Zero temperature superconductor–edge metal–insulator transition in two-dimensional bosonic systems

Motivated by the recent experimental observation of an intermediate bosonic\nmetallic state in the two-dimensional superconductor-insulator transition at\n$T=0$, we study an extended Bose Hubbard model in the limit of large number of\nparticles per site. Using a representation of this in terms of two coupled $XY$\nmodels, we find, in addition to an insulating phase and a $(2+1)D$ superfluid\nphase, two other phases. One phase is a $2D$ superfluid phase where a crossover\nfrom $(2+1)D$ to $2D$ has taken place as a result of incipient charge ordering,\nsignaled by $\\theta$ disordering, and which is closely related to a supersolid\nphase. The other new phase is an edge metal state characterized by zero\nsuperfluid stiffness, zero charge ordering, and zero bulk compressibility.\nHowever, the edge compressibility of the system is nonzero. While we do not\nfind any intermediate state with $2D$ metallic conductivity, we are able to\nconnect these results to STM experiments on $\\mathrm{MoS_2}$ showing brims of\nfinite density of states around the entire edge of $2D$ $\\mathrm{MoS_2}$\nsamples.\n