Dislocations and Bragg glasses in two dimensions

Abstract

We discuss the question of the generation of topological defects (dislocations) by quenched disorder in two-dimensional periodic systems. In a previous study [Phys. Rev. B, 52 (1995) 1242], we found that, contrary to d=3, unpaired dislocations appear in d=2 above a length scale ξ D, which we estimated. We extend this description to include effects of freezing and pinning of dislocations at low temperature. The resulting ξ D at low temperature is found to be larger than our previous estimate, which is recovered above a characteristic temperature. The dependence of ξ D in the bare core energy of dislocation is a stretched exponential. We stress that for all temperatures below melting ξ D becomes arbitrarily large at weak disorder compared to the translational order length R a≫ a. Thus, there is a wide region of length scales, temperature and disorder where Bragg glass-like behavior should be observable.