Robustness of the Edge States in Graphene Quantum Hall System: Does the Chiral Symmetry Degraded by t′ Matter?

While usual edge states in the quantum Hall effect 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, small but finite second‐neighbor hopping exists, which degrades the chiral symmetry in the bipartite lattice. Here we have found that the edge mode is again embedded in the n = 0 bulk Landau level despite the broken chiral symmetry due to the second‐neighbor hopping, where the charge is accumulated along the zigzag edge. Hence the behavior of the zero mode has turned out to be distinguished from the case of zero magnetic field, which is related to the stability of topological compensation. This charge density accumulated along the zigzag edge can be measured with an STM imaging in magnetic fields.