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

TL;DR

This paper analyzes the electronic band structure of ABC-stacked multilayer graphene, focusing on trigonal warping, Berry's phase, and the Lifshitz transition, revealing how these phenomena are affected by layer number, electric fields, and magnetic fields.

Contribution

It provides a detailed study of trigonal warping and Berry's phase in multilayer graphene, especially for trilayers, and explores how external fields influence these effects.

Findings

Trigonal warping causes Fermi circle breakup at low energy.

Berry's phase N pi characterizes chiral quasiparticles in multilayer graphene.

Electric and magnetic fields significantly enhance trigonal-warping effects.

Abstract

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 N pi 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 N pi. 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.