Vortex structure and intervortex interaction in superconducting structures with intrinsic diode effect

TL;DR

This work develops a one-parameter Ginzburg-Landau description for superconducting thin-film hybrids with intrinsic diode (magnetochiral) anisotropy, incorporating a cubic gradient term γ that encodes interfacial spin-orbit coupling and in-plane exchange fields. It yields analytic expressions for chiral distortions of the vortex velocity field, noncentral forces in vortex–antivortex pairs, and geometry-dependent modifications of the Bean–Livingston barrier, and it verifies these predictions with high-accuracy time-dependent GL simulations. The results reveal a vortex-core shift linear in γ, a skewed current distribution around vortices, and anisotropic vortex dynamics, all enabling controlled, nonreciprocal vortex behavior in nanoscale superconducting circuits. These findings offer concrete guidance for designing non-reciprocal superconducting devices, fluxonic logic elements, and kinetic-inductance components, while suggesting experimental probes via scanning probes and magneto-optical imaging.

Abstract

We demonstrate that the intrinsic superconducting diode effect can affect the structure, interactions and dynamics of Abrikosov vortices in non-centrosymmetric superconductor/ferromagnet hybrid structures. The Ginzburg-Landau (GL) theory accounting for the spin-orbit and exchange-field effects predicts a chiral distortion of the superfluid velocity, non-central interaction forces and resulting torque in a vortex-antivortex pair, and anisotropy of the Bean-Livingston barrier. These closed-form results are fully confirmed by time-dependent GL numerical simulations carried out with a fourth-order least-squares finite-difference solver, which captures equilibrium single vortex configuration in realistic mesoscopic geometries. The analysis shows that the cubic gradient term shifts vortex cores by an amount proportional to the in-plane exchange field and simultaneously generates a lateral torque that can rotate entire vortex ensembles, showing how spin-orbit coupling and the exchange field enable breakdown of the vortex-antivortex symmetry in a finite-size sample. By combining transparent analytics with quantitative numerics, the work provides the hallmarks of vortex physics in superconducting structures with an intrinsic diode effect and supplies concrete guidelines for designing non-reciprocal superconducting circuits, fluxonic logic elements, and kinetic-inductance devices.

Figures (14)

• Figure 1: A thin superconducting layer (orange, S) rests on a ferromagnetic insulator (teal, FI). The ferromagnet’s uniform in‐plane exchange field $\mathbf{h}$ and the interface normal $\mathbf{n}$ (along $z$) produce the intrinsic direction $[\mathbf{n}\times\mathbf{h}]$ in the $xy$-plane. In the superconductor we depict the circular supercurrent of a single vortex, whose profile is deformed by the cubic spin-orbit term aligned with $x$. The axes $x$, $y$, and $z$ indicate the laboratory frame; arrows show the directions of $\mathbf{h}$, $\mathbf{n}$, and the vortex circulation.
• Figure 2: Schematic geometry used to analyze the intervortex interaction. We introduce here a polar coordinate system ${\bf r}=(r,\theta)$, the coordinate origin is placed midway between the two vortices. a) Two vortices with coinciding vorticity which generates superfluid velocities $\mathbf v_{1}$ and $\mathbf v_2$. b) Analogous configuration of two vortices with opposite vorticities. The conventional intervortex interaction forces $\mathbf f_0$ and $\gamma$-dependent non-central forces $\mathbf f_\gamma$ are shown.
• Figure 3: A schematic view of a single vortex confined in a superconducting disk of radius $R$. A center of polar coordinate system $(r,\theta)$ is placed in the vortex center and shifted from the disk center by the distance $y_0$. A vortex-induced current $\mathbf j_{vort}$, screening current $\mathbf j_B$ and current of an image vortex $\mathbf j_{image}$ are shown by blue, green and red, respectively.
• Figure 4: Schematic picture of a single vortex located at the distance $a$ from the superconducting film edge. Curved arrows show the direction of the supercurrents around the real (blue) vortex and image (red) antivortex. The area of integration is indicated by shading.
• Figure 5: Schematic picture illustrating the motion of a single vortex in a superconducting film in the presence of transport current $\mathbf j$. $\mathbf F_L=c^{-1}\Phi_0[\mathbf j\times\mathbf z_0]$ is a Lorentz force, $\mathbf V_L$ is the vortex velocity and $\mathbf E$ is an induced electric field.