Low Energy Intraband Plasmons and Electron Energy Loss Spectra of Single and Multilayered Graphene

We present a theory for the calculation of the low energy intraband plasmon frequencies and the electron energy loss (EEL) spectra of single layer and multilayer graphene sheets. Our calculation shows that the number of plasmons that can be excited is equal to the number of graphene layers in the sample. One of these is the dominant in-phase plasmon having a square root dependence on the wave number at low wave vectors, whereas the others are out-of-phase plasmons having near linear dependences on the wave number. The EEL spectra of a single layer graphene shows a single peak at the plasmon frequency, which has been observed experimentally. The EEL spectra of all multilayer graphenes have two peaks, one corresponding to the dominant in-phase plasmon and the other due to the out of phase plasmons. We predict that careful measurement of the EEL of multilayer graphene will show both peaks due to the low energy intraband plasmons.