High-Dimensional Topological Insulators with Quaternionic Analytic Landau Levels

TL;DR

This paper explores 3D topological insulators with quaternionic Landau levels, revealing their topological properties, surface states, and potential for higher-dimensional generalizations, with implications for experiments and interactions.

Contribution

It introduces quaternionic analyticity in 3D Landau levels and connects these to topological surface states, extending the concept to arbitrary dimensions.

Findings

Landau levels exhibit quaternionic analyticity.

Surface spectra include gapless helical Dirac modes.

Flat Landau levels can be generalized to higher dimensions.

Abstract

We study the 3D topological insulators in the continuum by coupling spin-1/2 fermions to the Aharonov-Casher SU(2) gauge field. They exhibit flat Landau levels in which orbital angular momentum and spin are coupled with a fixed helicity. The 3D lowest Landau level wavefunctions exhibit the quaternionic analyticity as a generalization of the complex analyticity of the 2D case. Each Landau level contributes one branch of gapless helical Dirac modes to the surface spectra, whose topological properties belong to the Z2-class. The flat Landau levels can be generalized to an arbitrary dimension. Interaction effects and experimental realizations are also studied.