  Superconducting nanofilms are tunable systems that can host a 3D-2D
dimensional crossover, leading to the Berezinskii-Kosterlitz-Thouless (BKT)
superconducting transition approaching the 2D regime. Reducing further the
dimensionality, from 2D to quasi-1D, superconducting nanostructures with
disorder can generate quantum and thermal phase slips (PS) of the order
parameter. Both BKT and PS are complex phase fluctuation phenomena of difficult
experimental detection. Here, we have characterized superconducting NbN
nanofilms thinner than 15 nm, on different substrates, by temperature dependent
resistivity and current-voltage (I-V) characteristics. Our measurements have
evidenced clear features related to the emergence of BKT transition and PS
events. The contemporary observation in the same system of BKT transition and
PS events and their tunable evolution in temperature and thickness, has been
explained as due to the nano-conducting paths forming in a granular NbN system.
In one of the investigated samples we have been able to trace and characterize
the continuous evolution in temperature from quantum to thermal PS. Our
analysis has established that the detected complex phase phenomena are strongly
related to the interplay between the typical size of the nano-conductive paths
and the superconducting coherence length.
