  Occurrence of the Berezinskii-Kosterlitz-Thouless (BKT) transition is
investigated by superfluid density measurements for two-dimensional (2D)
disordered NbN films with disorder level very close to a
superconductor-insulator transition (SIT). Our data show a robust BKT
transition even near this 2D disorder-tuned quantum critical point (QCP). This
observation is in direct contrast with previous data on deeply underdoped
quasi-2D cuprates near the SIT. As our NbN films approach the QCP, the
vortex-core energy, an important energy scale in the BKT transition, scales
with the superconducting gap, not with the superfluid density, as expected
within the standard 2D-XY model description of BKT physics.
