Energy loss spectra of doped graphene and armchair carbon nanotubes at finite temperature

We have studied the dynamical polarizability associated to energy loss spectra of armchair carbon nanotubes in the context of tight binding model Hamiltonian including long range electronic interaction. Linear response theory in the context of random phase approximation has been implemented to obtain charge response function via calculating correlation function of density operators. The effects of both temperature and electron doping as well as the diameter on the frequency behaviour of charge response have been investigated. The sharp peak in the energy loss spectra of the armchair carbon nanotube disappears upon raising the temperature. This is not the case of non interacting case where temperature has no considerable effect on the dynamical susceptibility. Also, the similar calculations have been performed for graphene sheet.