Changing character of electronic transitions in graphene: From single particle excitations to plasmons

In this paper we clarify the nature of $\pi$ and $\pi+\sigma$ electron excitations in pristine graphene. We clearly demonstrate the continuous transition from single particle to collective character of such excitations and how screening modifies their dispersion relations. We prove that $\pi$ and $\pi+\sigma$ plasmons do exist in graphene, though occurring only for a particular range of wavevectors and with finite damping rate. The particular attention is paid to compare the theoretical results with available EELS measurements in optical ($\mathrm{Q\approx 0}$) and other ($\mathrm{Q\neq 0}$) limits. The conclusions, based on microscopic numerical results, are confirmed in an approximate analytical approach.