Robustness of the Berezinskii-Kosterlitz-Thouless transition in ultrathin NbN films near the superconductor-insulator transition

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. This observation is in direct contrast with previous data on deeply underdoped quasi-2D cuprates near the SIT. As our NbN films approach the quantum critical point, 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.