Rayleigh instability of confined vortex droplets in critical superconductors

Depending on the Ginzburg–Landau parameter K, superconductors can either be fully diamagnetic if K<1/SQRT(2) (type I superconductors) or allow magnetic flux to penetrate through Abrikosov vortices if K>1/SQRT(2) (type II superconductors; refs 1,2). At the Bogomolny critical point, K=Kc=1/SQRT(2), a state that is infinitely degenerate with respect to vortex spatial configurations arises [3,4]. Despite in-depth investigations of conventional type I and type II superconductors, a thorough understanding of the magnetic behaviour in the near-Bogomolny critical regime at K~Kc remains lacking. Here we report that in confined systems the critical regime expands over a finite interval of K forming a critical superconducting state. We show that in this state, in a sample with dimensions comparable to the vortex core size, vortices merge into a multi-quanta droplet, which undergoes Rayleigh instability [5] on increasing and decays by emitting single vortices. Superconducting vortices realize Nielsen–Olesen singular solutions of the Abelian Higgs model, which is pervasive in phenomena ranging from quantum electrodynamics to cosmology [6–9]. Our study of the transient dynamics of Abrikosov–Nielsen–Olesen vortices in systems with boundaries promises access to non-trivial effects in quantum field theory by means of bench-top laboratory experiments.