• 文献标题:   Spectral butterfly and electronic localization in rippled-graphene nanoribbons: Mapping onto effective one-dimensional chains
  • 文献类型:   Article
  • 作  者:   ROMANTABOADA P, NAUMIS GG
  • 作者关键词:  
  • 出版物名称:   PHYSICAL REVIEW B
  • ISSN:   2469-9950 EI 2469-9969
  • 通讯作者地址:   Univ Nacl Autonoma Mexico
  • 被引频次:   9
  • DOI:   10.1103/PhysRevB.92.035406
  • 出版年:   2015

▎ 摘  要

We report an exact map into one-dimensional effective chains of the tight-binding Hamiltonian for electrons in armchair and zigzag graphene nanoribbons with any uniaxial ripple. This mapping is used for studying the effect of uniaxial periodic ripples, taking into account the relative orientation changes between pi orbitals. Such effects are important for short-wavelength ripples, while for long-wave ones, the system behaves nearly as strained graphene. The spectrum has a complex nature, akin to the Hofstadter butterfly with a rich localization behavior. Gaps at the Fermi level and dispersionless bands were observed, as well. The complex features of the spectrum arise as a consequence of the quasiperiodic or periodic nature of the effective one-dimensional system. Some features of these systems can be understood by considering weakly coupled dimers. The eigenenergies of such dimers are highly degenerate, and the net effect of the ripple can be seen as a perturbation potential that splits the energy spectrum. Several particular cases were analytically solved to understand this feature.