We study the changes induced by the effective gauge field due to ripples on the low energy electronic structure of graphene. We show that zero-energy Landau levels will form, associated with the smooth deformation of the graphene layer, when the height corrugation, $h$, and the length of the ripple, $l$, are such that $h^2∕la\gtrsim 1$, where $a$ is the lattice constant. The existence of localized levels gives rise to a large compressibility at zero energy and to the enhancement of instabilities arising from electron-electron interactions including electronic phase separation. The combined effect of the ripples and an external magnetic field breaks the valley symmetry of graphene, leading to the possibility of valley selection.

• Received 4 November 2007

DOI:https://doi.org/10.1103/PhysRevB.77.075422