Wigner crystal phases in bilayer graphene

It is generally believed that a Wigner Crystal in single layer graphene can not form because the magnitudes of the Coulomb interaction and the kinetic energy scale similarly with decreasing electron density. However, this scaling argument does not hold for the low energy states in bilayer graphene. We consider the formation of a Wigner Crystal in weakly doped bilayer graphene with an energy gap opened by a perpendicular electric field. We argue that in this system the formation of the Wigner Crystal is not only possible, but different phases of the crystal with very peculiar properties may exist here depending on the system parameters.