Dislocations and Bragg glasses in two dimensions

TL;DR

This paper investigates how quenched disorder induces dislocations in two-dimensional periodic systems, revealing conditions under which Bragg glass behavior persists despite topological defects.

Contribution

It extends previous work by including effects of freezing and pinning, showing that the dislocation correlation length can be significantly larger at low temperatures.

Findings

Dislocation correlation length $\xi_D$ increases at low temperature due to pinning effects.

$\xi_D$ depends on the core energy via a stretched exponential.

Bragg glass behavior persists over a wide range of scales below melting.

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 $\xi_D$, which we estimated. We extend this description to include effects of freezing and pinning of dislocations at low temperature. The resulting $\xi_D$ at low temperature is found to be {\it larger} than our previous estimate, which is recovered above a characteristic temperature. The dependence of $\xi_D$ in the bare core energy of dislocations is a stretched exponential. We stress that for all temperatures below melting $\xi_D$ becomes arbitrarily large at weak disorder compared to the translational order length $R_a \gg a$. Thus there is a wide region of length scales, temperature and disorder where Bragg glass like behavior should be observable.