BKT 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, Js, is found to be much lower than that predicted by considering the reduction in the geometric area. This effect is also reproduced theoretically via Monte Carlo simulations on a 2D XY model with different nanopore geometries. For a 5 nm thick NP film, a distinct BKT transition is observed. BKT renormalization group flow equations, incorporating the broadening in Js due to the presence of inhomogeneities, are used to fit the experimental data. From this analysis we see that both Js and the vortex core energy, mu, decrease in the presence of nanopores. Our results show that nanopore geometries effectively enhance the 2D nature of the films, thereby increasing the parameter space to explore BKT physics in superconducting films.