Distortion of the perfect lattice structure in bilayer graphene

We consider the instability of bilayer graphene with respect to a distorted configuration in the same spirit as the model introduced by Su, Schrieffer and Heeger. By computing the total energy of a distorted bilayer, we conclude that the ground state of the system favors a finite distortion. We explore how the equilibrium configuration changes with carrier density and an applied potential difference between the two layers.