  We study the formation and evolution of vortices in $U(1)$ dark photon dark
matter and dark photon clouds that arise through black hole superradiance. We
show how the production of both longitudinal mode and transverse mode dark
photon dark matter can lead to the formation of vortices. After vortex
formation, the energy stored in the dark photon dark matter will be transformed
into a large number of vortex strings, eradicating the coherent dark photon
dark matter field. In the case where a dark photon magnetic field is produced,
bundles of vortex strings are formed in a superheated phase transition, and
evolve towards a configuration consisting of many string loops that are
uncorrelated on large scales, analogous to a melting phase transition in
condensed matter. In the process, they dissipate via dark photon and
gravitational wave emission, offering a target for experimental searches.
Vortex strings were also recently shown to form in dark photon superradiance
clouds around black holes, and we discuss the dynamics and observational
consequences of this phenomenon with phenomenologically motivated parameters.
In that case, the string loops ejected from the superradiance cloud, apart from
producing gravitational waves, are also quantised magnetic flux lines and can
be looked for with magnetometers. We discuss the connection between the
dynamics in these scenarios and similar vortex dynamics found in type II
superconductors.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology