Landau level quantization of Dirac electrons on the sphere

TL;DR

This paper extends the formalism for Dirac electrons on a sphere to include magnetic fields, enabling better understanding of Landau level quantization in systems like graphene and topological insulators.

Contribution

It generalizes existing formalism for Dirac electrons on the sphere to incorporate the effects of an external magnetic field.

Findings

Formalism now includes magnetic field effects on Dirac electrons.

Applicable to systems like graphene and topological insulators.

Facilitates numerical studies of Landau levels on curved surfaces.

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.