Twisted Bilayer Graphene: Moire with a Twist

A multiscale model is developed to predict the equilibrium structure of twisted bilayer, graphene (tBLG). Two distinct, modified Moire structures are observed. The breathing mode, stable at large twist angle, has small amplitude (opposite budding of the two layers. The bending mode is characterized-by large amplitude (same sign) budding of the layers. The latter gives rise to a, distorted Moire pattern consisting of a twisted dislocation structure., The relaxation of the Moire 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.