Plasmons in graphene nanoribbons

Abstract

We calculate the dielectric function and plasmonic response of armchair (aGNRs) and zigzag (zGNRs) graphene nanoribbons using the self-consistent-field approach within the Markovian master equation formalism (SCF-MMEF). We accurately account for electron scattering with phonons, ionized impurities, and line-edge roughness and show that electron scattering with surface optical phonons is much more prominent in GNRs than in graphene. We calculate the loss function, plasmon dispersion, and the plasmon propagation length in supported GNRs. Midinfrared plasmons in supported (3N+2)-aGNRs can propagate as far as several microns at room temperature, with 4--5-nm-wide ribbons having the longest propagation length. In other types of aGNRs and in zGNRs, the plasmon propagation length seldom exceeds 100 nm. Plasmon propagation lengths are much longer on nonpolar (e.g., diamondlike carbon) than on polar substrates (e.g., ${\mathrm{SiO}}_{2}$ or hBN), where electrons scatter strongly with surface optical phonons. We also show that the aGNR plasmon density is nearly uniform across the ribbon, while in zGNRs, because of the highly localized edge states, plasmons of different spin polarization are accumulated near the opposite edges.