Abstract

A fundamental understanding of superconducting nanodevices is required to develop emerging quantum technologies. We use time-dependent Ginzburg-Landau theory to investigate the magnetic response of a three-dimensional monolithic superconducting nano-bridge in the presence of two external magnetic fields. Our analysis focuses on the behavior of the Gibbs free energy density, magnetization, superconducting Cooper pair density, current flow as a function of geometry, external magnetic fields, and induced currents. In three distinct cases, we explore the interplay between geometry, induced current, and vortex dynamics. First, we analyze the stability of vortices under variations of the geometry without induced currents. Second, we examine the influence of induced currents (given by a second external magnetic field) on the left single boundary of the superconducting nano-bridge sample while keeping the geometric parameters fixed. Third, we introduce left and right-induced currents at the boundaries and investigate their impact on vortex nucleation. Our results demonstrate that the nano-bridge dimensions play a crucial role in stabilizing and controlling single-vortex states in the nano-bridge sample. We find that induced currents generate vortex motion within the superconducting nano-bridge sample, highlighting the intricate dependence of vortex dynamics on currents under geometrical constraints. Our findings provide valuable insights into controlled vortex manipulation in nano-scale superconductors, with potential applications in superconducting electronics and quantum technologies. © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2025.