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      Hofstadter butterfly of graphene with point defects

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      Author
      Aslamoğlu, S.
      Oktel, M. Ö.
      Gülseren, O.
      Date
      2012
      Source Title
      Physical Review B
      Print ISSN
      2469-9950
      Electronic ISSN
      2469-9969
      Publisher
      American Physical Society
      Volume
      85
      Issue
      23
      Pages
      235414-1 - 235414-8
      Language
      English
      Type
      Article
      Item Usage Stats
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      Abstract
      We investigate the structure of Hofstadter's butterfly of graphene with point defects under a perpendicular magnetic field. We use a tight-binding method with interactions up to second-nearest neighbors. First of all, we present the Hofstadter butterfly spectrum of pure graphene, including all four valence orbitals with second-order hopping. To model defects, we perform calculations within an enlarged unit cell of seven carbon atoms and one defect atom. We find that impurity atoms with smaller hopping constants result in highly localized states which are decoupled from the rest of the system. The bands associated with these states form a nearly E=0 eV line. On the other hand, impurity atoms with higher hopping constants are strongly coupled with the neighboring atoms. These states modify the Hofstadter butterfly around the minimum and maximum values of the energy by forming two self-similar bands decoupled from the original butterfly. We also show that the bands and gaps due to the impurity states are robust with respect to the second-order hopping. © 2012 American Physical Society.
      Keywords
      73.22.Pr
      71.55.−i
      71.70.Di
      73.22.Gk
      Permalink
      http://hdl.handle.net/11693/21438
      Published Version (Please cite this version)
      http://dx.doi.org/10.1103/PhysRevB.85.235414
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