Orientational and positional order in flux lattices of type-II superconductors

A detailed theory of a hexatic vortex glass, recently observed in high-${\mathit{T}}_{\mathit{c}}$ superconductors, is developed. The vortex lattice in this phase is characterized by short-range positional order, which decays as exp(-αr) in three dimensions (3D) and as exp(-β${\mathit{r}}^2$) in 2D, and by extended orientational correlations, which may be long range in a 3D sample and decay algebraically in a 2D film. For 2D and 3D the angular and field dependence of positional and orientational correlation functions is obtained; these may be easily tested experimentally.