pubs.acs.org/NanoLett
Letter
Direct Visualization of Ultrastrong Coupling between LuttingerLiquid Plasmons and Phonon Polaritons
Gergely Németh,* Keigo Otsuka, Dániel Datz, Á ron Pekker, Shigeo Maruyama, Ferenc Borondics,*
and Katalin Kamarás
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sı Supporting Information
*
ABSTRACT: Ultrastrong coupling of light and matter creates new
opportunities to modify chemical reactions or develop novel
nanoscale devices. One-dimensional Luttinger-liquid plasmons in
metallic carbon nanotubes are long-lived excitations with extreme
electromagnetic field confinement. They are promising candidates to
realize strong or even ultrastrong coupling at infrared frequencies.
We applied near-field polariton interferometry to examine the
interaction between propagating Luttinger-liquid plasmons in
individual carbon nanotubes and surface phonon polaritons of silica
and hexagonal boron nitride. We extracted the dispersion relation of the hybrid Luttinger-liquid plasmon−phonon polaritons
(LPPhPs) and explained the observed phenomena by the coupled harmonic oscillator model. The dispersion shows pronounced
mode splitting, and the obtained value for the normalized coupling strength shows we reached the ultrastrong coupling regime with
both native silica and hBN phonons. Our findings predict future applications to exploit the extraordinary properties of carbon
nanotube plasmons, ranging from nanoscale plasmonic circuits to ultrasensitive molecular sensing.
KEYWORDS: s-SNOM, near-field, infrared, plasmon, phonon, Luttinger-liquid, carbon nanotube, ultrastrong coupling
S
Dirac electrons.32 Multiple experiments proved the existence of
the Luttinger-liquid state in carbon nanotubes from photoemission,33 NMR,34 and ESR35 to electrical transport.36
Recently, Luttinger plasmons were also visualized in real
space by near-field microscopy.37 Because of the Luttingerliquid state, the scattering channels of CNT plasmons are
limited, and thus, they are coherent excitations with high
quality factor.38−40 The linear dispersion of Luttinger-liquid
plasmons, which depends on the Fermi velocity vf, places their
excitation frequency into the mid-infrared.41 These exceptional
properties of CNT Luttinger-liquid plasmons make them ideal
candidates to observe strong coupling with other quasiparticles.
Plasmon−phonon resonances of a CNT thin film and SiO2
substrate were demonstrated by Falk et al.42 using far-field
spectroscopy with specially engineered samples. However, the
interaction of propagating Luttinger-liquid plasmons and
surface phonon polaritons at the individual nanotube level
has not been studied so far.
urface plasmon polaritons (SPPs) are hybrid light−matter
quasiparticles formed by the coupling of electromagnetic
waves and collective charge oscillations.1,2 They enable
subwavelength trapping of light that yields extreme concentration of the electromagnetic field, enabling nanoscale
modification of light−matter interactions.3 Low-dimensional
materials such as 2D van der Waals structures and onedimensional nanotubes support various polaritonic excitations
from the mid-infrared to the visible range.4−10 Low-dimensional plasmons have the advantage of high confinement ratio
and easy tunability by the dielectric environment or carrier
density.11−16 A particularly important phenomenon is strong
coupling of quasiparticles which permits applications like
induced transparency, polariton lasing, changing of the rate of
chemical reactions, or enhanced sensitivity in infrared and
Raman spectroscopy.17−23 Strong coupling of low-dimensional
plasmons was demonstrated by showing hybridization of
graphene plasmons with phonon polaritons of various
substrates.24−26 Importantly, graphene plasmons were also
exploited to enhance the sensitivity of infrared and Raman
spectroscopy, but only localized modes were studied.27−29
Carbon nanotubes (CNTs) can provide an even higher
degree of electromagnetic field confinement than graphene.31
As CNT electrons are constrained in one dimension, their
interaction exerts a significant influence on the collective
behavior of conduction electrons. The strong electron−
electron correlation results in the Luttinger-liquid state of
© XXXX The Authors. Published by
American Chemical Society
Received: December 13, 2021
Revised: March 15, 2022
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Figure 1. (a) Schematic illustration of nanotube polariton imaging with s-SNOM. (b) AFM topography of an individual nanotube partially on
silicon/native silica and partially on a 6 nm thick hBN flake. Also shown is a line profile across the nanotube along the orange line, yielding a
nanotube diameter of 0.8 nm. (c) Corresponding near-field phase image (φ4) taken at 920 cm−1. Phase values were normalized to that of silicon.
