Broadband microwave study of 2D superconductor-insulator quantum phase transition

Using our broadband microwave spectrometer, we investigate the complex AC conductance of disordered InO$_x$ films as a function of magnetic field through the 2D superconductor-insulator quantum phase transition. We have studied the behaviors of the frequency dependent complex response function of a particular InO$_x$ sample near the critical point in the limit of $\hbar \omega < K _{B} T$ and $\hbar \omega > K _{B} T$ and compare our results to theoretical models. We discuss the possibility for a novel insulating state on the insulating side of the transition through the frequency dependent conductance.