Enhancement of Raman scattering from molecules placed near metal nanoparticles
Large Raman scattering cross sections from molecules on surfaces of metallic nanoparticles are described within a renormalization-group theory. In this approach the valence electrons of the molecules are embedded in an effective medium described by a dielectric function, which integrates out the eff...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2017
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Barbiellini, B. 2018-01-19T14:09:50Z 2018-01-19T14:09:50Z 2017 Enhancement of Raman scattering from molecules placed near metal nanoparticles / B. Barbiellini // Физика низких температур. — 2017. — Т. 43, № 1. — С. 190-192. — Бібліогр.: 32 назв. — англ. 0132-6414 PACS: 78.30.–j, 78.67.Вf https://nasplib.isofts.kiev.ua/handle/123456789/129366 Large Raman scattering cross sections from molecules on surfaces of metallic nanoparticles are described within a renormalization-group theory. In this approach the valence electrons of the molecules are embedded in an effective medium described by a dielectric function, which integrates out the effect of the plasmonic excitations of the metallic nanoparticles. The source of the enhanced photon inelastic scattering is produced by the resonant excitation of surface plasmons at the metallic nanoparticles. A similar theory has been successfully used to explain the resonant x-ray inelastic scattering and the behavior of nonlinear susceptibilities at the x-ray edges. This work is supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences grant number DE-FG02-07ER46352 (core research), and benefited from Northeastern University’s Advanced Scientific Computation Center (ASCC), the NERSC supercomputing center through DOE grant number DE-AC02-05CH11231, and support (applications to layered materials) from the DOE EFRC: Center for the Computational Design of Functional Layered Materials (CCDM) under DE-SC0012575. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур К 100-летию со дня рождения И.М. Лифшица Enhancement of Raman scattering from molecules placed near metal nanoparticles Article published earlier |
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Enhancement of Raman scattering from molecules placed near metal nanoparticles |
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Enhancement of Raman scattering from molecules placed near metal nanoparticles Barbiellini, B. К 100-летию со дня рождения И.М. Лифшица |
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Enhancement of Raman scattering from molecules placed near metal nanoparticles |
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Enhancement of Raman scattering from molecules placed near metal nanoparticles |
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Enhancement of Raman scattering from molecules placed near metal nanoparticles |
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Enhancement of Raman scattering from molecules placed near metal nanoparticles |
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enhancement of raman scattering from molecules placed near metal nanoparticles |
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Barbiellini, B. |
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Barbiellini, B. |
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К 100-летию со дня рождения И.М. Лифшица |
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К 100-летию со дня рождения И.М. Лифшица |
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English |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Large Raman scattering cross sections from molecules on surfaces of metallic nanoparticles are described within a renormalization-group theory. In this approach the valence electrons of the molecules are embedded in an effective medium described by a dielectric function, which integrates out the effect of the plasmonic excitations of the metallic nanoparticles. The source of the enhanced photon inelastic scattering is produced by the resonant excitation of surface plasmons at the metallic nanoparticles. A similar theory has been successfully used to explain the resonant x-ray inelastic scattering and the behavior of nonlinear susceptibilities at the x-ray edges.
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0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/129366 |
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Enhancement of Raman scattering from molecules placed near metal nanoparticles / B. Barbiellini // Физика низких температур. — 2017. — Т. 43, № 1. — С. 190-192. — Бібліогр.: 32 назв. — англ. |
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| fulltext |
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 1, pp. 190–192
Enhancement of Raman scattering from molecules
placed near metal nanoparticles
B. Barbiellini
Department of Physics, Northeastern University, Boston, MA 02115, USA
E-mail: B.Amidei@neu.edu
Received August 1, 2016, published online November 25, 2016
Large Raman scattering cross sections from molecules on surfaces of metallic nanoparticles are described
within a renormalization-group theory. In this approach the valence electrons of the molecules are embedded in
an effective medium described by a dielectric function, which integrates out the effect of the plasmonic excita-
tions of the metallic nanoparticles. The source of the enhanced photon inelastic scattering is produced by the res-
onant excitation of surface plasmons at the metallic nanoparticles. A similar theory has been successfully used to
explain the resonant x-ray inelastic scattering and the behavior of nonlinear susceptibilities at the x-ray edges.
