Microwave Properties of Superconductors Close to the Superconductor-Insulator Transition

Strongly disordered pseudogapped superconductors are expected to display arbitrarily high values of kinetic inductance close to the superconductor-insulator transition (SIT), which make them attractive for the implementation of large dissipationless inductance. We develop the theory of the collective modes in these superconductors and discuss associated dissipation at microwave frequencies. We obtain the collective mode spectra dependence on the disorder level and conclude that collective modes become a relevant source of dissipation and noise in the outer proximity of the SIT.

Figure 1

Schematics of the phase diagram, order parameter distribution function, and collective mode spectra at low $T$ of strongly disordered superconductors obtained from the solution of the model (1) in the cavity approximation. At large disorder, $K<K_1$, the distribution of the order parameter becomes anomalously broad (upper panel) and $T_c$ is rapidly suppressed and becomes $T_c=0$ at $K<K_c$ (lower panel). In the regime of the critical suppression of $T_c$, $K<K_1$, delocalized collective modes exist for all frequencies. For smaller disorder, $K_1<K<K_2$, very low frequency modes are localized. The modes $\omega =0$ disappear completely only for $K_2<K$. The numerical values of $K$ shown here correspond to the interaction constant $g=0.129$, which gives $T\approx {10}^{-3}{E}_F$. Arrows indicate the values of $K$ for which the distribution is shown in the upper plot.