Power-Law Suppression of Superfluid Stiffness in High-Kinetic-Inductance NbN Films

Disorder is a powerful route to high kinetic inductance in superconducting ultrathin films, enabling compact high-impedance quantum circuits. This functionality, however, comes at the cost of reduced phase rigidity and potentially anomalous electrodynamics. Here, we use NbN microwave resonators with thicknesses down to 2.8 nm and sheet kinetic inductance up to 300 pH per square to probe how this trade-off reshapes the superconducting response. In the thinnest films, transport shows signatures of a Berezinskii-Kosterlitz-Thouless transition, while the microwave response reveals a pronounced low-temperature power-law suppression of the superfluid stiffness, inconsistent with Mattis-Bardeen theory. With increasing thickness, this anomalous regime is progressively suppressed, marking a continuous crossover toward conventional, gap-dominated electrodynamics. Cross-sectional transmission electron microscopy reveals a nanocrystalline twin-domain structure, pointing to oriented microstructural disorder as a crucial factor in the observed response. Overall, the crossover is governed by the ratio of superfluid stiffness to pairing energy, Theta(0)/Tc, identifying this ratio as a parameter governing the boundary between phase-fluctuation-dominated and gap-dominated superconducting electrodynamics in disordered nanofilms.