Phase diagram of planar U(1)xU(1) superconductors: condensation of   vortices with fractional flux and a superfluid state
  We discuss a phase diagram of two-dimentional $U(1)\times U(1)$ superconductor in the field theoretic formalizm of Ref. [17]. In particular we discuss that in the type-I case the system exhibit a quasi-neutral quasi-superfluid state. 
Egor Babaev