Self-assembled vortex crystals induced by inhomogeneous magnetic textures.

We investigate the self-assembly of vortices in a type-II superconducting disk subjected to highly nonuniform confining potentials produced by inhomogeneous magnetic textures. Using a series of numerical experiments performed within the Ginzburg-Landau theory, we show that vortices can arrange spontaneously in highly nonuniform, defect-free crystals, reminiscent of conformal lattices, even though the strict conditions for the conformal crystal are not fulfilled. These results contradict continuum-limit theory, which predicts that the order of a nonuniform crystal is unavoidably frustrated by the presence of topological defects. By testing different cooling routes of the superconductor, we observed several different self-assembled configurations, each of which corresponding to one in a set of allowed conformal transformations, which depends on the magnetic and thermal histories of the system.