{π}-Plasmon Dispersion in Free-Standing Graphene by Momentum-Resolved Electron Energy-Loss Spectroscopy

The {\pi}-plasmon dispersion in graphene was scrutinized by momentum(q)-resolved electron energy-loss spectroscopy with an improved q resolution and found to display the square root of q dispersion characteristic of the collective excitation of two-dimensional electron systems, in contrast with previous experimental and theoretical studies which reported a linear q dispersion. Our theoretical elaborations on the q-dependent spectra affirm this square root of q relation and further unveil an in-plane electronic anisotropy. The physical property of the {\pi} plasmon is thoroughly compared to that of the two-dimensional plasmon due to carriers of the Dirac fermions. A clear distinction between the {\pi} plasmon and the two-dimensional Dirac plasmon was demonstrated, clarifying the common notion on correlating the linearly-dispersed Dirac cones to the linear dispersion of the {\pi} plasmon previously reported.