The inset shows the profile extracted along the dashed purple line. We note that the first less intense spot at the material boundary was excluded
from the profile. Its lower intensity is caused by the phase shift upon reflection, discussed in the Supporting Information.30 (d) Near-field phase
images at several different laser frequencies. In the map taken at 1100 cm−1, the phase contrast of the nanotube on silicon is near zero and the
plasmon fringes are missing. On the other hand, the phase contrast on hBN is still apparent but vanishes at 1400 cm−1. These two frequencies
correspond to the Reststrahlen band of silica and hBN, respectively, and highlight that plasmons are coupled to the phonons of each substrate
yielding a significant dip in the near-field phase spectrum.
Here, we demonstrate real-space imaging of ultrastrong
coupling between Luttinger-liquid plasmons in individual
carbon nanotubes and a thin native silicon oxide (silica)
layer using near-field microscopy. This method provides spatial
information at the scale of the plasmon wavelength and reveals
the impact of the local environment on the plasmon
propagation as well. Our results show that plasmons in
individual nanotubes are significantly more confined than in
nanotube ensembles,42 and we also analyze the strength of
coupling more rigorously. With the help of near-field polariton
interferometry, we extract the dispersion relation of the
plasmon−phonon hybrid system which shows anticrossing
and mode splitting. To evaluate the coupling, we used the
classical coupled harmonic oscillator model to fit both the
plasmon spectrum and the dispersion relation. The interaction
can be modified by increasing the distance of the nanotube
from the silica layer by inserting a hexagonal boron nitride
(hBN) flake between the nanotube and the substrate.
Figure 1a illustrates the schematics of our experiments. To
study CNT plasmons in individual nanotubes, we applied
scattering-type near-field infrared microscopy (s-SNOM). In
our instrument (NeaSNOM, Neaspec GmbH) a metal-coated
atomic force microscope (AFM) tip (Arrow-NCPt, Nanoworld) is illuminated by a focused laser beam of a tunable
infrared quantum cascade laser (MIRCat QT, Daylight
Solutions). The illuminated tip acts as a nanoscale light source
used to locally probe the optical properties of the sample. The
AFM is working in tapping mode, and the scattered light
arising from the tip−sample near-field interaction is detected
by the combination of higher harmonic demodulation and
pseudoheterodyne interferometry (PsHet). In a typical
measurement, the AFM topography and near-field optical
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Figure 2. (a) Dielectric function of SiO2 with the orange dashed lines marking the Reststrahlen band. (b) Imaginary part of the Fresnel reflection
coefficient of a 2 nm thick native silica layer on undoped silicon. It shows a pronounced excitation that corresponds to the air−silica interface
phonon mode. (c) Color plot presenting the amplitude of the Fourier transform of plasmon interference fringes taken along the nanotube for each
illumination frequency (dispersion map) together with the manually measured wavevector values with error bars (yellow plot).
