Dislocations and Bragg glasses in two dimensions

We discuss the question of the generation of topological defects (dislocati ons) by quenched disorder in two-dimensional periodic systems. In a previou s study [Phys. Rev. B, 52 (1995) 1242], we found that, contrary to d = 3, u npaired dislocations appear in d = 2 above a length scale xi(D), which we e stimated. We extend this description to include effects of freezing and pin ning of dislocations at low temperature. The resulting xi(D) at low tempera ture is found to be larger than our previous estimate, which is recovered a bove a characteristic temperature. The dependence of xi(D) in the bare core energy of dislocation is a stretched exponential. We stress that for all t emperatures below melting xi(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 be havior should be observable. (C) 2000 Elsevier Science B.V. All rights rese rved.