Theory of the spontaneous buckling of doped graphene

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.