Vortex matter in superconducting films with different nanopatterns

In this work, we numerically investigated the transport and magnetic properties of a superconducting thin square film containing two antidots arranged in three distinct geometries: circle–circle (cc), rhombus–rhombus (rr) and rhombus–circle (rc). By solving the generalized time-dependent Ginzburg–Landau nonlinear partial differential equations, we analyzed two complementary scenarios: (i) in the absence of an external magnetic field ([Formula: see text]) under an applied direct current ([Formula: see text]) and (ii) in the absence of applied current ([Formula: see text]) but under an external magnetic field ([Formula: see text]). Our findings reveal that the internal surface topology of the antidots plays a decisive role in current crowding effects, which, together with short separation distances, enhances vortex nucleation events through local concentration of the screening current density and the consequent suppression of the Bean–Livingston barrier. At larger separations, the critical current density [Formula: see text], the individual pinning strength of each antidot, mainly governs. In contrast, geometric asymmetry manifests itself as a nonuniform phase gradient reflecting the interplay between the strong pinning of the circular antidot and the weaker pinning of the rhombus. Furthermore, the penetration magnetic field exhibits an inverse dependence on the antidot separation up to a saturation threshold, directly linked to both the internal surface topology and the London penetration depth [Formula: see text]. The analysis of magnetization plateaus allowed us to determine the optimal geometry and separation distance that maximizes the Bean–Livingston barrier, thus stabilizing the Meissner state. With this in mind, we found a specific configuration for which the energy barrier is at its maximum. Beyond providing insights into the mechanisms of vortex–antivortex nucleation and kinematic vortex formation, these results establish design guidelines for controlled vortex manipulation in superconducting devices, with potential applications in superconducting memory, fluxonics and low-dissipation circuits.