Topological quantum materials are a class of compounds featuring electronic band structures, which are topologically distinct from common metals and insulators. These materials have emerged as exceptionally fertile ground for materials science research. The topologically nontrivial electronic structures of these materials support many interesting properties, ranging from the topologically protected states, manifesting as high mobility and spin-momentum locking, to various quantum Hall effects, axionic physics, and Majorana modes. In this article, we describe different topological matters, including topological insulators, Weyl semimetals, twisted graphene, and related two-dimensional Chern magnetic insulators, as well as their heterostructures. We focus on recent materials discoveries and experimental advancements of topological materials, and their heterostructures. Finally, we conclude with prospects for the discovery of additional topological materials for studying quantum processes, quasiparticles and their composites, as well as exploiting potential applications of these materials.

拓扑量子材料是一类具有电子能带结构的化合物，其在拓扑结构上不同于普通金属和绝缘体。这些材料已经成为材料科学研究的沃土。这些材料的拓扑非平凡的电子结构支持许多有趣的特性，从拓扑保护状态（表现为高迁移率和自旋动量锁定）到各种量子霍尔效应，轴键物理和Majorana模式。在本文中，我们描述了不同的拓扑问题，包括拓扑绝缘体，Weyl半金属，扭曲石墨烯和相关的二维Chern磁绝缘体，以及它们的异质结构。我们专注于拓扑材料的最新材料发现和实验进展，及其异质结构。最后，我们得出了发现其他拓扑材料的前景，这些材料用于研究量子过程，准粒子及其复合材料，以及利用这些材料的潜在应用。