Weyl Semimetals with $S_4$ symmetry

TL;DR

This paper introduces a symmetry-based criterion using invariants and indicators to identify Weyl semimetals in time-reversal-invariant systems with $S_4$ symmetry, revealing new candidate materials and their Weyl point configurations.

Contribution

It establishes a new symmetry analysis method to classify Weyl semimetals in $S_4$ symmetric systems, expanding the search beyond previously known materials.

Findings

Identifies Weyl semimetals among materials previously predicted as topological insulators.

Locates four pairs of Weyl points in specific planes with same chirality.

Provides an effective model capturing the nontrivial topology of these materials.

Abstract

In the time-reversal-breaking centrosymmetric systems, the appearance of Weyl points can be guaranteed by an odd number of all the even/odd parity occupied bands at eight inversion-symmetry-invariant momenta. Here, based on symmetry analysis and first-principles calculations, we demonstrate that for the time-reversal-invariant systems with $S_4$ symmetry, the Weyl semimetal phase can be characterized by the inequality between a well-defined invariant $\eta$ and an $S_4$ indicator $z_2$. By applying this criterion, we find that some candidates, previously predicted to be topological insulators, are actually Weyl semimetals in the noncentrosymmetric space group with $S_4$ symmetry. Our first-principles calculations show that four pairs of Weyl points are located in the $k_{x,y}$ = 0 planes, with each plane containing four same-chirality Weyl points. An effective model has been built and captures the nontrivial topology in these materials. Our strategy to find the Weyl points by using symmetry indicators and invariants opens a new route to search for Weyl semimetals in the time-reversal-invariant systems.