Electrodynamic response and local tunneling spectroscopy of strongly disordered superconducting TiN films

We have studied the electrodynamic response of strongly disordered superconducting TiN films using microwave resonators, where the disordered superconductor is the resonating element in a high-quality superconducting environment of NbTiN. We describe the response assuming an effective pair-breaking mechanism modifying the density of states and compare this to local tunneling spectra obtained using scanning tunneling spectroscopy. For the least disordered film ($k_{\mathrm{F}}l=8.7$, $R_{\mathrm{s}}=13\Omega$), we find good agreement, whereas for the most disordered film ($k_{\mathrm{F}}l=0.82$, $R_{\mathrm{s}}=4.3\mathrm{k}\Omega$), there is a strong discrepancy, which signals the breakdown of a model based on uniform properties.

Figure 1

(a) Optical microscope image of the resonator design used in this paper. A TiN half-wave resonator is embedded in a NbTiN ground plane and capacitively coupled to the NbTiN transmission line. (b) Transmission line throughput $S_{21}$ as a function of microwave frequency, for a resonator from film E. The design allows us to follow the resonance curve for a temperature range from $T=50$ mK (blue curve) to $T=417$ mK (red curve). Inset: The curve for $T=50$ mK (circles) together with a fit of Eq. (1) to the measured data [solid (red) curve].

Figure 2

Measured resonance frequency as a function of temperature for films C, E, G, and I. Solid curves are a fit of the model to the data (see text for details). Inset: Superconducting densities of states corresponding to these fits, compared to the BCS density of states (dashed curve).

Figure 3

(a) Measured tunneling spectrum of film I (solid curve). (b) Average tunneling spectrum of film C (solid curve) at $T=50$ mK, together with the normal-state tunneling spectrum at $T=1.4$ K [dashed (red) curve]. (c) Tunneling spectra of film C at three positions (solid curves) and the average tunneling spectrum (dashed curve). Curves are shifted for clarity (dotted lines give the zero-conductance levels). The normal-state background is removed from these measurements (see text for details). Dash-dotted black curves in (a) and (c) are the tunneling spectra that are expected from the electrodynamics measurements. (d) Histogram of the characteristic energy scale $E_{\mathrm{t}}$ in the local spectra in film C. The Gaussian fit (solid curve) is used to extract the mean value.