Hofstadter butterfly of graphene with point defects
Author
Aslamoğlu, S.
Oktel, M. Ö.
Gülseren, O.
Date
2012Source 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
ArticleItem Usage Stats
123
views
views
116
downloads
downloads
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.