Flux trapping in NbTiN strips – Part 2: Simulations

We present computational simulations that complement Bai et al.’s experimental study of NbTiN superconducting strips in perpendicular magnetic fields, using scanning SQUID microscopy. Our model focuses on thin superconducting films where the strip thickness is much smaller than the London penetration depth, and the Pearl length is significantly larger than the strip width, resulting in negligible magnetic screening.

Following Bronson et al. [Phys. Rev. B, 73, 144501 (2006)], we minimize Gibbs free energy by considering individual and pairwise Pearl vortex interactions. We explore thermodynamic equilibrium configurations of Pearl vortices using three models: (M1) no-pinning infinite-length strips with one vortex row, (M2) no-pinning infinite-length strips with multiple vortex rows, and (M3) finite-length strips with pinning for a single vortex row.

M1 and M2 use the vortex core radius as a fitting parameter, resulting in uniformly spaced vortex lattices. In M3, simulated annealing via the Metropolis Monte Carlo method incorporates two additional parameters: the Pearl length and pinning parameters. This model reproduces the observed threshold field for vortex entry and predicts a steep rise in vortex count with increasing field, followed by gradual, linear growth. The variation of core radius with strip width challenges the assumption of a uniform freezing temperature, suggesting that vortex kinetics must be considered. Ongoing research aims to enhance understanding of vortex behavior and develop predictive models for flux trapping in superconducting circuits.