Layered Quantum Hall Insulators with Ultracold Atoms

TL;DR

This paper extends quantum Hall insulators to a 3D layered system with non-Abelian gauge groups, demonstrating topological properties and proposing an ultracold atom experimental setup.

Contribution

It introduces a layered 3D quantum Hall insulator with non-Abelian gauge symmetry and suggests a feasible ultracold atom realization.

Findings

Layered 3D insulator exhibits nontrivial topology.

Quantized transverse conductivities can be engineered.

Surface modes are connected to the topological nature.

Abstract

We consider a generalization of the 2-dimensional (2D) quantum-Hall insulator to a non-compact, non-Abelian gauge group, the Heisenberg-Weyl group. We show that this kind of insulator is actually a layered 3D insulator with nontrivial topology. We further show that nontrivial combinations of quantized transverse conductivities can be engineered with the help of a staggered potential. We investigate the robustness and topological nature of this conductivity and connect it to the surface modes of the system. We also propose a simple experimental realization with ultracold atoms in 3D confined to a 2D square lattice with the third dimension being mapped to a gauge coordinate.