Landau level degeneracy and quantum Hall effect in a graphite bilayer

TL;DR

This paper derives an effective Hamiltonian for graphite bilayers, revealing unique Landau level degeneracies and quantum Hall effect features that differ from monolayer graphene, including distinct Hall conductivity plateaus.

Contribution

It introduces a new effective Hamiltonian for graphite bilayers, explaining their low-energy electronic structure and quantum Hall effect behavior.

Findings

Landau levels form almost equidistant groups with four-fold degeneracy.

Hall conductivity exhibits plateaus at multiples of 4e^2/h.

Distinct double step of 8e^2/h across zero density.

Abstract

We derive an effective two-dimensional Hamiltonian to describe the low energy electronic excitations of a graphite bilayer, which correspond to chiral quasiparticles with a parabolic dispersion exhibiting Berry phase $2\pi$. Its high-magnetic-field Landau level spectrum consists of almost equidistant groups of four-fold degenerate states at finite energy and eight zero-energy states. This can be translated into the Hall conductivity dependence on carrier density, $\sigma_{xy}(N)$, which exhibits plateaus at integer values of $4e^{2}/h$ and has a ``double'' $8e^{2}/h$ step between the hole and electron gases across zero density, in contrast to $(4n+2)e^{2}/h$ sequencing in a monolayer.