Quantum anomalous semimetals

Abstract The topological states of matter and materials have been attracting extensive interests as one the frontier topics in condensed physics science since discovery quantum Hall effect 1980s. So far all phases such integer insulators are characterized by invariants. None is a half or fractional. Here we propose type semimetals which hosts single cone Wilson fermions. fermions possess linear dispersion near Dirac point, but break chiral parity symmetry that an unpaired can be realized on lattice. In order to avoid fermion doubling problem, must broken explicitly if hermiticity, locality translational invariance hold. We find system classified relative homotopy group, half-integer invariant. term nontrivial phase anomalous semimetal. work opens door towards exploring novel with fractional charge.