How Intrinsic Phonons Manifest in Infrared Plasmonic Resonances of

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How Intrinsic Phonons Manifest in Infrared Plasmonic Resonances of Crystalline Lead Nanowires Jochen Vogt, Chung Vu Hoang, Christian Huck, Frank Neubrech, and Annemarie Pucci J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05674 • Publication Date (Web): 03 Aug 2016 Downloaded from http://pubs.acs.org on August 4, 2016

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The Journal of Physical Chemistry

How Intrinsic Phonons Manifest in Infrared Plasmonic Resonances of Crystalline Lead Nanowires Jochen Vogt,†,ǁ Chung Vu Hoang,†,§,ǁ Christian Huck,† Frank Neubrech,†,# and Annemarie Pucci†,* †

Kirchhoff Institute for Physics, Heidelberg University, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany

§

Institute for Materials Science, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Cau Giay, Ha Noi, Viet Nam #

4th Physics Institute, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

ACS Paragon Plus Environment

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ABSTRACT: Single-crystalline lead nanowires with length of about one micron and with effective diameters of a few ten nanometers have been grown on vicinal silicon by a selfassembly process. They show strong plasmonic resonances in the infrared with a remarkable enhancement of the extinction upon the cooling below room temperature. The increase of the plasmonic extinction at resonance is linear with decreasing temperature but saturates before the Debye temperature is approached. This observation is in full accordance with the quasi-static description of plasmonic extinction with the intrinsic damping dominated by phonons and thus linearly temperature dependent well above the Debye temperature. The different slopes of this linear function for different wire thickness indicate the importance of surface and near surface phonon properties that can be described by a Debye temperature that is lower than the bulk value. The careful spectral analysis also yields temperature-independent contributions to the electronic scattering rates for various wire thicknesses and, furthermore, a resonance frequency decreasing with temperature, which corresponds to the predicted trend in renormalization theory for electron-phonon interaction in a metal like lead.


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1. INTRODUCTION Bottom-up formation of metal nanostructures by self-assembling processes is of great importance because such structures are mostly more stable than top-down produced structures and may show high crystallinity. Single-crystalline (“ideal”) materials are also important for basic studies of plasmonic excitations.1,2 Because of missing defects, electronic damping is low and therefore plasmonic excitations feature especially high quality factors.3 So, single crystalline plasmonic nanorods enable strong enhancement of the fluorescence of weak fluorophores.4 In defect-free silver nanorods, the propagation length of plasmon-polaritons becomes 10 µm in the visible, which enables the application of the wires as Fabry-Perot resonators.3 Also surface enhanced Raman scattering (SERS) profits from the stronger plasmonic near-field enhancement of crystalline nanoparticles.5 By annealing polycrystalline nanostructures, which removes grain boundaries, the enhancement of the quality factor was demonstrated even for lithographically made structures.6 However, there are remaining damping mechanisms in defect-free singlecrystalline nanoparticles, also well below the onset of electronic interband transitions. For the optimization of plasmonic material properties and for the development of gentle structuring methods that preserve the crystalline nature of the material, this limit should be well understood, not only for bulky material but also for nanoparticles for which surface effects become important. In order to see how condensed matter theory on electron transport in crystalline metals works for plasmonic nanoparticles we have investigated antenna-like resonances of self-assembled single-crystalline Pb nanowires with a narrow distribution in their size. In the infrared (IR) where the plasmonic behavior is not disturbed by interband transitions we analyze how plasmonic resonance spectra of the single-crystalline metal nanowires change upon cooling down to 20 K.


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The observed temperature dependence of the resonance spectrum follows the well-known condensed matter theory on electron-phonon interaction and its relation to temperature. So, this result demonstrates the importance of this condensed matter physics of metals for nanoplasmonics. However, clear differences in the linear slope of the electron scattering rate with temperature indicate a phonon softening that can be described as a decrease in the Debye temperature for decreasing nanowire thickness in quantitative accord to the existing knowledge on the surface-Debye temperature of lead. As the main consequence, the temperature dependence of the plasmonic line width gets stronger with decreasing diameter.

