Topological gauge theory of vortices in type-III superconductors

Usual superconductors fall into two categories, type I, expelling magnetic fields, and type II, into which magnetic fields exceeding a lower critical field ${H}_{\mathrm{c}1}$ penetrate in a form of vortices characterized by two scales, the size of the normal core, $\ensuremath{\xi}$, and the London penetration depth $\ensuremath{\lambda}$. Here we demonstrate that a type-III superconductivity, realized in granular media in any dimension, hosts vortex physics in which vortices have no cores, are logarithmically confined, and carry only a gauge scale $\ensuremath{\lambda}$. Accordingly, in type-III superconductors ${H}_{\mathrm{c}1}=0$ at zero temperature and the Ginzburg-Landau theory must be replaced by a topological gauge theory. Type-III superconductivity is destroyed not by Cooper pair breaking but by vortex proliferation generalizing the Berezinskii-Kosterlitz-Thouless mechanism to any dimension.