Dissipation due to Bulk Localized Low-Energy Modes in Strongly Disordered Superconductors.

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 Δ_{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 ω. We analyze the resonator quality factor Q(ω,T) in the practically relevant range ℏω,T≪Δ≤Δ_{P}, where Δ is the typical superconducting order parameter, distinct from Δ_{P}. We show that low-ω dissipation is dominated by a new type of bulk localized collective modes arising from spatial inhomogeneity of the superconducting state. Consequently, Q(ω) decreases strongly with ω and exhibits two-level-system-like growth with T for T≪T_{c}. Our theory provides a microscopic understanding of existing and future experiments on thin films of 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.