Suppressed plasmon excitations, enhanced damping and static screening in Kek-Y strained $α-\mathcal{T}_3$ model

We performed a rigorous theoretical and numerical investigation into the polarization function, plasmon excitations, and plasmon damping in the Kek-$\alpha$ model, a two-dimensional material combining the key features of the $\alpha-\mathcal{T}_3$ lattice and Kekule-distorted graphene. Unlike conventional Kek-Y graphene, the Kekule modulation in the Kek-$\alpha$ model affects only one of the two sublattices, giving rise to a fundamentally new model with unusual electronic properties. The low-energy spectrum consists of two degenerate flat bands and two inequivalent Dirac cones with different Fermi velocities, referred to as the fast and slow cones. The particle-hole continuum responsible for Landau damping exhibits two distinct branches associated with transitions involving these Dirac cones. An additional particle-hole mode originates from electron transitions associated with the fast Dirac cone, appearing above the main diagonal. As the parameter $\alpha$ increases, the contribution from the fast Dirac cone becomes dominant. The additional transitions involving the flat bands and the fast Dirac cone substantially reduce the region where undamped plasmons can exist, similarly to the conventional $\alpha-\mathcal{T}_3$. Consequently, stable plasmons are observed only for relatively small values of $\alpha$ or at very small wave vectors. These unusual electronic and collective properties make the Kek-$\alpha$ model a promising platform for future plasmonic and nanoscale electronic applications.