Strongly disordered superconductors (SDSCs) are widely used in qubits, microwave resonators, photon detectors, and other superconducting quantum devices. In SDSC-based devices, coherence times are limited by low-temperature microwave dissipation in the material. However, the standard Mattis-Bardeen theory fails in SDSCs because their single-particle spectrum exhibits a hard pseudogap ${\mathrm{\Delta }}_P$ both below and above the transition temperature $T_c$. We develop a novel microscopic theory of the dependence of ac dissipation in such systems on temperature $T$ and frequency $\omega$. We analyze the resonator quality factor $Q(\omega ,T)$ in the practically relevant range $\hslash \omega ,T\ll \mathrm{\Delta }\le {\mathrm{\Delta }}_P$, where $\mathrm{\Delta }$ is the typical superconducting order parameter, distinct from ${\mathrm{\Delta }}_P$. We show that low-$\omega$ dissipation is dominated by a new type of bulk localized collective modes arising from spatial inhomogeneity of the superconducting state. Consequently, $Q(\omega )$ decreases strongly with $\omega$ and exhibits two-level-system-like growth with $T$ for $T\ll T_c$. Our theory provides a microscopic understanding of existing and future experiments on thin films of ${\mathrm{InO}}_x$, TiN, NbN, and similar SDSCs, and is phenomenologically relevant to granular aluminum films. The results suggest strategies to mitigate intrinsic microwave losses in SDSC-based quantum devices.

Close

PrevNext

View figure in article

• Pseudogap
• Superconducting order parameter
• s-wave
• Disordered systems
• Low-temperature superconductors
• Superconducting devices
• Thin films
• Cavity methods