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3.4.2
Evidence for Acoustic-Like Plasmons
To measure plasmon dispersion (see Sect. 3.2), values for the parameters
Ep
, im-
pinging energy, and
θi,
the incident angle, were chosen so as to obtain the highest
signal-to-noise ratio. The primary beam energy use for the dispersion,
Ep
7-12 eV,
provided, in fact, the best compromise among surface sensitivity, the highest cross
section for mode excitation and momentum resolution.
To obtain the energies of loss peaks, a polynomial background was subtracted
from each spectrum. The resulting spectra were fitted by a Gaussian line shape (not
shown herein). All measurements were made at room temperature.
Measurements were performed for both symmetry directions (
-
K
and
-
M
), but
no remarkable differences were recorded as a consequence of the existence of differ-
ently oriented domains on the sample, as observed in previous low-energy electron
microscopy experiments (Sutter et al.
2009
). Loss measurements of MLG/Pt(111)
recorded as a function of the scattering angle
θs
are reported in Fig.
3.18
. HREEL
spectra show a low-energy feature which develops and disperses up to 3 eV as a
function of the scattering angle. This resonance exhibits a clear linear dispersion and
its frequency approaches zero in the long-wavelength limit. We assign it to the sheet
plasmon of MLG, in agreement with theoretical (Hill et al.
2009
; Horing
2010a
;
Hwang and Das Sarma
2007
,
2009
; Hwang et al.
2010
) and experimental (Langer
et al.
2010
,
2011
; Tegenkamp
2011
; Liu and Willis
2010
;Luetal.
2009
) results.
The dispersion of the sheet plasmon fo
r
MLG on SiC(0001) well agrees with
Stern's (Stern
1967
) prediction (
ω
∝
√
q
||
). However, the plasmon dispersion
recorded in our experiments (Fig.
3.19
) is well described by a linear relationship, as
in the case of ASP on bare metal surfaces (Diaconescu et al.
2007
; Park and Palmer
2010
; Pohl et al.
2010
):
=
hω
2
D
=
Aq
||
¯
where A
0.1 eV Å.
The sheet plasmon with a linear dispersion owes its existence to the interplay of the
underlying metal substrate with the
π
-charge density in the MLG in the same region
of space. It resembles the ASP in metal surfaces that support a partially occupied
surface state band within a wide bulk energy gap (Silkin et al.
2004
,
2005
).
The nonlocal character of the dielectric function (Horing
2010b
) and the screening
processes in graphene (Yan et al.
2011
; Schilfgaarde and Katsnelson
2011
) prevent
the sheet plasmon from being screened out by the 3D bulk states of Pt(111).
Recently, Horing (Horing
2010a
) predicted that the linear plasmon in graphene
systems
ma
y arise from the Coulombian interaction between the native sheet plasmon
(
ω
=
7.4
±
∝
√
q
||
) in MLG and the surface plasmon of a nearby thick substrate hosting a
semi-infinite plasma. Calculations taking into account the electronic response of the
Pt substrate could in principle put this effect in evidence, but this is not trivial due
to the existence of a Moiré reconstruction in the MLG lattice on top of the Pt(111)
substrate. The slope of the dispersion relation of the sheet plasmon in MLG/Pt(111)
