Energy spectrum and quantum Hall effect in twisted bilayer graphene

Pilkyung Moon, Mikito Koshino

Research output: Contribution to journalArticlepeer-review

211 Citations (Scopus)


We investigate the electronic structure and the quantum Hall effect in twisted bilayer graphenes with various rotation angles in the presence of magnetic field. Using a low-energy approximation, which incorporates the rigorous interlayer interaction, we computed the energy spectrum and the quantized Hall conductivity in a wide range of magnetic field from the semiclassical regime to the fractal spectrum regime. In weak magnetic fields, the low-energy conduction band is quantized into electronlike and holelike Landau levels at energies below and above the van Hove singularity, respectively, and the Hall conductivity sharply drops from positive to negative when the Fermi energy goes through the transition point. In increasing magnetic field, the spectrum gradually evolves into a fractal band structure called Hofstadter's butterfly, where the Hall conductivity exhibits a nonmonotonic behavior as a function of Fermi energy. The typical electron density and magnetic field amplitude characterizing the spectrum monotonically decrease as the rotation angle is reduced, indicating that the rich electronic structure may be observed in a moderate condition.

Original languageEnglish
Article number195458
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number19
Publication statusPublished - 2012 May 29

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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