In a first principle computational study, using density functional theory, we have identified four types of 2D carbon sheets, similar to graphene, made entirely of non-regular hexagons. In one case, we get a structure where the non-regular hexagons have four sides of length d1 = 1.416 Å and two sides of length d2 = 1.68 Å. Next case, in the non-regular hexagons the side d1 (two times) and d2 (four times) are exchanged. In two other cases, the non-regular hexagons have three pairs (opposite sides) of different lengths (d1 = 1.529 Å, d2 = 1.567 Å, and d3 = 1.612 Å; d1 = 1.387 Å, d2 = 1.348 Å, and d3 = 1.387 Å). By propper choice of the non-regular hexagon sides, one could arrive at a 2D carbon system like graphene, but with a tunable band gap. The structure is more stable when the system has more number of regular C-C bonds than the longer C-C bonds. Due to its non-regular hexagons, special atomic configuration, this system may have, like graphene, unusual properties. It is semiconducting, and there is no need to functionalize it for opening the band gap as is the case with graphene.
Keywords: 2D Dirac carbon; Band structure; Density functional theory; Graphene; Non-regular hexagon; Semiconductor.