the tip reflect back from the material boundary: it serves as a
geometric obstacle as the nanotube is distorted where it
reaches the hBN flake. The fringe pattern arising from the
plasmon interference is clearly visible in both the Si/SiO2 and
the hBN domain. Figure 1c also contains the near-field phase
line profiles taken along the purple line. The plasmon
wavelength λp is then simply calculated as twice the distance
between adjacent peaks. For the illumination frequency of 920
cm−1 the plasmon wavelength on the Si/SiO2 substrate
becomes λp = 109.2 ± 3.8 nm, in good agreement with
previously reported values.41 The small discrepancy between
these and previous experiments originates from the exact
plasmon wavelength being a function of the nanotube diameter
and the dielectric environment.41
To spectrally study the plasmon excitation and to retrieve
the plasmon dispersion, we tuned the laser frequency from 920
to 1700 cm−1 in 20 cm−1 steps. By reimaging the same area at
each laser frequency, we determined the ω(q) nanotube
plasmon dispersion, where q = 2π/λp is the plasmon
wavevector corresponding to its momentum. Upon near-field
excitation, the plasmon momentum has to match the in-plane
wavevector of a tip-generated near-field component. In Figure
1 d we present several near-field phase maps that highlight the
spectral characteristics of the plasmon excitations. In each map,
phase values are normalized to that of the underlying substrate
by calculating φ4 = φ4,CNT − φ4,subs. This way we can remove
phase differences between the substrates and we focus only on
the nanotube signal.
Two important effects are apparent already from the nearfield maps. First, the periodicity of the plasmon interference
fringes changes with excitation frequency, unraveling the ω(q)
relationship. Further, the amplitude of the oscillations also
depends on the excitation energy. There are two very
prominent maps (1100 and 1400 cm−1) where the phase
contrast completely vanishes: these are the ranges of SiO2 and
hBN phonons, respectively. The Reststrahlen band of a
medium that supports lattice vibrations is located between
the TO and LO phonon frequencies where the real part of the
dielectric function is negative. For SiO2 the frequencies are
ωTO = 1071 cm−1 and ωLO = 1184 cm−1,50 while for hBN ωTO
= 1378 cm−1 and ωLO = 1610 cm−1.51 We attribute the lack of
phase contrast, thus excited states, to the hybridization
images are collected simultaneously. The PsHet detection
permits acquisition of both the amplitude (sn) and the phase
(φn) of the scattered light, where the subscript denotes the
demodulation order.43
The optical near fields generated at the apex of the tip have
sufficiently high momentum to launch propagating plasmons.
The tip-launched plasmons propagate along the nanotube and
can reflect on different defects or perturbations (edges,
geometric or dielectric obstacles). The reflected plasmons
then propagate back to the tip and interfere with the forward
propagating ones. This results in plasmon interference fringes
along the direction of propagation. By raster scanning of the
sample, plasmons can be visualized through their interference
fringes. This so-called polariton interferometry was previously
used to examine various polaritonic effects in low-dimensional
materials.41,44,45
Long, parallel, and straight individual single-walled carbon
nanotubes were grown by chemical vapor deposition (CVD)
on quartz and transferred subsequently via PMMA support
film onto an undoped silicon substrate with thin hBN flakes
previously exfoliated onto the surface. PMMA was washed
away by acetone, and the sample was annealed in Ar
atmosphere at 350 °C (details in Supporting Information
section 2).
In this study, we concentrate on metallic carbon nanotubes
as they support strong tip-launched Luttinger-liquid plasmons
at ambient conditions, in contrast to semiconducting ones that
require additional doping.46 The metallic nanotubes can be
easily identified based on their very pronounced near-field
phase contrast compared to semiconducting ones..47−49
Additionally, phase contrast is much more resilient to the
topographic artifacts whereas the amplitude is very sensitive to
the tip−sample distance variations (Supporting Information
section 1). On the basis of these findings, we present only nearfield phase maps in this article.
Figure 1b shows a representative nanotube that is located
partially on the Si/SiO2 surface (left side) and partially on an
hBN flake (right side). As the profile shows, the nanotube itself
is 0.8 nm in diameter. The hBN flake height is 6 nm which
separates the nanotube from the Si/SiO2 surface. The fourth
harmonic demodulated phase (φ4) was acquired simultaneously and is plotted in Figure 1c. The plasmons launched by
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Figure 3. (a) Each row in the color plot presents the Fourier transform of the plasmon interference fringes taken at the corresponding illumination
frequency (dispersion map). The white dashed lines show the bare plasmon dispersion and the silica surface phonon mode. The red dashed line
plots the eigenmode frequencies of the hybridized Luttinger-liquid plasmon−phonon polariton (LPPhP) states considering coupling strength g =
150 cm−1. The lines properly match the dispersion map. At zero detuning, the mode splitting corresponds to Ω = 2g. We also plot the polariton
amplitude taken as a vertical line cut at zero detuning (yellow plot). (b) Dispersion map of LPPhP hybrid states calculated by using the harmonic
oscillator model. The manually determined plasmon wavevector values (with white error bars) are superimposed onto the map showing excellent
agreement. Red dashed dispersion lines were calculated by eq 3.
