Plasmonic extinction of gated graphene nanoribbon array analyzed by a scaled uniform Fermi level

A uniform Fermi level profile is typically assumed in the analysis of a gated graphene nanoribbon, whose Fermi level is actually nonuniform in the experimental measurements. Here, we show that the uniform Fermi level has to be downshifted when it is used to analyze a backgated graphene nanoribbon array (GNRA). The plasmonic extinction behaviors of the GNRAs are perfectly preserved by assuming properly scaled uniform Fermi levels. The scaling factor is independent of the average value of the actual Fermi level profile, but it is a function of the ratio of the nanoribbon width to the distance of the nanoribbons from the backgate. This study facilitates the data postprocessing in the experiments, and may be helpful for analyzing the electron behaviors in GNRAs.