Berezinskii-Kosterlitz-Thouless phase transition in nanoporous films of superconducting NbN

We present a study of the Berezinskii-Kosterlitz-Thouless (BKT) transition in mildly disordered NbN nanoporous (NP) films. The measured superfluid stiffness, ${J}_{s}$, is found to be much lower than that predicted considering a reduced geometric area. For a 5 nm thick NP film, a distinct BKT transition is observed. By fitting the experimental data via the BKT renormalization-group equations, we show how both ${J}_{s}$ and the vortex-core energy, $\ensuremath{\mu}$, decrease in the presence of nanopores. The variation of ${J}_{s}$ and $\ensuremath{\mu}$ is also reproduced theoretically via Monte Carlo numerical simulations on a 2D diluted XY model. Our results show that nanopore geometries effectively enhance the 2D nature of the superconducting films, increasing the parameter space to explore the BKT physics while offering a pathway to systematically control the two energy scales, ${J}_{s}$ and $\ensuremath{\mu}$, that govern the vortex physics in these systems.