The Berezinskii-Kosterlitz-Thouless (BKT) transition in ultra-thin NbN films is investigated in presence of weak perpendicular magnetic fields. A jump in the phase stiffness at the BKT transition is detected up to 5 G, while the BKT features are smeared between 5 G and 50 G, disappearing altogether at 100 G, where conventional current-voltage behavior is observed. Our findings demonstrate that weak magnetic fields, insignificant in bulk systems, deeply affect our ultra-thin system, promoting a crossover regime from the Halperin-Nelson fluctuations to the BCS-like state with G fluctuations, as the field increases. This behavior is related to field-induced free vortices that screen the vortex-antivortex interaction and smear the BKT transition.
Sharma et al. (Wed,) studied this question.