Far-infrared conductivity and anomalous below-gap absorption in superconducting granular NbN

Abstract

The far-infrared (10-100 ${\mathrm{cm}}^{\ensuremath{-}1}$) complex conductivity of superconducting granular NbN films has been determined from reflection and transmission data. Moderately granular films, with ${R}_{\ensuremath{\square}}=150$ and $200 \frac{\ensuremath{\Omega}}{\ensuremath{\square}}$, followed Leplae-modified Bardeen-Cooper-Schrieffer---theory predictions with no absorption below the gap frequency ${\ensuremath{\omega}}_{g}$. The derived values of $\frac{2\ensuremath{\Delta}}{k{T}_{c}}$ were 3.8 and 4.0, slightly below the results for homogeneous films. Highly granular films, with ${R}_{\ensuremath{\square}}\ensuremath{\ge}500 \frac{\ensuremath{\Omega}}{\ensuremath{\square}}$, displayed dc resistive tails and evidence of Josephson coupling. The real part of the far-infrared conductivity was BCS-type for frequencies above ${\ensuremath{\omega}}_{g}$ but showed an anomalous absorption below ${\ensuremath{\omega}}_{g}$. This excess absorption may arise from two-dimensional fluctuations in the form of vortices or from normal conducting regions mixed in with the superconducting grains.