3D Quantum Anomalous Hall Effect in Hyperhoneycomb Lattices

TL;DR

This paper explores how short-range interactions in a 3D hyperhoneycomb lattice can induce a quantum anomalous Hall phase characterized by Weyl fermions and surface Fermi arcs, with quantifiable Hall conductivity.

Contribution

It demonstrates that strong interactions in a hyperhoneycomb lattice can lead to a 3D quantum anomalous Hall phase with unique topological features.

Findings

Weak interactions lead to a line-node semimetal.

Strong interactions induce a 3D quantum anomalous Hall phase.

The Hall conductivity is quantized as e^2/(√3 a h).

Abstract

We address the role of short range interactions for spinless fermions in the hyperhoneycomb lattice, a three dimensional (3D) structure where all sites have a planar trigonal connectivity. For weak interactions, the system is a line-node semimetal. In the presence of strong interactions, we show that the system can be unstable to a 3D quantum anomalous Hall phase with loop currents that break time reversal symmetry, as in the Haldane model. We find that the low energy excitations of this state are Weyl fermions connected by surface Fermi arcs. We show that the 3D anomalous Hall conductivity is $e^{2}/(\sqrt{3}ah)$, with $a$ the lattice constant.