We show that in two-dimensional type-II superconductors, the vortex liquid-solid transition is not accompanied by a simultaneous divergence of the phase correlation length. Even in the ‘‘vortex-solid’’ phase, despite a finite shear modulus and quasi-long-range density correlations, the phase coherence remains short ranged, with a correlation length of order one magnetic length. We also find that, in the solid phase, there is no ‘‘Bose condensation,’’ in the sense that any particular Abrikosov lattice state has zero statistical weight in the thermodynamic limit. The vortex-solid phase in two dimensions is therefore best described as a Cooper-pair charge-density wave with no superconducting phase order.

• Received 22 June 1994

DOI:https://doi.org/10.1103/PhysRevB.51.3042