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Landau level degeneracy and quantum Hall effect in a graphite bilayer

Edward McCann·Vladimir I. Fal'ko
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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 $2π$. 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, $σ_{xy}(N)$, 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.

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Edward McCann, Vladimir I. Fal'ko. 2006-03-03. Landau level degeneracy and quantum Hall effect in a graphite bilayer. https://doi.org/10.1103/physrevlett.96.086805

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