Edge states for the n=0 Laudau level in graphene

TL;DR

This paper theoretically investigates the unique E=0 edge states in graphene's n=0 Landau level, revealing their topological origin, wave function behavior along zigzag edges, and potential observability in STM experiments.

Contribution

It provides a detailed analysis of the E=0 edge mode in graphene, highlighting its topological nature and distinct wave function properties, which differ from conventional quantum Hall edge states.

Findings

E=0 edge states are localized along zigzag edges with width scaling with magnetic length

These edge states have a topological origin outside the continuum model

Edge mode contribution decays algebraically but is compensated by bulk contribution

Abstract

In the anomalous quantum Hall effect (QHE), a hallmark of graphene, nature of the edge states in magnetic fields poses an important question, since the edge and bulk should be intimately related in QHE. Here we have theoretically studied the edge states, focusing on the E=0 edge mode, which is unusual in that the mode is embedded right within the n=0 bulk Landau level, while usual QHE edge modes reside across adjacent Landau levels. Here we show that the n=0 Landau level, including the edge mode, has a wave function amplitude accumulated along zigzag edges whose width scales with the magnetic length, l_B. This contrasts with the usual QHE where the charge is depleted from the edge. The implications are: (i) The E=0 edge states in strong magnetic fields have a topological origin in the honeycomb lattice, so that they are outside the continuum ("massless Dirac") model. (ii) The edge-mode contribution decays only algebraically into the bulk, but this is "topologically" compensated by the bulk contribution, resulting in the accumulation over l_B. (iii) The real space behavior obtained here should be observable in STM experiments.