superconducting Goldstone mode in granular aluminum: Experiments and theory

Recent advances in the experimental growth and control of disordered thin films, heterostructures, and interfaces provide fertile ground for the observation and characterization of the collective superconducting excitations emerging below Tc after breaking the U(1) gauge symmetry. Here we combine THz experiments in a nanostructured granular Al thin film and theoretical calculations to demonstrate the existence of optically active phase modes, which represent the Goldstone excitations of the broken gauge symmetry. By measuring the complex transmission through the sample we identify a sizable and temperature-dependent optical subgap absorption, which cannot be ascribed to quasiparticle excitations. A quantitative modeling of this material as a disordered Josephson array of nanograins allows us to determine, with no free parameters, the structure of the spatial inhomogeneities induced by shell effects. Besides being responsible for the enhancement of the critical temperature with respect to bulk Al, already observed in the past, this spatial inhomogeneity provides a mechanism for the optical visibility of the Goldstone mode. By computing explicitly the optical spectrum of the superconducting phase fluctuations we obtain a good quantitative description of the experimental data. Our results demonstrate that nanograin arrays are a promising setting to study and control the collective superconducting excitations via optical means.