Microwave response and electrical transport studies of disordered s wave superconductor: NbN thin films

Abstract

It is now well known that the properties of the disordered s wave superconductors can deviate significantly from the prediction of standard Bardeen-Cooper-Schrieffer (BCS) theory. By measuring the temperature dependence of the resonance frequency, $f_0$, of microwave resonators made from disordered NbTiN and TiN thin films, at low temperatures, below half of the superconducting critical temperature, $T_c$, Driessen et al. \cite{driessen2012PRL} demonstrated that $f_0$ vanishes faster than predicted from the BCS theory. Here, we report on the temperature dependence of $f_0$ of microwave resonators made from disordered NbN thin films at higher temperatures--- typically from 0.4 to 0.8$T_c$. In this temperature range, we demonstrate that $f_0$ vanishes slower than predicted from the BCS theory. We discuss the possible role of electronic inhomogeneity and possibility of appearing a pseudogap-like feature. We also discuss the possibility of a faster downturn of the superfluid density, $n_s$, near $T_c$, resembling a Berezinski--Kosterlitz--Thoules (BKT) type transition.