Edge States and the Quantized Hall Effect in Graphene

TL;DR

This paper analyzes edge states in graphene ribbons under quantum Hall conditions, showing how different edge terminations affect the electronic states and resulting Hall conductance, aligning with experimental observations.

Contribution

It provides a continuum Dirac model description of edge states in graphene with zigzag and armchair edges, explaining their impact on Hall conductance quantization.

Findings

Zigzag edges host dispersionless and current-carrying edge states.

Armchair edges involve valley mixing, leading to distinct edge state sets.

Hall conductance step for the lowest Landau level is half that of higher levels.

Abstract

We study edges states of graphene ribbons in the quantized Hall regime, and show that they can be described within a continuum model (the Dirac equation) when appropriate boundary conditions are adopted. The two simplest terminations, zigzag and armchair edges, are studied in detail. For zigzag edges, we find that the lowest Landau level states terminate in two types of edge states, dispersionless and current-carrying surface states. The latter involve components on different sublattices that may be separated by distances far greater than the magnetic length. For armchair edges, the boundary conditions are met by admixing states from different valleys, and we show that this leads to a single set of edges states for the lowest Landau level and two sets for all higher Landau levels. In both cases, the resulting Hall conductance step for the lowest Landau level is half that between higher Landau levels, as observed in experiment.