  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.
