In this study, we explore the behavior of a superconducting meso-wedge geometry in 3+1 dimensions (three spatial dimensions plus time) subjected to external transport currents at its boundaries and surfaces, as well as external fields applied along the z z ̂ -direction. The transport currents are included as two opposite polarities, J;gt0 J > 0 and J J 0, respectively. Using the generalized time-dependent Ginzburg-Landau theory and considering the order parameter κ, we focus on two scenarios: a fixed external magnetic field with variable κ, and fixed κ with variable external magnetic field. As a result, under both scenarios, we analyze the voltage-current characteristics of the superconducting meso-wedge, finding that the critical currents differ between polarities, demonstrating the system’s non-reciprocity. We further examine the efficiency of the diode as a function of κ and the external magnetic field applied. Furthermore, our observations reveal that the current polarity strongly influences the vortex configuration, the parameter κ, and the applied magnetic field. In particular, the formation of Abrikosov-type vortices exhibits pronounced inhomogeneity depending on the direction of the transport currents. This underscores that the diode effect in the superconducting meso-wedge is intimately associated with the anisotropic nucleation of Abrikosov vortices. Notably, the emergence of polarity-dependent vortex patterns can serve as a distinctive hallmark of the diode effect in these superconducting meso-wedge geometries.
Aguirre et al. (2026) studied this question.