Carbon has numerous one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) allotropic structures. The study of carbon materials has been a major focus of material science and condensed matter physics. Previous studies have identified different classes of topological semimetallic carbon allotropes with different topological phases. In this review, we first give a brief summary of the development of carbon allotropes from 1D to 3D. Next, we discuss topological properties of carbon materials and their physical origin. Then, we consider possible expansion of the topological study of carbon materials to other light-element materials such as boron. Finally, we present future prospects in pursue of topological physics within carbon allotropes.

中文翻译：

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拓扑碳材料：新视角

碳具有许多一维 (1D)、二维 (2D) 和三维 (3D) 同素异形结构。碳材料的研究一直是材料科学和凝聚态物理学的一个主要焦点。先前的研究已经确定了具有不同拓扑相的不同类别的拓扑半金属碳同素异形体。在这篇综述中，我们首先简要总结了碳同素异形体从 1D 到 3D 的发展。接下来，我们讨论碳材料的拓扑性质及其物理起源。然后，我们考虑将碳材料的拓扑研究扩展到其他轻元素材料，如硼。最后，我们提出了在碳同素异形体中追求拓扑物理学的未来前景。