Bandgap opening induced by electron localization in graphene antidot lattices

Graphene antidot lattices (GALs) have garnered significant attention for their potential in semiconductor applications, yet the origin of bandgap opening remains controversial. Combining the octet rule, we propose a low-parameter physical model with weighted information entropy to quantitatively determine the electron density distribution, and the tight-binding parameters are obtained from the occupancy numbers based on the maximum entropy method. The results from our model reveal a complex bandgap opening mechanism in zigzag-edged hexagonal GALs (ZH-GALs), where specific inter-ribbon connections and quantum confinement cause the localization of π-electrons between antidots, leading to the elimination of energy levels degeneracy. We also observe that the anisotropy of rectangular ZH-GALs is enhanced as the defect radius increases, indicating a transition from GALs-like to graphene nanoribbons-like bandgap behavior. This study tells us that more than 1/9 ZH-GALs have considerable bandgaps, addressing the deficiency in band structure engineering between regimes dominated by defect scattering and quantum confinement.