Introduction . Beyond Landau’s classic approach based on spontaneously broken symmetries, topological theory provides a new perspective on the classification paradigm, including gapped phases like topological insulators1, and gapless phases like topological semimetals2. During the past decade, topological semimetals have been widely discussed for emulating relativistic quasiparticles3, for example, fourfold Dirac fermions4 , 5and even twofold Weyl fermions6 ...