Fig. 1: Quantum anomalous semimetal.

a The phase diagram and topological invariant of trivial insulator, quantum anomalous semimetal and topological insulator. b The dispersion of the Wilson fermions along the wave vector kx and keeping all other ki = 0. c The spin texture of 1D Wilson fermions. d The spin texture of 2D Wilson fermions. e The relative homotopy group mapping of band structure and spin texture of the parity anomalous semimetal. The whole torus on the first Brillouin zone maps to the semi-Bloch sphere (green line) and the small loop around crossing point to the equator of the Bloch sphere (red line).