Isotropic Landau levels of Dirac fermions in high dimensions

TL;DR

This paper extends the concept of Landau levels from two-dimensional Dirac fermions to higher dimensions, revealing a symmetric spectrum and zero-energy fractional modes, thus broadening understanding of relativistic Landau quantization.

Contribution

It introduces a generalization of Landau levels for Dirac fermions in three and higher dimensions with full rotational symmetry, including zero-energy fractional modes.

Findings

Existence of zero-energy fractional fermion modes.

Symmetric Landau level spectra scaling with square root of level index.

Mechanism involves nonminimal coupling to background fields.

Abstract

We generalize the Landau levels of two-dimensional Dirac fermions to three dimensions and above with the full rotational symmetry. Similarly to the two-dimensional case, there exists a branch of zero energy Landau levels of fractional fermion modes for the massless Dirac fermions. The spectra of other Landau levels distribute symmetrically with respect to the zero energy scaling with the square root of the Landau-level indices. This mechanism is a nonminimal coupling of Dirac fermions to the background fields. This high dimensional relativistic Landau-level problem is a square-root problem of its previous studied nonrelativistic version investigated in Li and Wu [arXiv:1103.5422 (2011)].