Dissipation due to bulk localized low-energy modes in strongly disordered superconductors

Anton V. Khvalyuk; Mikhail V. Feigel'man

Paper

Dissipation due to bulk localized low-energy modes in strongly disordered superconductors

Abstract

We develop a theory of the temperature

and frequency

dependence of ac dissipation in strongly disordered superconductors featuring a pseudogap

in the single-particle spectrum. Our theory applies to the regime

, where

is the typical superconducting gap. The dissipation is expressed in terms of the quality factor

of microwave resonators made of these materials. We show that low-

dissipation is dominated by a new type of bulk localized collective modes. Due to the strongly nonuniform spectral density of these modes,

decreases sharply with frequency, while its temperature dependence exhibits a two-level-system-like growth as a function of

for

. Our theory is applicable to InO

, TiN, NbN, and similar strongly disordered materials. We further argue that the experimentally observed behavior of disordered films of granular Aluminum is explained by similar physics, although this case requires a separate theoretical analysis.