This paper aims to justify the existence of a two-dimensional Bose metal, i.e., a metallic phase made out of Cooper pairs at $T=0.\mathrm{}$ To this end, we consider the physics of quantum phase fluctuations in (granular) superconductors in the absence of disorder and emphasize the role of two order parameters in the problem, viz. phase order and charge order. We focus on the two-dimensional (2D) Bose Hubbard model in the limit of very large fillings, i.e., a 2D array of Josephson junctions. We find that the algebra of phase fluctuations is that of the Euclidean group $E_2$ in this limit, and show that the model is equivalent to two coupled $\mathrm{XY}$ models in $\mathrm{}(2+1)\mathrm{}$ dimensions, one corresponding to the phase degrees of freedom, and the other to the charge degrees of freedom. The Bose metal, then, is the phase in which both these degrees of freedom are disordered (as a result of quantum frustration). We analyze the model in terms of its topological excitations and suggest that there is a strong indication that this state represents a surface of critical points, akin to the gapless spin liquid states. We find a remarkable consistency of this scenario with certain low-$T_c$ thin film experiments.

• Received 9 June 1998

DOI:https://doi.org/10.1103/PhysRevB.60.1261