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 the random space dependent Fermi velocity induced by the curvature. This last term leads to 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.