Probing the Bose solid: A finite frequency study of the magnetic field-tuned superconductor-insulator transition in two-dimensions

The finite frequency complex conductivity of thin highly disordered InO x films was studied as a function of temperature and magnetic field through the nominal field-tuned 2D superconductor-insulator transition. In zero magnetic field we detect various superconducting fluctuations over a broad range of temperatures. The resistive transition from the normal state is marked first by regions with gaussian fluctuations, then by regions of transverse phase fluctuations, until at low temperature the film undergoes a Kosterlitz-Thouless transition into the superconducting state. In finite perpendicular magnetic fields we have found a significant finite frequency superfluid stiffness well into the insulating regime, giving the first definitive evidence for superconducting correlations in the insulating state. A phase diagram is established that includes the superconducting state, a transition to a 'Bose' insulator and then an eventual crossover to a 'Fermi' insulating state at high fields. We speculate on the consequences of these observations and their impact on the understanding of the insulating state and purported intervening low temperature metal. Finally, given the relevance of vortex excitations, we perform an analysis which incorporates vortices in the framework of the Coffey-Clem model. We find evidence of vortices in the flux-flow regime and extract their viscosity.