High-Throughput Screening of Two-Dimensional Planar sp² Carbon Space Associated with a Labeled Quotient Graph

The configurational space of two-dimensional planar sp² carbon has been systematically scanned by a random strategy combined with group and graph theory, and 1114 new carbon allotropes have been identified. These allotropes are energetically more favorable than most of the previously predicted 120 carbon allotropes. By fitting the HSE06 band structures of six old structures, we optimize the parameters for a general and transferable tight-binding model for high-throughput band structure calculations. We identified that there are 190 Dirac semimetals, 241 semiconductors, and 683 normal metals among the new allotropes. Interestingly, several stable low-energy carbon systems with exotic electronic properties are proposed, such as type III, type I/II mixed, and type I/III mixed semimetals, which are very rare in planar carbon systems. In particular, one nodal-line semimetal has been discovered among these thousands of allotropes, which is the first nodal-line semimetal in sp² carbon systems. Our discoveries greatly enrich our knowledge of the structures and electronic properties of the two-dimensional carbon family.