Graphene as an electronic membrane

We investigate the membrane aspect of graphene and its impact on the electronic properties. We show that rippling generates spatially varying electrochemical potential that is proportional to the square of the local curvature. This is due to the rehybridization effects and the change in the next-neighbor hopping caused by curvature. We estimate the electrochemical- potential variation associated with the rippling observed in recent scanning tunneling microscopy (STM) to be of order 30 meV. Further we show that the charge inhomogeneity in turn stabilizes ripple formation.