superconducting films, revealing that boundary quality and film thickness can cause temperature-dependent kinks, aiding in identifying pairing types.

Contribution

It introduces a microscopic derivation of boundary conditions and demonstrates their significant effect on the upper critical field and kink behavior in superconducting films.

Findings

Boundary conditions significantly affect the upper critical field.

Kinks in the critical field depend on boundary quality and film thickness.

A new test distinguishes pairing types in hexagonal superconductors.

Abstract

Boundary conditions for unconventional superconducting order parameter are obtained on the basis of a microscopic theory. The upper critical field in a superconducting film is examined for unconventional superconductors with two-component order parameter and is compared with the case of accidental degeneracy. It is shown, that for both cases temperature dependences of the upper critical field in a superconducting film may depend substantially on the quality of boundaries, and under certain conditions have a kink due to the influence of film boundaries. The location of a kink point appears to be dependent on a film thickness. If for a massive sample there is another reason for the existance of a kink, the interplay of the reasons may lead to a specific behaviour of a kink point location as a function of a temperature or a film thickness. A new test is suggested permitting to distinguish between $E_{1}$ and $E_{2}$ types of pairing in a hexagonal superconductor near $T_c$.