Topological insulators with SU(2) Landau levels

TL;DR

This paper develops models of higher-dimensional topological insulators using SU(2) gauge fields, revealing new Landau level structures, boundary states, and quantized 4D quantum Hall effects.

Contribution

It introduces continuum models of 3D and 4D topological insulators with SU(2) gauge fields, generalizing Landau levels and uncovering boundary states and quantized effects.

Findings

Spatially separated helical and Weyl modes in higher dimensions

Presence of stable Fermi surfaces on boundaries

Quantized 4D quantum Hall effect observed

Abstract

We construct continuum models of 3D and 4D topological insulators by coupling spin-1/2 fermions to an SU(2) background gauge field, which is equivalent to a spatially dependent spin-orbit coupling. Higher dimensional generalizations of flat Landau levels are obtained in the Landau-like gauge. The 2D helical Dirac modes with opposite helicities and 3D Weyl modes with opposite chiralities are spatially separated along the third and fourth dimensions, respectively. Stable 2D helical Fermi surfaces and 3D chiral Fermi surfaces appear on open boundaries, respectively. The charge pumping in 4D Landau level systems shows quantized 4D quantum Hall effect.