Graphene in a Strong Magnetic Field: Massless Dirac Particles vs. Skyrmions

TL;DR

This paper explores models of massless Dirac fermions in a magnetic field on a sphere, linking single-particle states to quantum Hall systems and revealing skyrmions in many-body states.

Contribution

It introduces models for massless Dirac fermions in spherical geometry, analogous to traditional charge carrier models, facilitating numerical studies of quantum Hall effects.

Findings

Single-particle states are compatible with existing quantum Hall codes.

Fully filled sublevels form skyrmions with respect to layer spin.

Models provide a new framework for studying Dirac fermions in magnetic fields.

Abstract

We discuss models for massless Dirac fermions being subject to a perpendicular magnetic field in spherical geometry. These models are analogues of Haldane`s spherical construction for massful charge carriers. The single particle states constructed here are easily implemented in existing numerical code for many-body problems in conventional quantum Hall systems. Moreover, the many-body states of fully filled sublevels in the subspace of lowest Landau level index are skyrmions with respect to the layer spin.