Dislocations in graphene

Ana Carpio,Luis L Bonilla,María A H Vozmediano,Fernando De Juan

doi:10.1088/1367-2630/10/5/053021

Abstract

We study the stability and evolution of various elastic defects in a flat graphene sheet and the electronic properties of the most stable configurations. Two types of dislocations are found to be stable: ‘glide’ dislocations consisting of heptagon–pentagon pairs, and ‘shuffle’ dislocations, an octagon with a dangling bond. Unlike the most studied case of carbon nanotubes, Stone Wales defects seem to be dynamically unstable in the planar graphene sheet. Similar defects in which one of the pentagon–heptagon pairs is displaced vertically with respect to the other one are found to be dynamically stable. Shuffle dislocations will give rise to local magnetic moments that can provide an alternative route to magnetism in graphene.

Highlights

We study the stability and evolution of various elastic defects in a flat graphene sheet and the electronic properties of the most stable configurations
SW defects are found to be unstable in the flat lattice whereas similar defects in which one of the pentagon–heptagon pairs is displaced vertically with respect to the other one are found to be dynamically stable
How do we find the defects in graphene that correspond to different edge dislocations? We first substitute (x, y) in the elastic field of a dislocation

Summary

Periodized discrete elasticity and stability of defects

Dislocations are usually described by the equations of linear elasticity with singular sources whose supports are the dislocation lines. If the singularity is placed in any other location different from a lattice point, the core of the singularity forms a ‘shuffle’ dislocation: an octagon having one atom with a dangling bond, as shown in figure 2. If we use the elastic field of an edge dislocation dipole as initial and boundary conditions, there are again different stable configurations depending on how we place the dislocation cores. Instead of a dislocation dipole, our initial configuration may be a dislocation loop, in which two edge dislocations with opposite Burgers vectors are displaced vertically by one hexagon side: E(x − x0 − a, y − y0) − E(x − x0, y − y0 − l) (l = a/√3 is the length of the hexagon side). If we displace the edge dislocations vertically by l/2, E(x − x0 − a, y − y0) − E(x − x0, y − y0 − l/2), the resulting dislocation loop evolves toward a single heptagon defect [26]

Electronic properties

Electronic structure of single dislocations

Conclusions and discussion