Vortex matter in labyrinthine configurations

In this work, we investigate numerically the vortex dynamics in thin superconducting films patterned with labyrinthine geometries using numerical solutions of the time-dependent Ginzburg–Landau equations (TDGL). We analyzed three complementary scenarios: (i) in the absence of an external magnetic field (H=0.0) under an applied direct current (J) and (ii) in the absence of an applied current (J=0.0) but under an external magnetic field (H) and finally (iii) in the absence of an external magnetic field (H=0.0) under an applied current with negative and positive polarity while varying the Ginzburg–Landau parameter (κ=2.0,3.0,4.0,5.0,6.0). By generating maze-like domains through a randomized Kruskal algorithm and sweeping the applied magnetic field H, we determine the magnetization M_z and extract the first critical field H₁. Our simulations reveal a pronounced dependence of H₁ on the underlying geometry of the labyrinth, showing that the intricate network of corridors significantly modifies the onset of vortex penetration. Current–voltage measurements obtained from the dynamics of TDGL reveal a clear variation in the critical current with the Ginzburg–Landau parameter (κ), highlighting the roles of coherence length and penetration depth in these confined structures. Despite the intentional breaking of spatial symmetry by the maze design, no superconducting diode effect is observed within the explored parameter space. Smaller labyrinth sections showed nearly zero magnetic penetration, preserving superconductivity at higher fields in agreement with Bean–Livingston barrier behavior.