Rayleigh instability of confined vortex droplets in critical superconductors

Depending on the Ginzburg-Landau parameter κ, superconductors can either be fully diamagnetic if κ>1/√2(type I superconductors) or allow magnetic flux to penetrate through Abrikosov vortices if κ<1/√2(type II superconductors; refs 1,2). At the Bogomolny critical point,κ=κ _c =1/√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 κ∼κ _c remains lacking. Here we report that in confined systems the critical regime expands over a finite interval of κ 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 κ 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.