Microwave Spectroscopic Investigation of the Superconductor Insulator Transition in a Strongly Disordered Superconductor

Superconductor insulator transitions (SIT) driven by disorder or perpendicular magnetic field in 2D disordered superconductor thin films is a protypical example of a quantum phase transition. There can be a field-tuned transition, as $T\rightarrow0$, from vortex glass (superconductor) to Cooper pair glass (insulator) wherein vortices Bose condense and delocalize. Here we measure the complex dynamical response within a broadband of frequencies ($50 MHz-\sim10 GHz$) of a strongly disordered $InO_x$ thin film across its SIT using Corbino microwave spectroscopy. We report the frequency dependence of complex conductance and the critical behavior of superfluid density and fluctuation rate, along with the temperature and field dependence of DC sheet resistance.