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Commensurate-incommensurate phase transition in bilayer graphene

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.