Magnetic-field dependent vortex dynamics and critical currents in superconducting microwires with regular large-area perforation by pinholes

We report on results of simulations and experiments of vortex states in superconducting micro-wires with periodic rectangular pinhole structures. The simulations have been performed by means of numerically solving the time-dependent Ginzburg-Landau (TDGL) equations. With increasing bias current and for different values of the external magnetic field applied normal to the structure plane, we observe at first a vortex free Meissner state, followed by a resistive vortex-flow mixed state and a state with a more complex vortex pattern. The resulting dependence of the critical current Ic on magnetic field exhibits two plateaus with distinctly different vortex dynamics. Corresponding experimentally measured magnetic-field dependences of Ic of WSi microwires with periodic pinhole structures and varying hole spacing confirmed the predictions of these simulations, showing two ranges of magnetic field with almost field-independent critical currents. The experimentally determined critical currents are larger for a smaller pinhole spacing, in agreement with the results of the TDGL simulations. The good agreement of the simulations with the experimental results provides a convenient strategy for the optimization of single-photon detectors with or without artificial and natural defects.

💡 Research Summary

This work combines time‑dependent Ginzburg‑Landau (TDGL) simulations with experimental measurements on tungsten‑silicide (WSi) superconducting microwires that contain a regular rectangular lattice of large‑area pinholes. The aim is to elucidate how such artificial perforations modify vortex dynamics and the magnetic‑field dependence of the critical current (Ic).

Simulation methodology – The authors employ the open‑source py‑TDGL package to solve the dimensionless TDGL equations on a two‑dimensional mesh representing a thin superconducting strip (length = 3 µm, width = 1 µm, thickness = 2 nm). Material parameters are chosen to match typical WSi films: London penetration depth λ≈960 nm, coherence length ξ≈13.6 nm, normal‑state resistivity ρ≈1000 Ω·nm. Pinholes of diameter D = 100 nm are placed in three parallel columns; the longitudinal and transverse spacings (Dx, Dy) are varied (150 nm, 200 nm, 250 nm) to study geometric effects. A voltage probe is defined at a fixed point, and a voltage‑threshold criterion is used to extract Ic for each applied perpendicular magnetic field B.

Key simulation findings – As the bias current I is increased, three distinct regimes appear:

1. Meissner regime – ψ (the order‑parameter amplitude) remains close to unity across the wire, the phase varies linearly, and no vortices are present. The pinholes merely cause slight current crowding but do not nucleate vortices.

2. Vortex‑flow regime (near Ic) – Rows of pinholes become linked by continuous lines of suppressed ψ. Vortex‑antivortex pairs nucleate at the edges or at pinhole sites, travel horizontally, and generate discrete voltage steps. The number of active pinhole rows correlates directly with the voltage magnitude, producing a stepwise increase in the simulated V(t) trace. In a finite magnetic field (e.g., B = 10 mT) vortex entry is triggered simultaneously in all rows because the Meissner screening current adds to the bias current on one side of the strip, enhancing current crowding.

3. Resistive regime (I > Ic) – ψ is strongly suppressed near many pinholes, normal‑state islands appear, the phase landscape becomes chaotic, and a large, roughly constant voltage is established.

A crucial observation is that Ic(B) exhibits two plateaus: the first at low fields where the Meissner state is stabilized by the pinhole lattice, and the second at higher fields where a stable vortex‑flow pattern persists. The width of the plateaus is essentially independent of the exact pinhole spacing, but the absolute value of Ic is larger for smaller Dx/Dy. This is attributed to reduced current crowding and more efficient vortex pinning when holes are closer together.

Experimental verification – WSi microwires with the same geometric parameters were fabricated by electron‑beam lithography and reactive ion etching. Three sets of devices with Dx = Dy = 150 nm, 200 nm, and 250 nm were measured at temperatures below 1 K. The measured Ic versus B curves reproduced the two‑plateau structure predicted by the simulations. Moreover, devices with the tighter pinhole lattice (150 nm spacing) displayed a higher Ic across the entire field range, confirming the simulated trend.

Implications for superconducting single‑photon detectors (SMSPDs) – In SMSPDs, detection events are believed to involve vortex nucleation and motion; thus, controlling vortex dynamics directly impacts dark‑count rates and detection efficiency. The presence of a regular pinhole lattice suppresses unwanted vortex entry at low fields, leading to a field‑independent Ic and reduced dark counts. By tuning the hole spacing, one can raise Ic, thereby increasing the bias margin and improving signal‑to‑noise ratios. The study demonstrates that TDGL simulations are a powerful design tool for engineering artificial defect landscapes in superconducting nanostructures.

Conclusion – The combined theoretical‑experimental approach shows that periodic large‑area pinholes dramatically reshape vortex behavior in superconducting microwires, creating two distinct Ic plateaus and enhancing the critical current when the holes are closely spaced. These insights provide a concrete route to optimize the performance of superconducting photon detectors and other devices where vortex motion governs functionality.