  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.