metallic carbon nanotubes. Owing to the wide distribution of
optical near fields at the apex of the AFM tip, there is available
momentum at every photon frequency to launch plasmons
which can electromagnetically couple to surface modes of the
oxide forming new hybrid Luttinger-liquid plasmon−phonon
polaritons (LPPhPs).
We analyze and confirm the hybridization by the classical
coupled harmonic oscillator model and take into account the
nanotube plasmons and the air−silica interface phonon mode
as two coupled harmonic oscillators. This system has
eigenmodes significantly different from those of the original
oscillators and can be calculated according to54
between surface phonon modes of the thin phononic layer
material (specifically native silica and hBN flake) and carbon
nanotube plasmons. First, we analyze more thoroughly the
effect of native silica.
From all near-field images, we extracted a line profile of the
plasmon fringes along the nanotube, similar to Figure 1c.
Figure 2c depicts the amplitude of the Fourier transform of the
plasmon fringes for all excitation frequencies assembled in a
frequency−momentum map. Additionally, we manually
determined the distances between adjacent maxima of the
fringe profiles and superimposed the manually calculated
plasmon wave vector values. The significant lack of modes is
well aligned with the Reststrahlen band of silica (marked by
the orange dashed lines in Figure 2) where thin-film phonon
modes can be excited. In this range, from 1070 to 1200 cm−1,
plasmon oscillations are suppressed and the corresponding
components are missing from the Fourier spectrum. The
manually measured plasmon wavevector values are also missing
because there are no recognizable oscillations in the images.
We determined the native silica layer thickness to be 2.17
nm by ellipsometry. The thin silica film supports surface
phonon−polariton modes both at the air−silica (close to ωLO)
and silica−silicon interfaces (close to ωTO).52,53 Figure 2b
depicts the imaginary part of the Fresnel reflection coefficient
of a SiO2/Si system for optical fields in the same momentum
and frequency range as in the experiments. The air−silica
interface phonon mode is clearly more prominent than the
silica−silicon mode. This mode has a polarization mostly
perpendicular to the surface; thus it matches the polarization of
the nanotube induced by the AFM tip. As the nanotubes are
located at this interface, we consider it to play the dominant
role in coupling.
The dispersion relation of Luttinger plasmons in metallic
carbon nanotubes is linear: ωp = vp·q, where the plasmon
velocity vp depends on the Luttinger-liquid interaction
parameter G via vp = vf/G (white dashed line in Figure 2
b).41 vf ≈ 0.8 × 106 m/s represents the Fermi velocity in
ω± =
ωCNT + ωSiO2
2
±
g2 +
γCNT − γSiO y2
1 ijj
2z
zz
Δ
−
i
j
z
4 jk
2
{
(1)
Here ωCNT and ωSiO2 are the resonance frequencies of the
uncoupled oscillators and γCNT and γSiO are the damping
2
parameters. Δ = ωCNT − ωSiO2 describes the detuning between
the nanotube plasmon resonance and the silica phonon mode.
