High-throughput screening for Weyl Semimetals with S4 Symmetry

Based on irreducible representations (or symmetry eigenvalues) and compatibility relations, a material can be predicted to be a topological/trivial insulator [satisfying compatibility relations] or a topological semimetal [violating compatibility relations]. However, Weyl semimetals usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy compatibility relations, or if the symmetry indicators are zero. In this work, we propose a new topological invariant χ for the systems with S4 symmetry [i.e., the improper rotation S4 (≡ IC4z) is a proper four-fold rotation (C4z) followed by inversion (I)], which can be used to diagnose the Weyl semimetal phase. Moreover, χ can be easily computed through the one-dimensional Wilson-loop technique. By applying this method to the high-throughput screening in first-principles calculations, we predict a lot of Weylsemimetals in both nonmagnetic and magnetic compounds. Various interesting properties (e.g. magnetic frustration effects, superconductivity and spin-glass order, etc.) are found in predicted Weyl semimetals, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states.