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

Abstract

The far-infrared (10-100 ${\mathrm{cm}}^{-1\mathrm{}}$) complex conductivity of superconducting granular NbN films has been determined from reflection and transmission data. Moderately granular films, with $R_{\square }=150\mathrm{}$ and $200 \frac{\Omega }{\square }$, followed Leplae-modified Bardeen-Cooper-Schrieffer—theory predictions with no absorption below the gap frequency ${\omega }_g$. The derived values of $\frac{2\Delta }{k{T}_c}$ were 3.8 and 4.0, slightly below the results for homogeneous films. Highly granular films, with $R_{\square }\ge 500 \frac{\Omega }{\square }$, displayed dc resistive tails and evidence of Josephson coupling. The real part of the far-infrared conductivity was BCS-type for frequencies above ${\omega }_g$ but showed an anomalous absorption below ${\omega }_g$. 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.