Landau level spectra and the quantum Hall effect of multilayer graphene

TL;DR

This paper analyzes the Landau level spectra and quantum Hall effect in ABA-stacked multilayer graphene using an effective mass approach, highlighting the importance of next-nearest layer couplings on low-energy properties.

Contribution

It provides a detailed analysis of the Landau levels and quantum Hall effect in multilayer graphene, emphasizing the role of next-nearest layer couplings and symmetry considerations.

Findings

Next-nearest layer couplings significantly affect the low-energy spectrum.

Energy shifts, level anti-crossings, and valley splitting are caused by these couplings.

The effective Hamiltonian can be approximated as block-diagonal, simplifying analysis.

Abstract

The Landau level spectra and the quantum Hall effect of ABA-stacked multilayer graphenes are studied in the effective mass approximation. The low-energy effective mass Hamiltonian may be partially diagonalized into an approximate block-diagonal form, with each diagonal block contributing parabolic bands except, in a multilayer with an odd number of layers, for an additional block describing Dirac-like bands with a linear dispersion. We fully include the band parameters and, taking into account the symmetry of the lattice, we analyze their affect on the block-diagonal Hamiltonian. Next-nearest layer couplings are shown to be particularly important in determining the low-energy spectrum and the phase diagram of the quantum Hall conductivity, by causing energy shifts, level anti-crossings, and valley splitting of the low-lying Landau levels.