Stability of anomalous states of a local potential in graphene

S. C. Kim, Y. H. Jeong, Sung Ryul Yang

Research output: Contribution to journalArticle

Abstract

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
Volume15
Issue number10
DOIs
Publication statusPublished - 2015 Oct 1

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Graphene
graphene
Electron energy levels
Cyclotrons
Cyclotron resonance
energy
Chirality
Coulomb potential
Electrons
Impurities
cyclotron resonance
chirality
quantum numbers
integers
energy levels
scaling
perturbation
impurities
electrons

Keywords

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

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Chemistry(all)
  • Materials Science(all)
  • Bioengineering
  • Biomedical Engineering

Cite this

Stability of anomalous states of a local potential in graphene. / Kim, S. C.; Jeong, Y. H.; Yang, Sung Ryul.

In: Journal of Nanoscience and Nanotechnology, Vol. 15, No. 10, 01.10.2015, p. 8263-8266.

Research output: Contribution to journalArticle

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