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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 $chi$ for the systems with S$_4$ symmetry [i.e., the improper rotation S$_4$ ($equiv$ IC$_{4z}$) is a proper four-fold rotation (C$_{4z}$) followed by inversion (I)], which can be used to diagnose the Weyl semimetal phase. Moreover, $chi$ 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 Weyl semimetals 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.
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 firs
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
We perform a systematic study of the Zitterbewegung effect of fermions, which are described by a Gaussian wave with broken spatial-inversion symmetry in a three-dimensional low-energy Weyl semimetal. Our results show that the motion of fermions near
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
In this paper, the chiral Hall effect of strained Weyl semimetals without any external magnetic field is proposed. Electron-phonon coupling emerges in the low-energy fermionic sector through a pseudogauge potential. We show that, by using chiral kine