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

TL;DR

This paper investigates the unique E=0 edge mode in graphene's quantum Hall effect, revealing its charge accumulation along zigzag edges and its topological nature, which differs from conventional edge states.

Contribution

The study demonstrates that the E=0 edge mode in graphene causes charge accumulation along edges, highlighting a topologically distinct edge state within the Landau level.

Findings

E=0 edge mode causes charge accumulation along zigzag edges

Charge redistribution indicates topological charge compensation

Edge states exhibit properties outside continuum models

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.