Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model

2020/11/02 by Cesar R. de Oliveira, César R de Oliveira, Vinicius L. Rocha +1
Materials Science · Mathematics · Physics and Astronomy · #2D Materials and Applications #Bilayer #Bilayer graphene #Dirac (video compression format) #Gapless playback #Graph #Graphene #Graphene research and applications #Quantum #Quantum tunnelling #Topological Materials and Phenomena #cond-mat.mes-hall #math-ph #math.MP #msc:47E05 #msc:81Q10 #quant-ph

paper · pdf · doi:10.1088/1751-8121/abc6c1

J. Phys. A: Math. Theor., 29 pages

openalex publication_date 2020/11/02 · openalex created_date 2020/11/09 · arxiv created 2020/11/17 · arxiv updated 2020/11/18 · openalex updated_date 2026/08/06

Abstract

Abstract A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac cones are then proven to be present only for trilayer graphene, although the bilayer has a gapless parabolic band component. Our model rigorously exhibits basic facts from tight-binding calculations, effective two-dimensional models and a π -orbital continuum model with nearest-neighbour tunnelling that have been discussed in the physics literature.

Citations

• Periodic Orbit Theory and Spectral Statistics for Quantum Graphs
• Kirchhoff's rule for quantum wires
• Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene
• On the Spectra of Carbon Nano-Structures
• Ab initiotheory of gate induced gaps in graphene bilayers
• Electronic transport in two-dimensional graphene
• The electronic properties of graphene
• Electronic Structure of Multilayer Graphene
• From graphene to fullerene: experiments with microwave photonic crystals

Cited by

• Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene