Edge states in graphene in magnetic fields: A specialty of the edge mode embedded in the n=0 Landau band

While usual edge states in the quantum Hall effect (QHE) reside between adjacent Landau levels, QHE in graphene has a peculiar edge mode at E=0 that resides right within the n=0 Landau level as protected by the chiral symmetry. We have theoretically studied the edge states to show that the E=0 edge mode, despite being embedded in the bulk Landau level, does give rise to a wave function whose charge is accumulated along zigzag edges. This property, totally outside continuum models, implies that the graphene QHE harbors edges distinct from ordinary QHE edges with their topological origin. In the charge accumulation the bulk states redistribute their charge significantly, which may be called a topological compensation of charge density. The real-space behavior obtained here should be observable in a scanning tunnel microscope imaging.