"Topological gauge theory of vortices in type-III superconductors" (2024) https://journals.aps.org/prb/abstract/10.1103/PhysRevB.110.0... :

> Abstract: Usual superconductors fall into two categories, type I, expelling magnetic fields, and type II, into which magnetic fields exceeding a lower critical field H_c⁢1 penetrate in a form of vortices characterized by two scales, the size of the normal core, \Xi, and the London penetration depth \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 \Lambda. Accordingly, in type-III superconductors H_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.