Disorder-Induced Phase Transitions in Two-Dimensional Crystals

We analyze a model of a two-dimensional crystal subject to a slowly varying random potential, and find evidence for the existence of a zero-temperature phase transition via the appearance of isolated dislocations above a critical disorder strength. The result is in contrast to earlier analyses of the model, which found that the crystal is always unstable with respect to dislocation formation. The argument is generalized to finite temperature and a phase boundary is derived. Molecular dynamics simulations of a model electron crystal show strong evidence of this phase transition at low temperatures.