Simple Ginzburg-Landau Theory for Vortices in a Crystal Lattice

TL;DR

This paper introduces a simple Ginzburg-Landau model incorporating nonlocal interactions to describe vortex lattice structures in superconductors, accounting for crystal lattice effects and thermal fluctuations.

Contribution

It presents a novel phenomenological model that captures the transition from triangular to square vortex lattices and analyzes vortex liquid structure factors nonperturbatively.

Findings

Vortex lattice can range from triangular to square in the model.

Bragg-like peaks with four-fold symmetry appear in vortex liquid structure factors.

Model enables study of thermal fluctuation effects on vortex arrangements.

Abstract

We study the Ginzburg-Landau model with a nonlocal quartic term as a simple phenomenological model for superconductors in the presence of coupling between the vortex lattice and the underlying crystal lattice. In mean-field theory, our model is consistent with a general oblique vortex lattice ranging from a triangular lattice to a square lattice. This simple formulation enables us to study the effect of thermal fluctuations in the vortex liquid regime. We calculate the structure factor of the vortex liquid nonperturbatively and find Bragg-like peaks with four-fold symmetry appearing in the structure factor even though there is only a short-range crystalline order.