Quantum materials hosting Weyl fermions have opened a new era of research in condensed matter physics. First proposed in 1929 in the context of particle physics, Weyl fermions have yet to be observed as elementary particles. In 2015, Weyl fermions were detected as collective electronic excitations in the strong spin–orbit coupled material tantalum arsenide, TaAs. This discovery was followed by a flurry of experimental and theoretical explorations of Weyl phenomena in materials. Weyl materials naturally lend themselves to the exploration of the topological index associated with Weyl fermions and their divergent Berry curvature field, as well as the topological bulk–boundary correspondence, giving rise to protected conducting surface states. Here, we review the broader class of Weyl topological phenomena in materials, starting with the observation of emergent Weyl fermions in the bulk and Fermi arc states on the surface of the TaAs family of crystals by photoemission spectroscopy. We then discuss several exotic optical and magnetic responses observed in these materials, as well as progress in developing related chiral materials. We discuss the conceptual development of high-fold chiral fermions, which generalize Weyl fermions, and we review the observation of high-fold chiral fermion phases by taking the rhodium silicide, RhSi, family of crystals as a prime example. Lastly, we discuss recent advances in Weyl line phases in magnetic topological materials. With this Review, we aim to provide an introduction to the basic concepts underlying Weyl physics in condensed matter, and to representative materials and their electronic structures and topology as revealed by spectroscopic studies. We hope this work serves as a guide for future theoretical and experimental explorations of chiral fermions and related topological quantum systems with potentially enhanced functionalities.

容纳魏尔费米子的量子材料开启了凝聚态物理研究的新纪元。魏尔费米子于1929年在粒子物理学的背景下首次提出，至今尚未被观察为基本粒子。2015年，在强自旋轨道耦合材料砷化钽TaAs中，Weyl费米子被检测为集体电子激发。这一发现之后，对材料中的韦尔现象进行了一系列的实验和理论探索。Weyl材料自然适合探索与Weyl费米子有关的拓扑指数及其发散的Berry曲率场，以及拓扑体-边界对应关系，从而产生受保护的导电表面态。在这里，我们回顾了材料中更广泛的Weyl拓扑现象类别，首先通过光发射光谱法观察TaAs族晶体表面上大量的Weyl费米子和费米弧态的出现。然后，我们讨论了在这些材料中观察到的几种奇特的光学和磁响应，以及开发相关手性材料的进展。我们讨论了高倍手性费米子的概念发展，概括了Weyl费米子，并以硅化铑RhSi晶体家族为主要例子，回顾了高倍手性费米子相的观察。最后，我们讨论了磁性拓扑材料中Weyl线相的最新进展。通过这篇综述，我们旨在介绍Weyl物理在凝聚态中的基本概念，以及光谱研究显示的代表性材料及其电子结构和拓扑。我们希望这项工作可以为将来手性费米子和具有潜在增强功能的相关拓扑量子系统的理论和实验探索提供指导。