Dislocations and Bragg glasses in two dimensions

Pierre Le Doussal; Thierry Giamarchi

doi:10.1016/S0921-4534(00)00005-8

paper

Dislocations and Bragg glasses in two dimensions

arXiv:cond-mat/9810218 · doi:10.1016/S0921-4534(00)00005-8

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 {\bf 52} 1242 (1995)] we found that, contrarily 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 {\it larger} than our previous estimate, which is recovered above a characteristic temperature. The dependence of $ξ_{D}$ in the bare core energy of dislocations 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.

6 pages, 4 figures, RevTex

Dislocations and Bragg glasses in two dimensions

Abstract

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