TY - JOUR

T1 - Trigonal warping and Berry’s phase Npi in ABC-stacked multilayer graphene.

AU - Koshino, Mikito

AU - McCann, Edward

PY - 2009/10/15

Y1 - 2009/10/15

N2 - 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-nearestlayer 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.

AB - 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-nearestlayer 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.

KW - Berry phase

KW - effective mass

KW - energy gap

KW - Fermi level

KW - graphene

KW - Landau levels

KW - multilayers

UR - http://www.scopus.com/inward/record.url?scp=72849113995&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.80.165409

DO - 10.1103/PhysRevB.80.165409

M3 - Journal article

VL - 80

SP - 165409

JO - Physical review B

JF - Physical review B

SN - 1550-235X

IS - 16

ER -