▎ 摘　　要

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 greater than or similar to 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.