Topological Order in the Vortex Glass Phase of High-Temperature Superconductors

The stability of a vortex glass phase with quasi-long-range positional order is examined for a disordered layered superconductor. The role of topological defects is investigated using a detailed scaling argument, supplemented by a variational calculation. The results indicate that topological order is preserved for a {\em wide range} of parameters in the vortex glass phase. The extent of the stability regime is given in terms of a simple Lindemann-like criterion.