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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 16 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.
Lamura et al. (Tue,) studied this question.