  Only one atom thick and not inclined to lattice defects, graphene represents
the ultimate crystalline membrane. However, its structure reveals unique
features not found in other crystalline membranes, in particular the existence
of ripples with wavelength of 100-300 Angstroms. Here, I trace the origin of
this difference to the free electrons in the membrane. The deformation energy
of the lattice creates a coupling between charge fluctuations and the
structure, resulting in ripples on the membrane, correlated with charge
inhomogeneities. In graphene this mechanism reproduces the experimental result
for both charge puddles and ripples.
