Commensurate-incommensurate phase transition in bilayer graphene

TL;DR

This paper models the phase transition in bilayer graphene from commensurate to incommensurate states, deriving analytical expressions and confirming them with atomistic calculations, and discusses experimental measurement possibilities.

Contribution

It extends the Frenkel-Kontorova model to bilayer graphene, providing analytical estimates for transition parameters and defect properties validated by DFT calculations.

Findings

Analytical expressions for critical elongation and defect properties.

Confirmation of estimates through atomistic DFT-D calculations.

Discussion on measuring interlayer motion barriers via defect formation.

Abstract

A commensurate-incommensurate phase transition in bilayer graphene is investigated in the framework of the Frenkel-Kontorova model extended to the case of two interacting chains of particles. Analytic expressions are derived to estimate the critical unit elongation of one of the graphene layers at which the transition to the incommensurate phase takes place, the length and formation energy of incommensurability defects (IDs) and the threshold force required to start relative motion of the layers on the basis of dispersion-corrected density functional theory calculations of the interlayer interaction energy as a function of the relative position of the layers. These estimates are confirmed by atomistic calculations using the DFT-D based classical potential. The possibility to measure the barriers for relative motion of graphene layers by the study of formation of IDs in bilayer graphene is discussed.