Ginzburg-Landau approach to the vortex-domain wall interaction in superconductors with nematic order

In this work, we study the interaction between vortices and nematic domain walls within the framework of a Ginzburg-Landau approach. The free energy of the system is written in terms of a complex order parameter characteristic of s-wave superconductivity and a real (Ising-type) order parameter associated with nematicity. The interaction between both order parameters is described by a biquadratic and a trilinear derivative term. To study the effects of these interactions, we solve the time-dependent dissipative Ginzburg-Landau equations using a highly effective pseudospectral method by which we calculate the trajectories of a vortex that, for different coupling parameters, is either attracted or repelled by a wall, as well as of the wall dynamics. We show that despite its simplicity, this theory displays many phenomena observed experimentally in Fe-based superconductors. In particular, we find that the sign of the biquadratic term determines the attractive (pinning) or repulsive (antipinning) character of the interaction, as observed in FeSe and BaFeCoAs compounds, respectively. The trilinear term is responsible for the elliptical shape of vortex cores as well as the orientation of the axes of the ellipses and vortex trajectories with respect to the axes of the structural lattice. For the case of pinning, we show that the vortex core is well described by a heart-shaped structure in agreement with scanning tunneling microscopy experiments performed in FeSe.