Two-dimensional phosphorus carbide: Competition between sp and sp bonding

We propose previously unknown allotropes of phosphorus carbide (PC) in the stable shape of an atomically thin layer. Different stable geometries, which result from the competition between sp bonding found in graphitic C and sp bonding found in black P, may be mapped onto 2D tiling patterns that simplify categorizing of the structures. Depending on the category, we identify 2D-PC structures that can be metallic, semi-metallic with an anisotropic Dirac cone, or direct-gap semiconductors with their gap tunable by in-layer strain.