Granularity-induced gapless superconductivity in NbN films: Evidence of thermal phase fluctuations

Using a single-coil mutual inductance technique, we measure the low-temperature dependence of the magnetic penetration depth in superconducting NbN films prepared with similar critical temperatures $\ensuremath{\approx}16 \mathrm{K}$ but with different microstructures. Only (100) epitaxial and weakly granular (100) textured films display the characteristic exponential dependence of conventional BCS s-wave superconductors. More granular (111)-textured films exhibit a linear dependence, indicating a gapless state in spite of the s-wave gap. This result is quantitatively explained by a model of thermal phase fluctuations favored by the granular structure.