2. THEORETICAL BACKGROUND The fundamental resonance of rod-like nanowires of length 𝐿 with a high aspect ratio can be considered as a standing wave phenomenon and its effective plasmonic wavelength 𝜆eff is equal to 2𝐿, like for a radio antenna. The main differences to radio antennas are the different 𝐿 and the different penetration depth 𝛿 of electromagnetic radiation, which in relation to the different diameters of IR and radio antennas gives a wavelength compression of external IR radiation into plasmonic waves at the same energy (or frequency). In the IR, the plasmonic resonance of a nanorod is dependent on both geometry and material parameters, which has been shown for example by L. Novotny.7 For a diameter 𝐷 with 𝛿 < 𝐷 ≪ 𝐿 he derived an analytical relation 2𝐿 = 𝑐2 𝜆res 𝜔p − 𝑐1

(1)

where 𝜔p denotes the plasma frequency of the antenna’s material. The relation describes the optical antenna behaviour for small intrinsic damping rates 𝜔τ and makes clear that at resonance the photon wavelength 𝜆res ~ 1 𝜔p (and the circular frequency 𝜔res ~𝜔p , respectively).7 The coefficients 𝑐1 and 𝑐2 depend on 𝐷 and on dielectric properties. Basically, the functionality of an


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IR optical antenna is limited by the intrinsic damping 𝜔τ that is due to scattering of conduction electrons, mainly by phonons and defects.8,9 Below diameters of the order of the mean free electron path that is ca. 20 nm for lead in the IR,10 surface scattering becomes increasingly important. Any changes in the Drude parameters 𝜔τ and 𝜔p clearly modify the plasmonic extinction. For the conditions of our experiment with normal incidence of light and antennas with a few 10 nm thickness the quasi-static approximation can be used for spectral modeling if a small radiation-damping correction is considered.11,12 In this approximation, the scattering cross section 𝜎sca = 𝜔p2 !

!4 !

!" host !

2 !! 2 !res

2

2 !! 2 !res

2

!! 2 !τ !! 2 !

2

(2)

2

(3)

and the absorption cross section 𝜎abs = 𝜔p2 !

! 2 !τ

!" host !

!! 2 !τ !! 2 !

for a Drude-type metal differ in their numerators only. The extinction cross section (the quantity that is measured in transmittance experiments) is the sum of the absorption and the scattering cross section. The parameter 𝑡 = 𝑉𝑅𝑛host 𝜔p2

6𝜋𝑐 3 is the Larmor time parameter (with the

vacuum velocity 𝑐 of light) depending on the volume 𝑉 (where the electrons are excited), the refractive index 𝑛host of the host medium outside, and the local-field ratio 𝑅. For a spheroid in 2 2 2 the quasi-static approximation, 𝑅 = 𝑛host 𝑛host + 𝐹 𝜀∞ − 𝑛host

with 𝐹 as the depolarization

factor and 𝜀∞ as the metal’s dielectric background. For a needle-like object, 𝑅 ≈ 1 if the electric field is parallel to the needle. In a recent work11 we have demonstrated how well this cross section model fits to experimental as well as computer-simulated spectra of infrared resonances of gold nanorods and that reasonable information on electronic damping is extracted.


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Furthermore, the model was successfully applied to the analysis of plasmonic resonances of finite gold-atom chains grown on vicinal Si(111) surfaces.13 Eq 1 is based on the fact that the IR-optical properties of a Drude-type metal are well described by the dielectric function 𝜀 𝜔 = 𝜀∞ − !

