Midgap states in corrugated graphene: Ab initio calculations and effective field theory

We investigate the electronic properties of corrugated graphene and show how rippling-induced pseudo-magnetic fields alter graphene's low-energy electronic properties by combining first-principle calculations with an effective field theory. The formation of flat bands near the Fermi level corresponding to pseudo-Landau levels is studied as a function of the rippling parameters. Quenched and relaxed ripples turn out to be fundamentally different is this respect: it is demonstrated, both numerically and analytically, that annealing of quenched ripples can destroy the flat bands.