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} <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mover> <mml:mi>z</mml:mi> <mml:mo accent="true">̂</mml:mo> </mml:mover> </mml:math> -direction. The transport currents are included as two opposite polarities, J;gt0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and J&lt;0 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>J</mml:mi> <mml:mo>&lt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> , respectively. Using the generalized time-dependent Ginzburg-Landau theory and considering the order parameter \kappa <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>κ</mml:mi> </mml:math> , we focus on two scenarios: a fixed external magnetic field with variable \kappa <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>κ</mml:mi> </mml:math> , and fixed \kappa <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>κ</mml:mi> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>κ</mml:mi> </mml:math> and the external magnetic field applied. Furthermore, our observations reveal that the current polarity strongly influences the vortex configuration, the parameter \kappa <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>κ</mml:mi> </mml:math> , 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.