Theory of the spontaneous buckling of doped graphene

Graphene is a realization of an uncommon 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, an 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.

Figure 1

(Color online) Dimensionless polarization operator ${\left(\hslash v_f\right)}^2\beta {\Pi }^V$ as a function of the dimensionless momentum $\hslash v_f\beta q$.