Edge states in graphene in magnetic fields -- a speciality of the edge mode embedded in the n=0 Landau band

Abstract

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 reside 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 re-distribute their charge significantly, which may be called a topological compensation of charge density. The real space behavior obtained here should be observable in an STM imaging.

4 pages, 9 figures

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Cited by in corpus (7)

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• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Non-local exchange effects in zigzag edge magnetism of neutral graphene nanoribbons
• Zero modes, energy gap, and edge states of anisotropic honeycomb lattice in a magnetic field
• Edge states of Spin-1/2 Two-Leg Ladder with Four-Spin Ring Exchange
• Topological quantum phase transition in the BEC-BCS crossover phenomena
• Propagation of acoustic edge waves in graphene under quantum Hall effect