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The Peierls-Nabarro (PN) model for dislocations is a hybrid model thatincorporates the atomistic information of the dislocation core structure intothe continuum theory. In this paper, we study the convergence from a fullatomistic model to the PN model with $\gamma$-surface for the dislocation in abilayer system (e.g. bilayer graphene). We prove that the displacement field ofand the total energy of the dislocation solution of the PN model areasymptotically close to those of the full atomistic model. Our work can beconsidered as a generalization of the analysis of the convergence fromatomistic model to Cauchy-Born rule for crystals without defects in theliterature.

From atomistic model to the Peierls-Nabarro model with $\gamma$-surface for dislocations