Superconducting diode effect in a meso-wedge geometry with Abrikosov vortices

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 $\hat{z}$-direction. The transport currents are included as two opposite polarities, $\textbf{J}>0$ and $\textbf{J}<0$. Using the generalized time-dependent Ginzburg-Landau theory and considering the order parameter $\kappa$, we focus on two scenarios: a fixed external magnetic field with variable $\kappa$, and fixed $\kappa$ 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 $\kappa$ and the external magnetic field applied. Furthermore, our observations reveal that the current polarity strongly influences the vortex configuration, the parameter $\kappa$, 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 systems.