Edge states in graphene quantum Hall system with bond vs potential disorder

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. In real graphene, disorder always exists, and here we study how the edge states appear in disordered graphene QHE. We have to discriminate bond disorder and potential disorder, since the former respects the chiral symmetry in the bipartite lattice while the latter does not. We have found that, for a bond disorder, the charge accumulation along zigzag edges persists to occur, while a potential disorder destroys them. The charge accumulation along zigzag edges should be measured with an STM imaging in magnetic fields.