Landau level quantization of Dirac electrons on the sphere

Abstract

Interactions in Landau levels can stabilize new phases of matter, such as fractionally quantized Hall states. Numerical studies of these systems mostly require compact manifolds like the sphere or a torus. For massive dispersions, a formalism for the lowest Landau level on the sphere was introduced by Haldane [F.D.M. Haldane, PRL 51, 605 (1983)]. Graphene and surfaces of 3D topological insulators, however, display massless (Dirac) dispersions, and hence require a different description. We generalize a formalism previously developed for Dirac electrons on the sphere in zero field to include the effect of an external, uniform magnetic field.

arXiv comment5 pages

References in corpus (5)

• The electronic properties of graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A symmetry-respecting topologically-ordered surface phase of 3d electron topological insulators
• Interacting surface states of three-dimensional topological insulators

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• Hearing the shape of a Dirac drum: Dual quantum Hall states on curved surfaces
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