Diverse carbon units in high-pressure C–K system predicted from first-principles and machine-learning methods

Metal-carbon compounds are significant for their diverse carbon units, which exhibit distinctive electronic and bonding properties, and broad application potential. In this article, we present a detailed C-K phase diagram, constructed using the crystal structure prediction method, MAGUS, based on machine-learning potentials fitted from first-principles calculations, revealing diverse carbon units, from allylenide ions to graphene-like two-dimensional layers. We found that the Pnma C12K16 phase contains allylenide ions, which contribute to its insulating behavior. Meanwhile, the ambient-pressure stable Cmcm C12K4 phase contains potassium-intercalated carbon layers with unique pentagonal-hexagonal-heptagonal (5-6-7) carbon rings, which we term "σ-graphene." This σ-graphene monolayer can be synthesized either by exfoliating bulk C12K4 using an electrochemical method or by removing potassium atoms via evaporating. Furthermore, Boltzmann transport calculations show that pristine σ-graphene exhibits a high electrical conductivity (∼5.5 × 107 S/m at 300 K), comparable with silver and copper, making it a promising material for electrical transport applications. In addition, σ-graphene demonstrates excellent adsorption capabilities for O2 and NO2, with adsorption energies of -0.503 and -0.528 eV, respectively, suggesting potential applications in catalysis and environmental monitoring. Our work highlights the C-K system as a versatile platform for synthesizing and applying novel carbon-based materials.