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

We have studied the dynamical polarizability associated to energy loss spectraof armchair carbon nanotubes in the context of tight binding model hamiltonian includinglong range electronic interaction. linear response theory in the context of random phaseapproximation has been implemented to obtain charge response function via calculatingcorrelation function of density operators. the eects of both temperature and electrondoping as well as the diameter on the frequency behaviour of charge response have beeninvestigated. the sharp peak in the energy loss spectra of the armchair carbon nanotubedisappears upon raising the temperature. this is not the case of non interacting case wheretemperature has no considerable eect on the dynamical susceptibility. also, the similarcalculations have been performed for graphene sheet.