Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4

In three dimensional (3D) momentum space of solid crystal, a topological phase boundary separating the Chern insulating layers from normal insulating layers may exist, where the gap must be closed, resulting in a "Chern semi-metal" state with topologically unavoidable band-crossings at fermi level. This state, if found to exist, is a condensed-matter realization of chiral fermions (or called Weyl fermions) in (3+1)D, and should exhibit remarkable features, like magnetic monopoles in the bulk and fermi arcs on the surface. Here we predict, based on first-principles calculations, that such novel quantum state can be realized in a known ferromagnetic compound HgCr2Se4, with a single pair of Weyl fermions separated in momentum space. The characteristic feature of this state in HgCr2Se4 is the presence of quantum Hall effect without external magnetic field in its quantum-well structure.