Phase diagram of planar U(1)×U(1) superconductor: Condensation of vortices with fractional flux and a superfluid state Original Research Article

We discuss a phase diagram of two-dimensional U(1)×U(1) superconductor in the field theoretic formalizm of [Phys. Rev. Lett. 89 (2002) 067001]. In particular we discuss that when penetration length is short the system exhibit a quasi-neutral quasi-superfluid state which is a state when quasi-long range order sets in only in phase difference while individually the phases are disordered.