Charge inhomogeneity in a single and bilayer graphene

We study the possibility of charge ordered state in both single and bilayer graphene using a real space tight binding model. We argue that there is no charge ordered state in a single layer graphene. We also predict that the bilayer graphene can undergo a transition to a charge ordered state that is a commensurate CDW at low enough carrier density. We find that aside from the Coulomb interaction of the carriers of two layers that stabilizes the charge ordered state, so does the inter layer coupling.