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Topological semimetals are under intensive theoretical and experimentalstudies. The first step of these studies is always the theoretical (numerical)predication of one of several candidate materials, starting from firstprinciples. In these calculations, it is crucial that all topological bandcrossings, including their types and positions in the Brillouin zone, arefound. While band crossings along high-symmetry lines, which are routinelyscanned in numerics, are simple to locate, the ones at generic momenta arenotoriously time-consuming to find, and may be easily missed. In this paper, weestablish a theoretical scheme of diagnosis for topological semimetals whereall band crossings are at generic momenta in systems with time-reversalsymmetry and negligible spin-orbital coupling. The scheme only uses thesymmetry (inversion and rotation) eigenvalues of the valence bands athigh-symmetry points in the BZ as input, and provides the types, numbers andconfigurations of all topological band crossings, if any, at generic momenta.The nature of new diagnosis scheme allows for full automation andparallelizations, and paves way to high throughput numerical predictions oftopological materials.

Diagnosis for topological semimetals in the absence of spin-orbital coupling