High-Throughput Calculation of 2D Carbon Allotropes

We systematically calculate the electronic and phononic properties of over 60 two-dimensional (2D) carbon allotropes. To accomplish this, we developed a graph theoretical method introducing the embedding tensor, enabling the discovery and characterization of three folded carbon allotropes. Additionally, we propose a unified taxonomy for sp2 nanocarbon allotropes in 2D, where each structure is assigned a unique symbol representing its geometry.<br/><br/>This naming scheme is demonstrated for all structures described in the literature and illustrated for several other topologically-allowed sp2 carbon systems. The symbol provides straightforward access to geometric features like polygon count and arrangement. It facilitates classifying reported structures, many of which had arbitrary names assigned by different authors.<br/><br/>The naming convention enables a systematic study of vibrational properties, allowing the search for unique features like topological phonons and determination of finite-temperature free energies. Calculations combine density functional theory (DFT) with a machine-learning force-field ("GAP") for faster computation.<br/><br/>Overall, our work provides a comprehensive framework for understanding the diverse properties of 2D carbon nanostructures through a novel topological perspective.