Temperature-dependent collective effects for silicene and germanene

We have numerically calculated electron exchange and correlation energies and dynamical polarization functions for recently discovered silicene, germanene and other buckled honeycomb lattices at various temperatures. We have compared the dependence of these energies on the chemical potential, field-induced gap and temperature and we have concluded that in many cases they behave qualitatively in a similar way, i.e. increasing with the doping, decreasing significantly at elevated temperatures, and displaying different dependences on the asymmetry gap at various temperatures. Furthermore, we have used the dynamical polarizability to study the 'split' plasmon branches in the buckled lattices and predicted a unique splitting, different from that in gapped graphene, for various energy gaps. Our results are crucial for stimulating electronic, transport and collective studies of silicene and germanene, as well as for enhancing silicene-based fabrication and technologies for photovoltaics and transistor devices.