Twisted Bilayer Graphene: Moiré with a Twist

A multiscale model is developed to predict the equilibrium structure of twisted bilayer graphene (tBLG). Two distinct, modified Moiré structures are observed. The breathing mode, stable at large twist angle, has small amplitude (opposite sign) buckling of the two layers. The bending mode is characterized by large amplitude (same sign) buckling of the layers. The latter gives rise to a distorted Moiré pattern consisting of a twisted dislocation structure. The relaxation of the Moiré structure reduces the symmetry and increases the period of the tBLG. On the basis of these results, we derive a quantitative analytical model for the angle dependence of the tBLG energy.