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In three dimensional (3D) momentum space of solid crystal, a topologicalphase boundary separating the Chern insulating layers from normal insulatinglayers may exist, where the gap must be closed, resulting in a "Chernsemi-metal" state with topologically unavoidable band-crossings at fermi level.This state, if found to exist, is a condensed-matter realization of chiralfermions (or called Weyl fermions) in (3+1)D, and should exhibit remarkablefeatures, like magnetic monopoles in the bulk and fermi arcs on the surface.Here we predict, based on first-principles calculations, that such novelquantum state can be realized in a known ferromagnetic compound HgCr2Se4, witha single pair of Weyl fermions separated in momentum space. The characteristicfeature of this state in HgCr2Se4 is the presence of quantum Hall effectwithout external magnetic field in its quantum-well structure.

Chern semi-metal and Quantized Anomalous Hall Effect in HgCr2Se4