During the experiments, we tune the nanotube plasmons
according to their linear dispersion. The slope of its dispersion
line is given by the plasmon velocity, which we found to be vp
= 3.32 × 106 m/s. The damping was determined in two
different ways. First, we fitted a Lorentzian curve to a vertical
line cut from the measured dispersion map in Figure 2c at q =
7 × 105 cm−1 which is away from zero detuning but still
provides sufficient signal-to-noise ratio for the fit. Next, we
fitted hybrid polariton peaks at zero detuning by the sum of
two Lorentzian functions which provided
γpol = (γCNT + γSiO )/2
2
We get the same value, γCNT = 150 cm−1, with both approaches
(details in Supporting Information section 5). The oscillator
parameters for the silica slab mode were taken from a vertical
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line from Im(r) at q = 6.65 × 105 cm−1. The frequency of the
peak is ωSiO2 = 1176.1 cm−1 and γSiO = 30 cm−1. With these
2
oscillator parameters the coupling strength g is the only free
parameter. We found that g = 150 cm−1 provides excellent
agreement between experiments and the calculated dispersion.
The result is shown in Figure 3a by the red dashed lines. As the
coupling strength (g) exceeds the damping of both oscillators,
the exchange of energy between them is faster than its leakage.
For further analysis, we reproduced the full dispersion map
with the coupled harmonic oscillator model. We assume that
the tip-induced near field provides the driving force (F = eEloc),
and only the nanotube plasmon is excited. The plasmon then
exchanges energy with the phonon mode of the silica slab
through electromagnetic coupling. The equation of motion of
the system is described by a linear differential equation
system55−58 (Supporting Information section 6). The steadystate solution for the displacement of the driven oscillator gives
the polarization induced by the plasmon excitation P = ex and
can be written as
P=e
To achieve ultrastrong coupling at mid-infrared frequencies
is challenging because of weak oscillator strengths.60 Generally,
g ∝ (N /V ) where N is the number of dipoles coupled to
the electric field mode and V is the mode volume of the
electric field. We attribute the high coupling strength to the
extreme concentration of electromagnetic field around the
nanotube. Previous studies estimated the electric field of the
nanotube plasmon via finite element simulations and showed
that the electric field distribution is concentrated to the close
proximity of the nanotube surface.15,61 Its electric field decays
on the scale of the nanotube diameter; thus in our case, the
plasmon field is strongly confined into the 2 nm thick silica
layer. The obtained value for η marks the exceptional
properties of nanotube plasmons allowing ultrastrong coupling
in the mid-infrared.
It is important to note that the polariton interference fringes
cannot be observed properly in every measurement. For
example, the phase contrast of nanotubes on the hBN flake
does not present recognizable oscillations along the nanotubes
for all excitation frequencies. However, the phase contrast itself
reaches high values where the sample shows significant
absorption due to the LPPhP excitation. Thus, we are unable
to calculate the dispersion but the phase contrast spectrum is
still retrievable. Such a phase spectrum corresponds to the
excitation of a polariton available at a specific frequency. This
spectrum can be reproduced by integrating all the momentum
components at each excitation frequency by integrating the
phase values along the horizontal lines of the calculated
dispersion map. The momentum components in the
calculation have to be weighted to match the measurements.
For this, we applied a Gaussian window (details in Supporting
Information section 7). In Figure 4 we plot the theoretical
E loc ΓSiO2
ΓCNTΓSiO2 + K 2
Letter
(2)
where Γj = ωj2 − iγjω − ω2 is the frequency-dependent
response of each oscillator and K = 2giω is the coupling term.
The amplitude of each polariton fringe is proportional to the
local absorption; thus we visualize the dispersion by plotting
Im(P(ω, q)). Figure 3b shows the calculated dispersion map
with the manually measured plasmon wavevector values. All
calculations were done with g = 150 cm−1.
