UC Berkeley

Carbon has numerous one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) allotropic structures. The study of carbon materials has long been a major focus of material sciences and condensed matter physics. Recently, a number of topological semi-metallic carbon allotropes with vastly different topological phases have been predicted from first-principles, showing exceptionally clean and robust topological properties near the Fermi surfaces. In this review, we provide a brief summary of the development of carbon allotropes from 1D to 3D. Then, we discuss topological properties of pure carbon materials, despite their exceedingly small spin–orbit coupling. Instead, the nearest-neighbor p z orbit interaction has been identified as the origin for the non-trivial topological properties, which vary due to different p z connectivity:​ zigzag, armchair, or pentagonal, as well as the interactions among further neighboring atoms. Next, we consider possible expansions of the topological properties of carbon materials to other light-element materials such as boron. Finally, we discuss future prospects in light of experimental feasibility and the recent surge in pursue of exotic carbon physics due to twisted graphene, which may also be viewed as a subset of the topological physics involving sp 2 /p z carbon.