Impact of magnetic field direction on anti-dot-based superconducting diodes

Abstract

The superconducting diode effect (SDE) is a fundamental building block for dissipationless nonreciprocal electronics, yet its microscopic origins in thin films often involve competing mechanisms that remain debated. Here, we demonstrate that the SDE can be engineered in niobium films by patterning macroscopic asymmetric antidots, revealing distinct control mechanisms under in-plane and out-of-plane magnetic fields. We identify two dominant contributions to nonreciprocal transport: edge flux pinning, which governs the low-field and in-plane field regimes via surface-barrier asymmetry, and bulk flux pinning, which drives the high-field response and correlates directly with the geometric asymmetry of the antidots. Supported by time-dependent Ginzburg-Landau simulations and an analytical model, we provide a unified description of these regimes, linking the diode efficiency to the specific pinning landscape. These findings establish a flexible design principle for engineering superconducting diodes with tunable functionality, paving the way for their integration into next-generation quantum and cryogenic circuits.

Figures (16)

• Figure 1: Colored SEM image of one of the devices and experimental setup. (a) Measurement scheme and sample overview, consisting of a Nb Hall-bar thin film with a thickness of 200 nm and a patterned region of length 200 $\mu$m. The patterned defects exhibit increasing geometrical asymmetry, as shown in the zoomed panels: (b) circular holes, (c) drop-shaped antidots, and (d) triangular antidots. The white and black scale bars correspond to 50 $\mu$m. The inset in panel (a) illustrates the supercurrent diode effect (SDE), showing dissipationless supercurrent in one direction and dissipative current in the opposite direction.
• Figure 2: Normalized critical currents across the four device geometries. Normalized positive and negative critical currents ($I_c^\pm$) are shown for two magnetic field ranges: low ($\pm 3\,\mathrm{mT}$) and high ($\pm 30\,\mathrm{mT}$), for Reference (a,b), Hole (c,d), Drop (e,f), and Triangle (g,h) antidot devices. Corresponding maximum currents are $I_{\text{max}}^R = 1.3\,\mathrm{mA}$, $I_{\text{max}}^H = 1.9\,\mathrm{mA}$, $I_{\text{max}}^D = 2.8\,\mathrm{mA}$, and $I_{\text{max}}^T = 2.5\,\mathrm{mA}$. Measurements were performed at $T = 1.8\,\mathrm{K}$ for Hole, Drop, and Triangle, and $T = 1.9\,\mathrm{K}$ for Reference. Blue shading indicates the Meissner state ($|H_z| < H_{\text{stop}}$), and red shading the mixed state. Linear fits in the Meissner regime (Eq. \ref{['eq.linear']}) yield $\mu_0 H_{\text{stop}}^R = 2.6\,\mathrm{mT}$, $\mu_0 H_{\text{stop}}^H = 5.6\,\mathrm{mT}$, $\mu_0 H_{\text{stop}}^D = 5.0\,\mathrm{mT}$, and $\mu_0 H_{\text{stop}}^T = 3.5\,\mathrm{mT}$. Blue dashed lines represent linear fits from Eq. \ref{['eq.linear_asy']}.
• Figure 3: SDE efficiency vs. out-of-plane magnetic fields. Comparison of the field evolution of the diode efficiency $\eta$ for the four devices under an out-of-plane field $H_z$. The panels show field ranges of (a) 3 mT and (b) 30 mT.
• Figure 4: Model for the SDE in the presence of an out-of-plane magnetic field. (a) Sketch of vortex dynamics in the presence of a bias current and Meissner screening currents in a film with different edge current thresholds ($j_s^r < j_s^l$). Three different field regimes are considered, corresponding to the intervals defined by $H_\delta$ and $H_{\text{stop}}$. (b) $I_c^\pm$ evaluated from Eq. \ref{['eq.linear_asy']} for $|H_z| < H_{\text{stop}}$ and using the system of equations from Ref. ic_p above $H_{\text{stop}}$. Model parameters: $p=0.2$ and $H_\delta=0.05 H_s$. (c) Example of $\eta(H_z)$ computed from Eqs. \ref{['eq.eta_low']}--\ref{['eq.eta_high']}. Parameters: $\eta_j=0.04$, $p=0.5$, $H_s=10$ mT, $\eta_p=-0.005$. In panels (b) and (c), the background colors represent the three relevant field ranges as described in (a).
• Figure 5: TDGL simulation of the diode effect for the reference sample. (a, b) Order parameter distribution under an applied field of $B = -65$ mT after a simulation time of $50\tau$ for (a) positive and (b) negative bias currents. (c, d) Corresponding current density distributions for the same conditions. Parameters used in TDGL simulations: coherence length $\xi = 0.9~\mu$m, penetration depth $\lambda = 1.35~\mu$m, and thickness $d = 0.2~\mu$m. These values satisfy the type-II superconductor condition $\kappa > 1/\sqrt{2}$.