Trigonal warping and Berry's phase Nπ in ABC-stacked multilayer graphene

Mikito Koshino, Edward McCann

Research output: Contribution to journalArticlepeer-review

170 Citations (Scopus)


The electronic band structure of ABC-stacked multilayer graphene is studied within an effective mass approximation. The electron and hole bands touching at zero energy support chiral quasiparticles characterized by Berry's phase Nπ for N layers, generalizing the low-energy band structure of monolayer and bilayer graphene. We investigate the trigonal-warping deformation of the energy bands and show that the Lifshitz transition, in which the Fermi circle breaks up into separate parts at low energy, reflects Berry's phase Nπ. It is particularly prominent in trilayers, N=3, with the Fermi circle breaking into three parts at a relatively large energy that is related to next-nearest-layer coupling. For N=3, we study the effects of electrostatic potentials which vary in the stacking direction, and find that a perpendicular electric field, as well as opening an energy gap, strongly enhances the trigonal-warping effect. In magnetic fields, the N=3 Lifshitz transition is manifested as a coalescence of Landau levels into triply degenerate levels.

Original languageEnglish
Article number165409
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number16
Publication statusPublished - 2009 Oct 12
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


Dive into the research topics of 'Trigonal warping and Berry's phase Nπ in ABC-stacked multilayer graphene'. Together they form a unique fingerprint.

Cite this