PACS: 78.30.–j Infrared and Raman spectra;
78.67.Вf Nanocrystals, nanoparticles, and nanoclusters.
Keywords: SERS, surface Plasmon, renormalization-group theory.
1. Introduction
Einstein’s hypothesis of granular light [1], previously
based on the photoelectric effect [2], was confirmed by the
discovery of the Compton effect. The experiment [3] de-
tected a modification in wavelength of an x-ray quantum
when scattering with a free electron in a material. The re-
sulting change in energy and momentum showed that the
photon behaves like a particle colliding with the electron [4].
Later on, Raman and Krishnam [5] observed a similar ef-
fect in liquids, which involves a change in wavelength
of monochromatic visible light scattering with phonons.
The effect was also observed independently in crystal by
Landsberg and Mandelstam [6]. Thus, the so-called Raman
effect further confirmed the quantum theory of light. Subse-
quently, Raman scattering became a standard spectroscopy
used to characterize molecular and material structures [7].
Nowadays, Raman scattering is also deployed to study
excitations in correlated systems such as high temperature
oxide superconductors [8].
In general the inelastic scattering cross section of pho-
tons is very small [9] and can be cast as the product of the
Thomson scattering differential cross section Th /d dσ Ω
with the dynamical structure factor ( , )S ωq :
2
Th= ( , ).
dd S
d d d
σσ
ω
Ω ω Ω
q (1)
The Thomson scattering cross section is determined by the
classical electron radius 0r
2
Th 0
8= .
3
rπ
σ (2)
This radius occurs in theory of phenomena considered as
classical [10,11] and it is given by
2
13
0 2
0
= = 2.82 10 cm,
4
er
mc
−⋅
πε
(3)
where e is the electron charge, m is the electron mass, c is
the speed of light and 0ε is the vacuum dielectric constant.
The dynamical structure factor ( , )S ωq describes various
excited states involving phonons or particle-hole excita-
tions, which produce a change in momentum q and a
change in energy ω of the scattered photons.
The surface-enhanced Raman scattering (SERS), in-
volving molecules near metallic nanoparticles [12,13], was
first observed in 1974 by Fleischmann et al. [14]. After
this discovery, further experiments [15,16] explained
SERS as a giant enhancement of the ordinary Raman scat-
tering. The enhancement of Raman scattering signals from
molecules absorbed on nanostructured metal surfaces can
reach 6 to 10 orders of magnitude [15,17]. Moreover, an
enhancement about 14 orders of magnitude was observed
on molecules near silver aggregates [18]. Therefore, this
striking effect can enable single molecule detection. The
© B. Barbiellini, 2017
Enhancement of Raman scattering from molecules placed near metal nanoparticles
enhancement mechanism in SERS seems to be well under-
stood within the classical plasmonic theory [19–23]. This
theory claims that SERS arises from the concentration of
electromagnetic energy in the vicinity of an a metal nano-
particle, when the incident light excites surface plasmons.
Semiclassical theories involving many-electron Green’s
function techniques have also been considered [24]. Inter-
estingly, models combining Quantum Mechanics and
Maxwell’s equation are presently used to describe hybrid
systems composed of molecules (or quantum dots) and
metallic nanoparticles [25]. Unfortunately, all these models
neglect the granular behavior of light.
The present paper explores the possibility to use a
renormalization-group approach [26] to derive the funda-
mental origin of the enhancement mechanism of SERS.
This method is beyond perturbation theory and can take in
account collision processes between light quanta and the
elementary excitations of molecules at metallic surfaces. A
similar approach has also been used to simplify the descrip-
tion of the resonant x-ray inelastic scattering (RIXS) for the
particle-hole excitations [9]. Moreover, within the same
scheme, one can derive an expression for the resonant term
of the nonlinear susceptibility at x-ray edges [27].
