Microwave spectroscopy studies on superconductor-to-insulator transition and the intervening Bose metal phase in indium oxide thin films*

The self-dual criticality of magnetic field tuned superconductor-to-insulator transition (H-SIT) in homogeneously disordered InO_x thin films is a profound problem, and could be connected to other types of quantum phase transitions. Although it is generally accepted that Bosons are dominant on both sides of the transition in this material and fluctuation of the phase of the order parameter is important, the nature of the insulating phase and an intervening Bose metal phase usually observed in less disordered samples remain mysteries to be unveiled. Here we present measurements of the broadband microwave conductivity spectra of InO_x thin films of different disorder levels across their magnetic field tuned quantum phase transitions.