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In this work we study the interaction between vortices and nematic domainwalls within the framework of a Ginzburg Landau approach. The free energy ofthe system is written in terms of a complex order parameter characteristic of$s$-wave superconductivity and a real (Ising type) order parameter associatedto nematicity. The interaction between both order parameters is described by abiquadratic and a trilinear derivative term. To study the effects of theseinteractions we solve the time-dependent dissipative Ginzburg Landau equationsusing a highly performant pseudospectral method by which we calculate thetrajectories of a vortex that, for different coupling parameters, is eitherattracted or repelled by a wall, as well as of the wall dynamics. We show thatdespite its simplicity, this theory displays many phenomena observedexperimentally in Fe-based superconductors. In particular we find that the signof the biquadratic term determines the attractive (pining) or repulsive(antipining) character of the interaction, as observed in FeSe and BaFeCoAscompounds respectively. The trilinear term is responsible for the ellipticalshape of vortex cores as well as for the orientation of the axes of theellipses and vortex trajectories with respect to the axes of the structurallattice. For the case of pining, we show that the vortex core is well describedby a heart-shaped structure in agreement with STM experiments performed inFeSe.

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