Vortices in a Ginzburg Landau Theory of Superconductors with Nematic Order

TL;DR

This paper investigates how nematic order influences vortex interactions in superconductors using a Ginzburg Landau model, revealing competing effects that alter vortex attraction and repulsion.

Contribution

It introduces a pseudo-spectral numerical method to study vortex interactions in a coupled superconductor-nematic system within the Ginzburg Landau framework.

Findings

Nematic coupling can induce either attractive or repulsive vortex interactions.

The pseudo-spectral method enhances computational efficiency and accuracy.

Nematic effects lead to a complex interplay affecting vortex behavior.

Abstract

In this work we explore the interplay between superconductivity and nematicity in the framework of a Ginzburg Landau theory with a nematic order parameter coupled to the superconductor order parameter, often used in the description of superconductivity of Fe based materials. In particular, we focus on the study of the vortex-vortex interaction in order to determine the way nematicity affects its attractive or repulsive character. To do so, we use a dynamical method based on the solutions of the Time Dependent Ginzburg Landau equations in a bulk superconductor. An important contribution of our work is the implementation of a pseudo-spectral method to solve the dynamics, known to be highly efficient and of very high order in comparison to the usual finite differences/elements methods. The coupling between the superconductor and the (real) nematic order parameters is represented by two terms in the free energy: a biquadratic term and a coupling of the nematic order parameter to the covariant derivatives of the superconductor order parameter. Our results show that there is a competing effect: while the former independently of its competitive or cooperative character generates an attractive vortex-vortex interaction, the latter always generates a repulsive interaction.