The study of topology as it relates to physical systems has rapidly accelerated during the past decade. Critical to the realization of new topological phases is an understanding of the materials that exhibit them and precise control of the materials chemistry. The convergence of new theoretical methods using symmetry indicators to identify topological material candidates and the synthesis of high-quality single crystals plays a key role, warranting discussion and context at an accessible level. This Perspective provides a broad introduction to topological phases, their known properties, and material realizations. We focus on recent work in topological Weyl and Dirac semimetals, with a particular emphasis on magnetic Weyl semimetals and emergent fermions in chiral crystals and their extreme responses to excitations, and we highlight areas where the field can continue to make remarkable discoveries. We further examine open questions and directions for the topological materials science community to pursue, including exploration of non-equilibrium properties of Weyl semimetals and cavity-dressed topological materials.

在过去的十年中，与物理系统有关的拓扑研究迅速发展。对实现新的拓扑阶段至关重要的是，要了解展示这些拓扑阶段的材料以及对材料化学的精确控制。使用对称性指标识别拓扑材料候选者的新理论方法的融合以及高质量单晶的合成起着关键作用，需要在可访问的水平上进行讨论和讨论。本“观点”广泛介绍了拓扑阶段，其已知属性和材料实现。我们专注于拓扑Weyl和Dirac半金属的最新研究，特别着重于磁性Weyl半金属和手性晶体中出现的费米子及其对激发的极端响应，我们重点介绍了该领域可以继续取得杰出发现的领域。我们进一步研究了拓扑材料科学界要追求的开放性问题和方向，包括探索Weyl半金属和腔体填充拓扑材料的非平衡特性。