The coupling regime can be determined by comparing the
coupling strength to the damping of the oscillators. The
strong-coupling criterion is defined by
ij γ 2
γSiO 2 yzz
jj CNT
2 z
zz > 1
+
C ≡ Ω /jj
jj 2
2 zz
k
{
2
where Ω = 2g (mode splitting).17 By using the presented
oscillator parameters, we obtain C = 7.7 that fulfills this
requirement. Furthermore, applying another measure, we
calculate the normalized coupling strength η = g/ωg where
ωg = 1176.1 cm−1 is the mid-gap frequency. The result of η =
0.13 > 0.1 shows that the hybridization between propagating
nanotube Luttinger-liquid plasmons and silica phonons reaches
the ultrastrong coupling regime;59 thus, the damping can be
neglected when calculating the eigenfrequencies. While eq 1 is
an approximation for the eigenfrequencies, in this case we can
formulate the exact solution as17,58
ω± =
Figure 4. Excitation spectrum of Luttinger-liquid plasmon−phonon
polaritons acquired from interference fringes by either taking the
average phase contrast (red) or calculating from the dispersion map
integrating all the Fourier components for each excitation frequency
(green). The solid blue line is calculated from the theoretical
dispersion map. Both spectra were normalized to their maximum
between 1200 cm−1 and 1300 cm−1 to fit on a common scale. Red
and green dashed lines are only guides to the eye.
1
2
ÄÅ
ÅÅ
ÅÅωCNT 2 + ωSiO2 2 + 4g 2
ÅÇ
±
ÉÑ1/2
Ñ
(ωCNT 2 + ωSiO2 2 + 4g 2)2 − 4ωCNT 2ωSiO2 2 ÑÑÑ
ÑÖ
(3)
phase spectrum in blue along with two experimentally obtained
phase spectra (green and red). One of the measured spectra
(green) was calculated the same way as described above but
from the experimental dispersion map. The other spectrum
(red) was measured by calculating the average phase contrast
along the nanotube. The result qualitatively matches the
Dispersion curves calculated this way are displayed in Figure
3b as red dashed lines. They align well with the maxima of the
theoretical dispersion map. We note that frequencies given by
eq 3 match those suggested by the quantum-mechanical
Hopfield model as shown previously.55,57,58,60
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Figure 5. (a) Dispersion map of a LPPhP formed by the interaction of an hBN phonon and a nanotube Luttinger-liquid plasmon calculated via the
coupled harmonic oscillator model. To correctly reproduce the experimental spectrum (b), the coupling strength had to be enhanced to g = 200
cm−1 which shows an even stronger coupling with the hBN phonons. The white dotted line shows the dispersion of the hBN slab phonon mode
acquired from Im(r) (calculated via transfer matrix method). The white solid line represents the dispersion of the bare Luttinger-liquid plasmon.
The red dashed lines present the eigenmode frequencies of the LPPhPs hybrid polariton given by eq 3. (b) Relative phase contrast spectrum of
nanotube-hBN plasmon−phonon polaritons representing their excitation spectrum. Red dots are the experimental phase contrast values, and the
solid blue line depicts the theoretical spectrum obtained from (a). Both spectra were normalized to their maximum above 1400 cm−1 to plot on a
common scale. The red dashed line is only a guide to the eye.
transparency gap, opened by the hybridization, in real space by
the disappearing near-field phase contrast of the nanotubes on
top of as thin as 2 nm native silica. We used near-field
polariton interferometry to reveal the dispersion of the hybrid
plasmon−phonon mode, analyzed the coupling strength by the
classical harmonic oscillator model, and determined that the
normalized coupling strength reaches the ultrastrong coupling
regime. A separation of the nanotube from the silica surface by
6 nm hBN completely removes the effect. Instead of silica,
hBN phonons participate in the coupling, yielding an even
stronger effect. Carbon nanotubes are promising candidates as
building blocks for photonic nanocircuitry,62 and our study
showed that a phononic substrate could add further customizability to the properties of nanotube-based circuits. Near-field
polariton interferometry could allow tracking reactions of
nanotube encapsulated molecules by vibrational strong
coupling to Luttinger-liquid plasmons and thus open the way
to ultrasensitive vibrational nanoanalytics.
experimentally obtained spectrum; however, the small difference at low frequencies suggests that a silica−silicon interface
phonon mode also has an effect on the LPPhP spectrum.
We also recorded the phase images of the nanotube on the
hBN flake (bottom parts of Figure 1d). Except for a few cases,
the polariton interference fringes are not observable properly
to reveal the dispersion; however, the spectral variation of the
near-field phase contrast is clearly detectable. We plot the
phase spectrum in Figure 5b.
