  Graphene, a single sheet of graphite, has attracted tremendous attention due
to recent experiments which demonstrate that carriers in it are described by
massless fermions with linear dispersion. In this note, we consider the
possibility of Wigner crystallization in graphene in the absence of external
magnetic field. We show that the ratio of potential and kinetic energy is
independent of the carrier density, the tuning parameter that usually drives
Wigner crystallization and find out that for given material parameters
(dielectric constant and Fermi velocity), Wigner crystallization is not
possible. We comment on the how these results change in the presence of a
strong external magnetic field.
