3D Quantum Anomalous Hall Effect in Hyperhoneycomb Lattices

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.