We observe that the position of the spectral dip shifted to
around 1400 cm−1. The absence of the spectral dip at around
1150 cm−1 proves that the 6 nm thick hBN slab separates the
nanotube from the silica sufficiently that its phonon mode
cannot interact with the nanotube plasmon; instead, the hBN
phonon forms the hybridized states. To reproduce the phase
spectrum theoretically, we calculated the Fresnel reflection
coefficient of the 6 nm thick hBN slab via the transfer matrix
method (see Supporting Information section 8). From the
maxima of Im(rhBN) we retrieved the frequency of the slab
mode. With the phonon oscillator values, we applied the
coupled harmonic oscillator model (the theoretical dispersion
map is shown in Figure 5a) and calculated the excitation
spectrum of the new hybridized state. We found an increased
coupling strength g = 200 cm−1 to fit the experimental
spectrum. With the higher value of g and lower value of
phonon damping γhBN = 5 cm−1 and mid-gap frequency 1427
cm−1, the value for the strong coupling criterion becomes C =
14.2 and the normalized coupling strength is η = 0.14. The
calculated spectrum is shown in blue in Figure 5b and is in
good agreement with the measurement.
In conclusion, our study demonstrates the unique properties
of Luttinger-liquid plasmons in individual metallic carbon
nanotubes to realize strong coupling in the mid-infrared
regime. Due to their high concentration of electromagnetic
fields, propagating Luttinger-liquid plasmons couple very
effectively to thin layer phonon modes. We observed the
■
ASSOCIATED CONTENT
sı Supporting Information
*
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/acs.nanolett.1c04807.
Comparison of near-field amplitude and phase maps,
PsHet setup schematics, sample preparation details,
Lorentz oscillator parameters for hBN and silica, and
details on the fitting procedure for nanotube plasmon
damping, classical coupled oscillator model, spectrum
calculation method, and phase shift upon polariton
reflection (PDF)
■
AUTHOR INFORMATION
Corresponding Authors
Gergely Németh − Wigner Research Centre for Physics, 1121
Budapest, Hungary; Budapest University of Technology and
F
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Economics, 1111 Budapest, Hungary; orcid.org/00000002-1590-2133; Email: nemeth.gergely@wigner.hu
Ferenc Borondics − Synchrotron SOLEIL, 91192 Gif Sur
Yvette, France; orcid.org/0000-0001-9975-4301;
Email: ferenc.borondics@synchrotron-soleil.fr
Authors
Keigo Otsuka − Department of Mechanical Engineering, The
University of Tokyo, Tokyo 113-8656, Japan; orcid.org/
0000-0002-6694-0738
Dániel Datz − Wigner Research Centre for Physics, 1121
Budapest, Hungary; Eötvös Loránd University, 1117
Budapest, Hungary; orcid.org/0000-0002-4431-8956
Á ron Pekker − Wigner Research Centre for Physics, 1121
Budapest, Hungary; orcid.org/0000-0003-1075-0502
Shigeo Maruyama − Department of Mechanical Engineering,
The University of Tokyo, Tokyo 113-8656, Japan;
orcid.org/0000-0003-3694-3070
Katalin Kamarás − Wigner Research Centre for Physics, 1121
Budapest, Hungary; orcid.org/0000-0002-0390-3331
Complete contact information is available at:
https://pubs.acs.org/10.1021/acs.nanolett.1c04807
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
This research was funded by Hungarian National Research
Fund (OTKA) Grants SNN 118012, PD 121320, and FK
125063. Research infrastructure was provided by the
Hungarian Academy of Sciences (MTA). Research in Tokyo
was funded by Grant JSPS KAKENHI JP20H00220 and by
Grant JST, CREST JPMJCR20B5. Japan. s-SNOM measurements were done at the SMIS beamline at Synchrotron
SOLEIL. Travel to Soleil (G.N.) was financed by Grant 20192.1.11-TÉ T-2019-00035. We are thankful to Benjamin Kalas
for the ellipsometry thickness measurement of the native silica
layer.
■
■
Letter
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