Chemistry Reference
In-Depth Information
Fig. 3.19
Plasmon dispersion
in MLG
/
Pt(111). Data have
been acquired for three
different impinging energies.
The thin solid line represents
the best fit for experimental
points. The dashed area
indicates the continuum of
intraband SPEs. The thick
solid line represents the
boundary for the continuum
of interband SPEs. The
plasmon mode enters the
Landau damping regime by
interband electron-hole
excitations when its
dispersion relation intercepts
the boundary for the
continuum of interband SPEs.
In the inset, the curves are
reported with respect to the
dimensionless units
E/EF
and
q
||
/
kF
0, the transition is not allowed at 0
<E <
2
E
F
.
If the collective mode
enters the SPE continuum, the plasmon mode can be damped. The plasmon lies
inside the interband SPE continuum, thus decaying into electron-hole pairs, above
the Fermi wave vector. Plasmon can propagate without damping only in the region
(see Fig.
3.19
) not included in the continuum of SPE (interband and intraband). Such
considerations are fully confirmed by the analysis of the FWHM of the plasmon
peak as a function of both
q
||
[Fig.
3.20
] and the plasmon energy [Fig.
3.20
]. Landau
damping for the MLG sheet plasmon occurs for momenta above the Fermi wave
vector (about 0.09 Å
−
1
) and for energies above 0.5 eV, as revealed by the sudden
increase of the FWHM. Interestingly, the sheet plasmon does not enter into the
intraband SPE continuum and it exists for all wave vectors. By contrast, for ASP,
Landau damping occurs via intraband transitions and the plasmon mode exists only
up to a few hundreds meV (Diaconescu et al.
2007
; Park and Palmer
2010
; Pohl
et al.
2010
). On the other hand, for MLG on SiC(0001), the FWHM continuously
increases with the momentum (Langer et al.
2010
; Liu et al.
2008
). For such system,
it has been shown (Langer et al.
2010
) that the existence of steps or grain boundaries
is a source of strong damping, while the dispersion is rather insensitive to defects.
For
q
||
=
