Edge States of Bilayer Graphene in the Quantum Hall Regime

TL;DR

This paper investigates the diverse behaviors of edge states in bilayer graphene under quantum Hall conditions, revealing how boundary geometry influences edge state dispersions and crossings.

Contribution

It provides a comprehensive analysis of edge state types in bilayer graphene, linking tight-binding results with continuum models and clarifying the effects of boundary conditions.

Findings

Identifies three types of edge state behaviors: weakly, strongly, and non-dispersive.

Shows the dependence of edge state crossings on boundary conditions and bulk energies.

Demonstrates the complexity of edge state spectra due to spin anticrossings.

Abstract

We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by non-linear transformations to the spectra of quantum Hall edge--states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a hole-like edge state of one valley and a particle-like state of the other on the same edge, which may or may not cross depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends BOTH on boundary conditions and the energies of the bulk states.