Diagnosis for Nonmagnetic Topological Semimetals in the Absence of Spin-Orbital Coupling

Abstract

Topological semimetals are under intensive theoretical and experimental studies. The first step of these studies is always the theoretical (numerical) predication of one or several candidate materials, based on first-principles numerics. In these calculations, it is crucial that all topological band crossings, including their types and positions in the Brillouin zone, are found. While band crossings along high-symmetry lines, which are routinely scanned in numerics, are simple to locate, the ones at generic momenta are notoriously time-consuming to find and may be easily missed. In this paper, we establish a theoretical scheme of diagnosis for topological semimetals where all band crossings are at generic momenta in systems with time-reversal symmetry and negligible spin-orbital coupling. The scheme uses only the symmetry (inversion and rotation) eigenvalues of the valence bands at high-symmetry points in the Brillouin zone as input and provides the types (lines or points), topological charges, numbers, and configurations of all robust topological band crossings, if any, at generic momenta. The nature of the new diagnosis scheme allows for full automation and parallelization and paves the way to high-throughput numerical predictions of topological semimetals.