Broadband microwave measurements of two dimensional quantum matter

Employing broadband microwave spectroscopy, we study a field tuned 2D superconductor-metal quantum phase transition in a low-disorder InO x film. We measure the complex conductance as a function of temperature, frequency and magnetic field. The zero field transition temperature Tc ≡ TKTB is determined as the temperature where the phase stiffness starts to acquire frequency dependence. The thermal phase transition is consistent with the Kosterlitz-Thouless-Berezinsky formalism. The AC data demonstrate the critical slowing down close to TKTB and in general the applicability of a vortex plasma model above TKTB. For finite field measurements, we find the strong suppression in the superfluid stiffness above the nominal quantum critical point Bcross where different isotherms of resistance as a function of magnetic field cross each other. The critical slowing down of the fluctuation rate near a continuous quantum phase transition supports a possible scenario that the quantum critical point is at a much lower field Bsm above which the film transits into an anomalous metallic state with superconducting correlations. A phase diagram is established that includes the magnetic field dependence of the superconducting transition temperatures, phase stiffness at the lowest and highest accessed frequencies, and the fluctuation rates at the base temperature.