Many-body effects and optical properties of single and double layer α-$T_3$ lattices

An extensive analytical and numerical investigation has been carried out to examine the role played by many-body effects on various α-$T_3$ materials under an off-resonance optical dressing field. Additionally, we explore its dependence on the hopping parameter α as well as the electron–light coupling strength λ ₀. The obtained dressed states due to mutual interaction between Dirac electrons and incident light are shown to demonstrate rather different electronic and optical properties in comparison with those in the absence of incident light. Specifically, various collective transport and optical properties of these electron dressed states are discussed in detail and compared for both single- and double layer α-$T_3$ lattices. All of these novel properties are due to the presence of a middle flat band and the interband transitions between it and an upper conduction band. Also, coupled plasmon dispersions for interacting double layer α-$T_3$ lattices are calculated, revealing a lower acoustic-like plasmon branch with tunable group velocity determined by both the layer separation and Fermi energy of each layer. Finally, a many-body theory is presented within the random-phase approximation for calculating the optical absorbance of doped multi-layered α-$T_3$ lattices in a linearly-polarized light field. We anticipate that the discoveries reported here could impact the design of the next-generation nano-optical and nano-plasmonic devices. (paper)