First Order Superconductor to Insulator Transition: Evidence for a Supersolid Phase

The superconductor to insulator transition in the presence of long-range Coulomb interactions is studied using Monte Carlo techniques. At integer filling the transition is second order. At half filling we find evidence of a first order transition to a state with non-zero $S_{\pi,\pi}$. No intervening supersolid phase is observed. Off half-filling two separate transitions are found. The transition from the superconducting to a supersolid phase is second order followed by another second order transition between the supersolid and an insulating phase.