Near-power-law Temperature Dependence of the Superfluid Stiffness in Strongly Disordered Superconductors

In BCS superconductors, the superfluid stiffness is virtually constant at low temperature and only slightly affected by the exponentially low density of thermal quasiparticles. Here, we present an experimental and theoretical study on the temperature dependence of superfluid stiffness Theta(T) in a strongly disordered pseudogaped superconductor, amorphous InOx, which exhibits non-BCS behavior. Experimentally, we report an unusual power-law suppression of the superfluid stiffness delta Theta(T) proportional to T-b at T << T-c, with b similar to 1.6, which we measured via the frequency shift of microwave resonators. Theoretically, by combining analytical and numerical methods to a model of a disordered superconductor with pseudogap and spatial inhomogeneities of the superconducting order parameter, we found a qualitatively similar low-temperature power-law behavior with exponent b similar to 1.6-3 being disorder-dependent. This power-law suppression of the superfluid density occurs mainly due to the broad distribution of the superconducting order parameter that is known to exist in such superconductors [B. Sacepe et al., Nat. Phys. 7, 239 (2011)], even moderately far from the superconductor-insulator transition. The presence of the power-law dependence delta Theta(T) proportional to T-b at low T << T-c demonstrates the existence of low-energy collective excitations; in turn, it implies the presence of a new channel of dissipation in inhomogeneous superconductors caused by subgap excitations that are not quasiparticles. Our findings have implications for the use of strongly disordered superconductors as superinductance in quantum circuits.