Broadening of the Berezinskii-Kosterlitz-Thouless transition by correlated disorder

The Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional superconductors is usually expected to be protected against disorder. However, its typical signatures in real system, like e.g. the superfluid-density jump, are often at odd with this expectation. Here we show that the disorder-induced granularity of the superconducting state modifies the nucleation mechanism for vortex-antivortex pairs. This leads to a considerable smearing of the universal superfluid-density jump as compared to the paradigmatic clean case, in agreement with experimental observations.