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 nonzero Sπ, π. 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.