Scaling law of band gap values in graphene with triangular defects in a superhoneycomb arrangement: A first-principles study

Modifications of the geometric structure of pristine graphene should be promising methods to expand the possibility of its applications. For example, it is expected that various graphenes with defects arranged periodically are semiconductors. Revealing a quantitative behavior of their band gap values is very important for designing future device materials. Here, we investigate the variations of the band gap value in graphene with triangular defects in a superhoneycomb arrangement in the framework of the density functional theory. In this study, we choose the shape of defects (triangular defects) considering experimental research. It is found that the dependence of band gap does not fully follow the conventional scaling law, which is applicable to various graphenes with defects arranged periodically. In the present system, the gap value is not proportional to the square root of the number of atoms removed. Instead, the universal new scaling law with the size of the triangular defect and the periodicity is obtained. This scaling law should give us the opportunity to design new device materials, and indicates that many interesting electronic properties of graphene with defects are still to be explored in the future.