Vortices in a Ginzburg-Landau theory of superconductors with nematic order

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. 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 pseudospectral method to solve the dynamics, known to be highly efficient and of very high order in comparison to the usual finite-differences and -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.