  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.
