The Phase Transition to a Square Vortex Lattice in Type-II Superconductors with Fourfold Anisotropy

TL;DR

This paper studies the transition from a distorted hexagonal to a square vortex lattice in tetragonal superconductors, combining perturbative and numerical methods to analyze phase boundaries and anisotropies.

Contribution

It introduces a combined perturbative and numerical approach to analyze the square vortex lattice transition considering fourfold symmetry effects.

Findings

Large corrections to perturbative results near $H_{c2}$

Calculated 4.5% anisotropy at transition temperature

Phase boundary in $H-T$ diagram has positive slope near $H_{c2}$

Abstract

We investigate the stability of the square vortex lattice which has been recently observed in experiments on the borocarbide family of superconductors. Taking into account the tetragonal symmetry of these systems, we add fourfold symmetric fourth-derivative terms to the Ginzburg-Landau(GL) free energy. At $H_{c2}$ these terms may be treated perturbatively to lowest order to locate the transition from a distorted hexagonal to a square vortex lattice. We also solve for this phase boundary numerically in the strongly type-II limit, finding large corrections to the lowest-order perturbative results. We calculate the relative fourfold $H_{c2}$ anisotropy for field in the $xy$ plane to be 4.5% at the temperature, $T_c^{\Box}$, where the transition occurs at $H_{c2}$ for field along the $z$ axis. This is to be compared to the 3.6% obtained in the perturbative calculation. Furthermore, we find that the phase boundary in the $H-T$ phase diagram has positive slope near $H_{c2}$.