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Cited by 491Topological Materials and PhenomenaGraphene research and applicationsQuantum and electron transport phenomena

Boundary conditions for Dirac fermions on a terminated honeycomb lattice

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Akhmerov, A. R., Beenakker, C. W. J.·2008·Physical Review B
DOI 10.1103/physrevb.77.085423
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Abstract

We derive the boundary condition for the Dirac equation corresponding to a tight-binding model on a two-dimensional honeycomb lattice terminated along an arbitrary direction. Zigzag boundary conditions result generically once the boundary is not parallel to the bonds. Since a honeycomb strip with zigzag edges is gapless, this implies that confinement by lattice termination does not, in general, produce an insulating nanoribbon. We consider the opening of a gap in a graphene nanoribbon by a staggered potential at the edge and derive the corresponding boundary condition for the Dirac equation. We analyze the edge states in a nanoribbon for arbitrary boundary conditions and identify a class of propagating edge states that complement the known localized edge states at a zigzag boundary.

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Crossref · 10.1103/physrevb.77.085423

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  • Since the honeycomb edge states are necessarily degenerate, a wavepacket made up of a superposition of such states will not spread.

    “Since the honeycomb edge states are necessarily degenerate 35 , i.e., they all possess the same propagation constant, a wavepacket (beam) made up of a superposition of such states will not spread.”

    From Strain-induced pseudomagnetic field and photonic Landau levels in dielectric structures (2013) · cites this paper as [35]

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Authors
Akhmerov, A. R., & Beenakker, C. W. J.
Affiliations
Leiden University (NL)
ORCID
Venue
Physical Review B
Publisher
American Physical Society (APS)
Published
2008-02-20
Volume
77
Issue
8
ISSN
  • 1098-0121 (ISSN-L)
  • 1550-235X
DOI
10.1103/physrevb.77.085423
OpenAlex
W2035533039
Cited by
491
References
0
Citations by year
2026: 11 · 2025: 15 · 2024: 13 · 2023: 16 · 2022: 21 · 2021: 22 · 2020: 59 · 2019: 28 · 2018: 33 · 2017: 20 · 2016: 28 · 2015: 14 · 2014: 39 · 2013: 25 · 2012: 48
FWCI
19.16
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review B (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • Leiden Repository (Leiden University) (submittedVersion)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
  • arXiv (Cornell University)
Funders
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
  • Physical Sciences › Materials Science › Materials Chemistry › Graphene research and applications
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
Keywords
Dirac fermions, honeycomb lattice, boundary conditions, graphene nanoribbons, zigzag edge, edge states, gap opening, staggered potential, tight-binding model, Dirac equation

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