Four-fold anisotropy of the parallel upper critical magnetic field in a pure layered d-wave superconductor at $T = 0$

TL;DR

This paper provides the first accurate calculation of four-fold anisotropy in the parallel upper critical magnetic field at zero temperature in pure layered d-wave superconductors, relevant for high-Tc and organic materials.

Contribution

It introduces a novel precise calculation method for the anisotropy at T=0, overcoming limitations of previous approximations for open electron orbits in Q2D superconductors.

Findings

Four-fold anisotropy reaches its maximum at T=0.

Results applicable to high-Tc and organic Q2D superconductors.

Accurate calculation method for open orbit effects at T=0.

Abstract

It is well known that a four-fold symmetry of the parallel upper critical magnetic field disappears in the Ginzburg-Landau (GL) region in quasi-two-dimensional (Q2D) $d$-wave superconductors. Therefore, it has been accurately calculated so far as a correction to the GL results, which is valid close to superconducting transition temperature and is expected to be stronger at low temperatures. As to the case $T=0$, some approximated methods have been used, which are good only for closed electron orbits and unappropriate for the open orbits which exist in a parallel magnetic field in Q2D superconductors. For the first time, we accurately calculate the four-fold anisotropy of the parallel upper critical magnetic field in a pure Q2D $d$-wave superconductor at $T=0$, where it has the highest possible value. Our results are applicable to Q2D $d$-wave high-Tc and organic superconductors.