High-throughput screening for Weyl semimetals with S4 symmetry

Based on irreducible representations (or symmetry eigenvalues) and compatibility relations (CR), a material can be predicted to be a topological/trivial insulator (satisfying CR) or a topological semimetal (violating CR). However, Weyl semimetals (WSMs) usually go beyond this symmetry-based strategy. In other words, Weyl nodes could emerge in a material, no matter if its occupied bands satisfy CR, or if the symmetry indicators are zero. In this work, we propose a new topological invariant x for the systems with S4 symmetry (i.e., the improper rotation S4?- IC4z? is a proper fourfold rotation (C4z) followed by inversion (I)), which can be used to diagnose the WSM phase. Moreover, x can be easily computed through the onedimensional Wilson-loop technique. By applying this method to the high-throughput screening in our first-principles calculations, we predict a lot of WSMs in both nonmagnetic and magnetic compounds. Various interesting properties (e.g., magnetic frustration effects, superconductivity and spin-glass order, etc.) are found in predicted WSMs, which provide realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states. ? 2020 Science China Press. Published by Elsevier B.V. and Science China Press. All rights reserved.

Automated summary

In this work, a new topological invariant x is proposed for diagnosing the Weyl semimetal phase, which can be easily computed through the one-dimensional Wilson-loop technique. By applying this method to high-throughput screening in first-principles calculations, numerous Weyl semimetals are predicted in both nonmagnetic and magnetic compounds. Various interesting properties are found in the predicted Weyl semimetals, providing realistic platforms for future experimental study of the interplay between Weyl fermions and other exotic states.