Quantum Hall ferromagnetism in graphene: a SU(4) bosonization approach

Abstract

We study the quantum Hall effect in graphene at filling factors ν= 0 and ν= \pm, concentrating on the quantum Hall ferromagnetic regime, within a non-perturbative bosonization formalism. We start by developing a bosonization scheme for electrons with two discrete degrees of freedom (spin-1/2 and pseudospin-1/2) restricted to the lowest Landau level. Three distinct phases are considered, namely the so-called spin-pseudospin, spin, and pseudospin phases. The first corresponds to a quarter-filled (ν=-1) while the others to a half-filled (ν= 0) lowest Landau level. In each case, we show that the elementary neutral excitations can be treated approximately as a set of n-independent kinds of boson excitations. The boson representation of the projected electron density, the spin, pseudospin, and mixed spin-pseudospin density operators are derived. We then apply the developed formalism to the effective continuous model, which includes SU(4) symmetry breaking terms, recently proposed by Alicea and Fisher. For each quantum Hall state, an effective interacting boson model is derived and the dispersion relations of the elementary excitations are analytically calculated. We propose that the charged excitations (quantum Hall skyrmions) can be described as a coherent state of bosons. We calculate the semiclassical limit of the boson model derived from the SU(4) invariant part of the original fermionic Hamiltonian and show that it agrees with the results of Arovas and co-workers for SU(N) quantum Hall skyrmions. We briefly discuss the influence of the SU(4) symmetry breaking terms in the skyrmion energy.

16 pages, 4 figures, final version, extended discussion about the boson-boson interaction and its relation with quantum Hall skyrmions

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Cited by in corpus (17)

• The electronic properties of graphene
• Electronic Properties of Graphene in a Strong Magnetic Field
• Theory of interacting electrons on the honeycomb lattice
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Tilted-Cone-induced easy-plane pseudo-spin ferromagnet and Kosterlitz-Thouless transition in massless Dirac fermions
• Theoretical expectations for a fractional quantum Hall effect in graphene
• SU(4) spin waves in the $\nu =\pm 1$ quantum Hall ferromagnet in graphene
• Flat-band ferromagnetism in a topological Hubbard model
• Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system
• Scattering of magnons at graphene quantum-Hall-magnet junctions
• Symmetry characterization of the collective modes of the phase diagram of the $\nu =0$ quantum Hall state in graphene: Mean-field and spontaneously broken symmetries
• Quantum Hall Skyrmions at $\nu =0,\pm 1$ in monolayer graphene
• Flat-band ferromagnetism and spin waves in the Haldane-Hubbard model
• Theoretical Aspects of the Fractional Quantum Hall Effect in Graphene
• Fractional quantum Hall effect of topological surface states under a strong tilted magnetic field
• Nuclear magnetic resonance line shapes of Wigner crystals in ${}^{13}$C-enriched graphene