  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.
