Plasmon dispersion in two-dimensional charge-sheets

The dispersion of sheet plasmons in two-dimensional electron systems was investigated in an in-situ ultra high vacuum environment by angle-resolved high-resolution electron-energy-loss spectroscopy (HREELS). In particular, the two-dimensional electron systems investigated were silver-induced surface superstructure, Si(111)( 3x3 )-Ag, and an epitaxially grown graphene layer on SiC(0001).;A two-dimensional sheet of charge was produced by precisely depositing a thin layer of silver onto Si(111)(7x7) to form Si(111)( 3x3 )-Ag superstructure and characterized by HREELS. Measurements for low silver coverage confirmed a two-dimensional adatom gas phase previously discovered by other experimental techniques and also determined the critical coverage to sustain this phase. A further deposition of silver adatoms destroyed the two-dimensional adatom gas phase, and silver grew in Stranski-Krastanov mode, forming silver micro-crystal after completion of the first silver layer. At this stage, the dispersion of sheet plasmons deviated from theoretical prediction, which features an opening of a gap where the momentum transfer vanishes. A calculation based on the theory of surface plasmons agreed with this observation, which implied this was a transition from a 2D-type plasmon to a 3D-type plasmon. This was a surprising result due to the unique electronic structure of Si(111)-( 3x3 )-Ag which maintained electron density roughly the same due to a depletion layer underneath the silicon surface. Eventually, the conventional surface plasmon was observed at the deposition of about 20 monolayers (ML) of silver, indicative of fully screening from the substrate.;HREELS studies of the sheet plasmon on a single graphene layer disclosed its two dimensional character and agreed with theoretical calculation of dispersion, but showed no damping where it was predicted. Also, we observed that the decay rate was roughly equal to the Fermi velocity.;The sheet-plasmon dispersion of few-layer graphene were characterized by HREELS. The 2-ML graphene had a similar behavior, whereas a peak splitting was observed around Fermi wavevector, due to the splitting of pi and pi* band at the corner (K point) of the hexagonal Brillouin zone. In measurements of 3- and 5-ML graphene layers, the opening gap between pi and pi* band induced a gap of dispersion behavior which indicated the failure of the free-electron-gas picture due to the reformed band structure. A qualitatively kinematic analysis of momentum transfer of electrons was used to explain the similarity between band gap and energy gap in dispersion diagrams.