Presentazioni e Articoli Tecnici

Numerical simulations of the electromagnetic responses of nanoscale superconductors subjected to transport currents and magnetic fields have been performed using COMSOL Multiphysics [1] with the aim of developing superconducting electronic devices. The simulations are based on the time-dependent Ginzburg–Landau (TDGL) equations, which describe the temporal evolution of the amplitude and phase of the complex superconducting order parameter [2, 3]. The governing equations are implemented using the Coefficient Form PDE interface without relying on dedicated physics modules.

We demonstrate simulations of vortex dynamics in four representative systems: (i) a superconducting disk subjected to an external magnetic field, (ii) a current-carrying superconducting nanostrip, (iii) a current-biased superconducting nanostrip after photon absorption, and (iv) a three-dimensional superconducting nanowire subjected to both magnetic field and transport current.

(i) For the superconducting disk, vortices penetrate from the edge of the disk under an applied magnetic field and eventually form a vortex lattice [4, 5]. (ii) In a superconducting nanostrip carrying a current exceeding the critical current, vortex motion or phase-slip events occur, resulting in a finite voltage across the strip. In strips with a notch, vortices are preferentially nucleated at the sharp tip because of current crowding [6, 7], as shown in Fig. 1. When a weak superconducting region is introduced across the width of the strip, vortex motion or phase-slip events are localized in that region, reproducing the behavior of a weak link or a Josephson junction. (iii) When a current-biased superconducting nanostrip absorbs a photon, the superconducting order parameter is locally suppressed in the absorption region, leading to the nucleation of a vortex–antivortex pair [8]. The pair is driven apart by the transport current and, depending on the operating conditions, may trigger a local transition to the normal state. This process corresponds to the fundamental operating mechanism of superconducting nanostrip single-photon detectors [9]. (iv) In a three-dimensional superconducting nanowire containing magnetic vortices, the application of a transport current drives vortex motion and generates a voltage. In particular, when the magnetic field is applied parallel to the transport current, helical vortex structures emerge, accompanied by vortex cutting and reconnection, resulting in complex three-dimensional vortex dynamics [10, 11].

These simulations provide visualizations of vortex penetration, nucleation, motion, vortex–antivortex pair generation, phase-slip phenomena, and superconducting-to-normal transitions in nanoscale superconductors. Such visualization using COMSOL Multiphysics facilitates a deeper understanding of the underlying physical mechanisms and provides useful insights for the design, optimization, and development of superconducting devices.