Gapless superconductivity from low-frequency electrodynamic response of two-dimensional granular composites

We measured the full complex ac conductance of two-dimensional granular In/InOx composites using the mutual inductance technique to explore the transition from a "failed superconductor turned anomalous metal" to a robust superconductor. In this system, room-temperature annealing was adopted to tune the InOx-mediated coupling between In grains, allowing for the observation of both a "true" superconductor-to-insulator transition and the emergence of an intervening anomalous metallic state. In this paper, we show that further annealing increases the intergrain coupling, eliminating the anomalous metallic phase but at the same time preventing the emergence of strong Bose-dominated insulating phase. The complex ac conductance revealed a T -> 0 finite dissipative response in a finite magnetic field, coexisting with a robust superfluid density. The anomalous powerlaw spectra for the dissipative response suggest quantum critical behavior as probed in the kilohertz range, and point to signatures of gapless superconductivity in our granular superconducting system.