Spatial variation in the electronic structures of carpetlike graphene nanoribbons and sheets

•We study carpetlike graphene nanoribbons and sheets using ab initio calculations.•We focus on the local electronic structure of graphene induced by the step regions.•Carpetlike graphene sheets show remarkable variation under applied electric fields.•The spatial modulation could be verified by the STM experiment.

Graphene, when deposited on a supporting substrate with a step edge, may be deformed in the presence of the step edges of the substrate. In this study, we have investigated a spatial variation in the local electronic structure near the step region, by performing first-principles calculations for carpetlike armchair graphene nanoribbons (C-AGNR) and two-dimensional periodic carpetlike graphene sheets (PCGS). Our results indicate no practical difference in the local density of states (LDOS) between those of flat and step regions. Interestingly, however, the PCGS shows a remarkable variation in the LDOS with an external electric field (E-field). Furthermore, we also discuss the dependence of the direction and the magnitude of the applied E-field on the spatial variation in the LDOS.