  Graphene is a realization of an esoteric class of materials -- electronic
crystalline membranes. We study the interplay between the free electrons and
the two-dimensional crystal, and find that it induces a substantial effect on
the elastic structure of the membrane. For the hole-doped membrane, in
particular, we predict a spontaneous buckling. In addition, attenuation of
elastic waves is expected, due to the effect of corrugations on the bulk
modulus. These discoveries have a considerable magnitude in graphene, affecting
both its mesoscopic structure, and its electrical resistivity, which has an
inherent asymmetry between hole- and electron-doped graphene.
