When materials undergo a phase transition from the normal to the superconducting state the magnetic field inside is expelled, due to the Meissner effect. However, in certain materials (the so-called Type II Superconductors) and when the field strength is large enough magnetic field can enter the sample in the form of vortices. The repulsive interaction between vortices gives rise to the famous Abrikosov lattice, a triangular arangement of vortices that has been succesfully caracterised both theoretically and experimentally. For mesoscopic samples, boundary conditions might largely effect the observed final configuration.

In recent years, a new family of superconductors based on Iron showed that a nematic phase, i.e a phase with spontaneous breaking of the C4 crystaline symmetry) can appear which has profound implications on physical properties. This anisotropy can be observed directly via the elongation of the vortex cores, going from a circular to an elliptical shape. It is expected that the different vortex shape has an effect on the resulting lattice configuration. In addition, due to the Ising character of the nematic order parameter, nematic domains walls can be present.

In this work, we analyse the influence of nematicity in the vortex lattice configurations in the framework of a Ginzburg-Landau type theory with two coupled order parameters. We performed numerical simulations using the Geophysical High-Order Suite for Turbulence (GHOST), a highly scalable pseudo-spectral code used to solve Partial Diffential Equations often encountered in studies of turbulent flows and magnetohydrodinamics. We modified this code to include the dynamics of the electromagnetic vector potential and the nematic order and study vortex lattice configurations when nematicity is constant and when it forms a domain wall. Our results show that the vortex lattice undergoes a transition from triangular to rectangular when nematicity is constant. Also, when nematicity forms domains, separated by domain walls, we find that superconductivity is depressed and therefore the wall can act as a channel for vortex entry. Finally, we study the competing role of the repulsive vortex-vortex interaction and the vortex-domain wall interaction as a function of coupling parameters.