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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.
Broken symmetry and tilting effects are ubiquitous in Weyl semimetals (WSMs). Therefore, it is crucial to understand their impacts on the materials electronic and optical properties. Here, using a realistic four-band model for WSMs that incorporates
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 rel
We show that compounds in a family that possess time-reversal symmetry and share a non-centrosymmetric cubic structure with the space group F-43m (No. 216) host robust ideal Weyl semi-metal fermions with desirable topologically protected features. Th
Higher-order topology yields intriguing multidimensional topological phenomena, while Weyl semimetals have unconventional properties such as chiral anomaly. However, so far, Weyl physics remain disconnected with higher-order topology. Here, we report
We have studied theoretically the Weyl semimetals the point symmetry group of which has reflection planes and which contain equivalent valleys with opposite chiralities. These include the most frequently studied compounds, namely the transition metal