Landau level degeneracy and quantum Hall effect in a graphite bilayer

Landau level degeneracy and quantum Hall effect in a graphite bilayer

3 Mar 2006 | Edward McCann and Vladimir I. Fal'ko
The authors derive an effective two-dimensional Hamiltonian to describe the low-energy electronic excitations of a graphite bilayer, which exhibit chiral quasiparticles with a parabolic dispersion and a Berry phase of \(2\pi\). The 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 results in a specific sequence of plateaus in the Hall conductivity \(\sigma_{xy}(N)\) as a function of carrier density, with plateaus at integer values of \(4e^2/h\) and a "double" \(8e^2/h\) step between the hole and electron gases across zero density. This behavior differs from the monolayer, where the sequence is \((4n+2)e^2/h\). The zero-energy Landau level in the bilayer is 8-fold degenerate due to spin and valley degeneracies, compared to the 4-fold degeneracy of other bilayer states and all Landau levels in a monolayer. The study highlights the unique properties of chiral quasiparticles in a graphite bilayer, including their Berry phase and the unusual degeneracy of the zero-energy Landau level.The authors derive an effective two-dimensional Hamiltonian to describe the low-energy electronic excitations of a graphite bilayer, which exhibit chiral quasiparticles with a parabolic dispersion and a Berry phase of \(2\pi\). The 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 results in a specific sequence of plateaus in the Hall conductivity \(\sigma_{xy}(N)\) as a function of carrier density, with plateaus at integer values of \(4e^2/h\) and a "double" \(8e^2/h\) step between the hole and electron gases across zero density. This behavior differs from the monolayer, where the sequence is \((4n+2)e^2/h\). The zero-energy Landau level in the bilayer is 8-fold degenerate due to spin and valley degeneracies, compared to the 4-fold degeneracy of other bilayer states and all Landau levels in a monolayer. The study highlights the unique properties of chiral quasiparticles in a graphite bilayer, including their Berry phase and the unusual degeneracy of the zero-energy Landau level.
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Understanding Landau-level degeneracy and quantum Hall effect in a graphite bilayer.