Magnetic Weyl semimetal materials

A Weyl semimetal (WSM) is a member of the topological semimetal family. An ideal WSM has, and only has, isolated band crossing points formed by the nondegenerate valence and conduction bands near the Fermi level. The low energy excitation of its quasiparticles can be characterized by the Weyl equation describing the chiral Weyl fermions. The formation of WSM states in three-dimensional solids requires breaking of the time reversal symmetry, inversion symmetry, and their combined symmetry. The Weyl point, i.e., the band crossing point, has topological stability and definite chirality or magnetic charge, and the left-and right-handed chiral Weyl points must appear in pairs. The discovery of the nonmagnetic Weyl semimetal Ta As family of materials makes it possible to study the electronic states with chiral properties and the new physical properties and phenomena caused by them. Compared with nonmagnetic WSMs, magnetic Weyl semimetals can have one pair of Weyl points, which is the simplest type and is useful for the analysis of physical mechanism. They can be used to realize the quantum anomalous Hall effect with intrinsic magnetism, which provides a new means to control Weyl points and related effects through the outer magnetic field. In this work we introduce the basic principles of magnetic WSMs, including a theoretical model and calculation of the topological number, then review the theoretical predictions and experimental studies of some typical materials, as well as the latest developments in magnetic topological quantum chemistry and high-throughput calculations of magnetic topological materials. Finally, we discuss the prospects for magnetic WSMs and future research directions. (authors)