lattice at finite temperatures*

Many-body electronic properties, including plasmons, their damping, static screening and transport coefficients have been
calculated based on the finite-temperature polarization function for the α-T₃ model. We have thoroughly
investigated the role of the coupling strength parameter $\alpha$ for the extra atom at the center of the honeycomb lattice, which in our case could be continuously varied from 0 (graphene) to 1 (the dice lattice). Specifically, we obtained and analyzed the dice lattice limit. We have derived several crucial semi-analytical approximations for the static and long
wavelength limits, related to the finite-temperature behavior of the plasmon excitations in α-T₃ materials.