Edge states in bilayer graphene in a magnetic field

TL;DR

This paper investigates the properties of edge states in biased bilayer graphene subjected to a magnetic field, analyzing their dispersion relations and wave functions for different edge geometries.

Contribution

It provides exact dispersion equations and analytic wave functions for edge states in bilayer graphene, considering both zigzag and armchair edges, within a four-band continuum model.

Findings

Edge states are characterized by exact dispersion relations.

Low-energy zigzag edge modes are analyzed in detail.

Numerical solutions reveal the spectrum of edge states for various boundary conditions.

Abstract

Edge states in biased bilayer graphene in a magnetic field are studied within the four-band continuum model. The analysis is done for the semi-infinite graphene plane and for the graphene ribbon of a finite width, in the cases of zigzag and armchair edges. Exact dispersion equations for the edge states and analytic expressions for their wave functions are written in terms of the parabolic cylinder functions. The spectrum of edge states for each type of the boundary conditions is found by numerically solving the corresponding dispersion equations. The low-energy modes localized at zigzag edges are explored in detail.