Edge stacking dislocations in two-dimensional bilayers with a small lattice mismatch

TL;DR

This paper models and analyzes the formation, structure, and energy of edge stacking dislocations in bilayer graphene with lattice mismatch, providing analytical solutions and discussing experimental implications.

Contribution

It introduces the concept of edge Burgers vector and derives analytical solutions for edge dislocations in bilayer graphene with lattice mismatch.

Findings

Analytical expressions for dislocation structure and energy.

Estimated barrier for dislocation penetration.

Potential methods to measure dislocation barriers and strain.

Abstract

Incomplete stacking dislocations are predicted to form at edges of the shorter upper layer in two-dimensional hexagonal bilayers upon stretching the longer bottom layer. A concept of the edge Burgers vector is introduced to describe such dislocations by analogy with the Burgers vector of standard bulk dislocations. Analytical solutions for the structure and energy of edge stacking dislocations in bilayer graphene are obtained depending on the magnitude of elongation and angles between the edge Burgers vector, direction of elongation and edge. The barrier for penetration of stacking dislocations inside the bilayer is estimated. The possibilities to measure the barrier to relative motion of graphene layers and strain of graphene on a substrate by observation of edge stacking dislocations are discussed.