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.
@article{arxiv.1008.5365,
title = {Layered Quantum Hall Insulators with Ultracold Atoms},
author = {A. Zamora and G. Szirmai and M. Lewenstein},
journal= {arXiv preprint arXiv:1008.5365},
year = {2011}
}