Minimal conductivity of rippled graphene with topological disorder

We study the transport properties of a neutral graphene sheet with curved regions induced or stabilized by topological defects. The proposed model gives rise to Dirac fermions in a random magnetic field and in a random scalar potential acting like a space-dependent Fermi velocity induced by the curvature. The last term leads to a singular long-range correlated disorder with special characteristics. The Drude minimal conductivity at zero energy is found to be inversely proportional to the density of topological disorder, a signature of diffusive behavior.