Disorder by order in graphene

We predict the existence of an intriguing disorder by order phenomenon in graphene transport where higher quality (and thus more ordered) samples, while having higher mobility at high carrier density, will manifest more strongly insulating (and thus effectively more disordered) behavior as the carrier density is lowered compared with lower quality samples (with higher disorder) which exhibit an approximate resistivity saturation phenomenon at low carrier density near the Dirac point. This predicted behavior simulating a metal-insulator transition, which we believe to have recently been observed in an experiment at Manchester University [L. A. Ponomarenko et al., Nat. Phys. 7, 958 (2011)], arises from the suppression of Coulomb disorder induced inhomogeneous puddles near the charge neutrality point in high quality graphene samples.