Spectra of graphene nanoribbons with armchair and zigzag boundary conditions

Pedro Freitas*, Petr Siegl

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We study the spectral properties of the two-dimensional Dirac operator on bounded domains together with the appropriate boundary conditions which provide a (continuous) model for graphene nanoribbons. These are of two types, namely, the so-called armchair and zigzag boundary conditions, depending on the line along which the material was cut. In the former case, we show that the spectrum behaves in what might be called a classical way; while in the latter, we prove the existence of a sequence of finite multiplicity eigenvalues converging to zero and which correspond to edge states.

Original languageEnglish
Article number1450018
JournalReviews in Mathematical Physics
Issue number10
Publication statusPublished - 22 Nov 2014
Externally publishedYes


  • Dirac operator
  • Graphene
  • Spectrum
  • Zigzag and armchair boundary conditions

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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