Plasmon dispersion in semimetallic armchair graphene nanoribbons

The dispersion relations for plasmons in intrinsic and extrinsic semimetallic armchair graphene nanoribbons (acGNR) are calculated in the random phase approximation using the orthogonal ${p}_{z}$-orbital tight-binding method. Our model predicts new plasmons for acGNR of odd atomic widths, $N=5,11,17,...$ Our model further predicts plasmons in acGNR of even atomic widths, $N=2,8,14,...$, related to those found using a Dirac continuum model but with different quantitative dispersion characteristics. We find that the dispersion of all plasmons in semimetallic acGNR depends strongly on the localization of the ${p}_{z}$ electronic wavefunctions. We also find that overlap integrals for acGNR behave in a more complex way than predicted by the Dirac continuum model, suggesting that these plasmons will experience a small damping for all $q\ensuremath{\ne}0$. Plasmons in extrinsic semimetallic acGNR with the chemical potential in the lowest (highest) conduction (valence) band are found to have dispersion characteristics nearly identical to their intrinsic counterparts, with negligible differences in dispersion arising from the slight differences in overlap integrals for the interband and intraband transitions.