Stability of anomalous states of a local potential in graphene

S. C. Kim, Y. H. Jeong, S. R.Eric Yang

Research output: Contribution to journalArticlepeer-review


Graphene Landau levels have discrete energies consisting zero energy chiral states and non-zero energy states with mixed chirality. Each Landau level splits into discrete energies when a localized potential is present. A simple scaling analysis suggests that a localized potential can act as a strong perturbation, and that it can be even more singular in graphene than in ordinary two-dimensional systems of massful electrons. Parabolic, Coulomb, and Gaussian potentials in graphene may have anomalous boundstates whose probability density has a sharp peak inside the potential and a broad peak of size magnetic length ≤ outside the potential. The n = 0 Landau level with zero energy has only one anomalous state while the n =±1 Landau levels with non-zero energy have two (integer quantum number n is related to the quantized Landau level energies). These anomalous states can provide a new magnetospectroscopic feature in impurity cyclotron resonances of graphene. In the present work we investigate quantitatively the conditions under which the anomalous states can exist. These results may provide a guide in searching for anomalous states experimentally.

Original languageEnglish
Pages (from-to)8263-8266
Number of pages4
JournalJournal of Nanoscience and Nanotechnology
Issue number10
Publication statusPublished - 2015 Oct 1

Bibliographical note

Publisher Copyright:
© 2015 American Scientific Publishers.


  • A localized potential
  • Anomalous state
  • Dirac electron
  • Graphene
  • Magnetic field

ASJC Scopus subject areas

  • Bioengineering
  • General Chemistry
  • Biomedical Engineering
  • General Materials Science
  • Condensed Matter Physics


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