Adjustable propagating plasmons in $\alpha-\mathcal{T}_3$ lattice-based armchair nanoribbons

We have obtained and analyzed the electronic states, polarization function and the plasmon excitations for $\alpha - \mathcal{T}_3$-based nanoribbons with armchair termination. The calculated plasmon dispersions strongly depend on the number of the atomic rows across the ribbon, and the presence of the energy gap between the valence and conduction bands which is also determined by the nanoribbon geometry. The bandgap was proven to have the strongest effect on both the plasmon dispersions and their Landau damping. We have also demonstrated that for a small electron doping the plasmon dispersions do not depend on the relative hopping parameter $\alpha$ of the considered $\alpha - \mathcal{T}_3$ material in the long-wave limit and investigated the conditions when $\alpha$ becomes an important factor which strongly affects the plasmons. We believe that our new uncovered electronic and collective properties of nano-size $\alpha - \mathcal{T}_3$ribbons will find their applications in the field of modern electronics and nanodevices.