2. Theory
The dimensionless coupling of quantum electrodynam-
ics (QED) is not constant but varies under changes of
scales [28–30]. In practice, the QED vacuum can be con-
sidered as a polarizable system, where virtual pairs of par-
ticles and anti-particles screen the electric charge. For in-
stance, the dimensionless coupling changes at the crossing
of particle production thresholds in the standard model of
particle physics [31]. Similarly, in materials such as FeTe
or TiSe2 [9], photons with energies near the 3L absorption
threshold produce virtual intermediate states involving a
2 p core hole and electron excited in a 3d state. In the case
of SERS, the threshold energy is given by the plasmonic
resonance of the metal nanoparticles. All these resonant ef-
fects can be captured by an effective dielectric function for
the valence electrons of the system (here, the molecule).
Consequently, the dimensionless coupling g in the system
can decrease by subjecting the system to a flux photons
having energies just below resonant edges, thereby increas-
ing the dielectric screening of the valence electrons of the
system. Thus, the inelastic scattering cross section σ is
enhanced because of an increased background polarizabi-
lity. The link between the effective coupling g and
the length scale = σ is given by
( ) = ,
ln( )
dgg
d
β
(4)
where the function 2( ) = 3g gβ − is a renormalization group
function [26] determining the scale for a given cou-
pling g. By solving Eq. (4), one finds that the inelastic
scattering cross section σ is renormalized by
1 0
2= exp ( / 1) ,
3
η ε ε − α
(5)
where α is the fine structure constant (i.e., the effective
coupling g when 0=ε ε ) and 1ε is the real part of an effec-
tive dielectric function ε. Near the plasmonic absorption
edges, there are anomalous dispersions that allow the ine-
lastic scattering cross section to be enhanced in the domain
where 1 0/ε ε is larger than unity.
3. Discussion and conclusion
We now consider a Raman scattering molecule placed
near a metallic nanoparticle. Both the molecule and the
metallic particle are subjected to a monochromatic light
field. When the incident photon energy is tuned near to the
plasma resonance, the effective coupling constant for the
valence electron of the molecule is modified through the
effective dielectric response, which integrates out the effect
of the plasmonic excitations at the metallic nanoparticles. As
explained before, the cross section depends strongly on the
effective coupling constant, which is inversely proportional
to 1ε . Figure 1 shows the evolution of the renormalization
factor as function of 1 0/ε ε . Interestingly, an increase of
1 0/ε ε as small as 30% can explain enhancements of 14 or-
ders of magnitude. Figure 1 also illustrates that 1 0/ > 1ε ε is a
crucial condition for the resonant enhancement. In fact,
when this ratio is smaller than one, the Raman signal weak-
ens instead of growing.
In the RIXS theory, 1ε can be evaluated by using first-
principles calculations [9]. The model is then able to cap-
ture the overall amplitude of the RIXS signal. The reason
for small discrepancies between model and experiment
above the absorption thresholds can be explained by the
fact that the model does not include the momentum inde-
Fig. 1. Cross section enhancement η as a function of the ratio
1 0/ε ε .
Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 1 191
B. Barbiellini
pendent resonant emission described by the Kramers–
Heisenberg theory [32].
For SERS the ab initio determination of 1ε is still lack-
ing. Therefore, the connection with first-principles calcula-
tions must be developed to validate the present theory and
to guide future experiments in this field. Clearly, surface
plasmon resonances can be exploited to enhance the Ra-
man cross section of molecules placed in vicinity of the
metallic nanoparticles. The renormalization group method
presented here could offer a powerful method in order to
predict huge enhancement factors.
This work is supported by the US Department of Ener-
gy (DOE), Office of Science, Basic Energy Sciences grant
number DE-FG02-07ER46352 (core research), and bene-
fited from Northeastern University’s Advanced Scientific
Computation Center (ASCC), the NERSC supercomputing
center through DOE grant number DE-AC02-05CH11231,
and support (applications to layered materials) from the
DOE EFRC: Center for the Computational Design of Func-
tional Layered Materials (CCDM) under DE-SC0012575.
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192 Low Temperature Physics/Fizika Nizkikh Temperatur, 2017, v. 43, No. 1
1. Introduction
2. Theory
3. Discussion and conclusion
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