Topological carbon materials: a new perspective

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.