Perfectly Conducting Channel and Universality Crossover in Disordered Nano-Graphene Ribbons

The band structure of graphene ribbons with zigzag edges have two valleys well separated in momentum space, related to the two Dirac points of the graphene spectrum. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at band center. This feature gives rise to a perfectly conducting channel in the disordered system, if the impurity scattering does not connect the two valleys, i.e. for long-range impurity potentials. Ribbons with short-range impurity potentials, however, through inter-valley scattering display ordinary localization behavior. The two regimes belong to different universality classes: unitary for long-range impurities and orthogonal for short-range impurities.