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Only one atom thick and not inclined to lattice defects, graphene representsthe ultimate crystalline membrane. However, its structure reveals uniquefeatures not found in other crystalline membranes, in particular the existenceof ripples with wavelength of 100-300 Angstroms. Here, I trace the origin ofthis difference to the free electrons in the membrane. The deformation energyof the lattice creates a coupling between charge fluctuations and thestructure, resulting in ripples on the membrane, correlated with chargeinhomogeneities. In graphene this mechanism reproduces the experimental resultfor both charge puddles and ripples.

Correlation between Charge Inhomogeneities and Structure in Graphene and Other Electronic Crystalline Membranes