Edge states in bilayer graphene in a magnetic field

2013/09/30 by P. K. Pyatkovskiy
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevb.88.205417

published as Phys. Rev. B 88, 205417 (2013) · 15 pages, 8 figures, v2: to match published version

openalex publication_date 2013/11/15 · arxiv created 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Spin-Filtered Edge States and Quantum Hall Effect in Graphene
• Charge and spin transport at the quantum Hall edge of graphene
• Theory of integer quantum Hall effect in graphene
• Electric Field Effect in Atomically Thin Carbon Films
• Quantum Hall Ferromagnetism in Graphene
• Edge state in graphene ribbons: Nanometer size effect and edge shape dependence
• Biased Bilayer Graphene: Semiconductor with a Gap Tunable by the Electric Field Effect