• 文献标题:   Spectra of graphene nanoribbons with armchair and zigzag boundary conditions
  • 文献类型:   Review
  • 作  者:   FREITAS P, SIEGL P
  • 作者关键词:   dirac operator, spectrum, graphene, zigzag armchair boundary condition
  • 出版物名称:   REVIEWS IN MATHEMATICAL PHYSICS
  • ISSN:   0129-055X EI 1793-6659
  • 通讯作者地址:   Univ Lisbon
  • 被引频次:   4
  • DOI:   10.1142/S0129055X14500184
  • 出版年:   2014

▎ 摘  要

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.