!p2

(4)

!!! !τ

where the background effects from interband transitions are included in 𝜀∞ . According to Matthiessen's rule, the total electronic relaxation rate 𝜔τ (inverse lifetime) is the sum of the various scattering contributions; 𝜔τ = 𝜔τ,e 𝑇, 𝜔 + 𝜔τ,p 𝑇 + 𝜔τ,s + 𝜔τ,d

(5)

with the temperature 𝑇 dependent rates 𝜔τ,e and 𝜔τ,p for the electron-electron and the electronphonon scattering, respectively. The temperature independent rates are due to the interaction with the surface (𝜔τ,s , linearly proportional to the inverse wire thickness, for example ref 10 and with bulk defects (𝜔τ,d ). At temperatures above several K electron-electron scattering among conduction electrons is negligibly small compared to the electron-phonon scattering. In the infrared, the relation for the electron-phonon scattering rate !

𝜔τ,p = !

0

!

+4 !

! !D

5

!D ! ! 4 𝑑𝑧 ! ! ! !!

(6)

as derived by Holstein describes the T-dependence and, as the Bloch-Grueneisen relation for the dc case, predicts 𝜔τ ∝ 𝑇 𝜃D for 𝑇 well above the Debye temperature 𝜃D . The rate 1 𝜏0 depends on the electron-phonon coupling strength, on electronic parameters of the metal (Fermi vector, Fermi energy, electron mass), on the atomic density and mass, and, importantly, on the Debye temperature. For the IR range of this study where the photon energies are higher than the thermal


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energy, 𝜏0 ~𝜃D is theoretically predicted.14 The electron-phonon interaction not only modifies the electronic scattering but also the effective plasma-frequency parameter changes into 𝜔p∗ 2 = 𝜔p2 1 + 𝜆 𝜔, 𝑇

(7)

with the function 1 + 𝜆 𝜔, 𝑇 15 that renormalizes the effective electron mass on the Fermi surface.16 For many metals including lead 𝜆 𝑇

was theoretically investigated for certain

frequency ranges with the result showing a decrease in 𝜆 𝑇 with increasing temperature above 20 K,16 i.e. an increase of 𝜔p∗ 2 with increasing temperature. This effect is especially important at low frequencies, for example for cyclotron resonance experiments, and it has been ignored in plasmonics so far. Because of this renormalization, eq 1 should yield a 𝑇-dependent resonance frequency also if there are no changes in the polarizability of the surrounding.

3. EXPERIMENTAL DETAILS AND SAMPLE DESCRIPTION The in-situ experiments were performed under ultra-high vacuum (UHV) conditions at a base pressure of 1×10-‐10 mbar. The experimental setup consisted of an UHV chamber (with a liquidhelium (LHe) cryostat for sample cooling) coupled to a purged Fourier-transform IR spectrometer (Bruker Tensor 27 with mercury-cadmium telluride detector) via KBr windows. Surface morphology was investigated by reflection high-energy electron diffraction (RHEED). A Si(557) vicinal wafer was used as substrate. The surface orientation corresponds to a miscut of the Si (111) plane by 9.45° towards the 112 direction. In UHV the wafer was resistively heated to remove the silicon dioxide layer and to get a stable surface reconstruction17 over a large lateral area.18 Lead was deposited onto the substrate at room temperature (RT) from an alumina crucible and the deposition rate of 0.2 ML/min was calibrated by a water-cooled quartz-crystal microbalance. The thickness of one monolayer (ML) of lead is 0.286 nm along the 111


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direction in the bulk; a relation that we use here to indicate the deposited Pb amount in term of an average Pb thickness given in ML. During Pb vapor deposition under these conditions, Pb nuclei are formed on a wetting layer first, and then they grow preferential in length and less in width.19-21 The dominating formation mechanism of nanowires is the anisotropic diffusion along the silicon step edges and on the Pb nanowires.19,21,22 The shape of the wires can be described as individual longish islands (see Fig. 1a) and they are composed of only one crystalline grain.19,21 Nevertheless these grains grow on a wetting layer that reduces strain, some remaining strain related defects (dislocations) can not be excluded. Up to now there is a long lasting debate on the role of strain for the growth of Pb on crystalline Si surface and on how much quantum size effects could be involved23-25 in the growth. Very recent dc conductivity studies even suggest the incorporation of the wetting layer into the Pb crystallites.23 From our previous work we know that Pb deposited onto Si(111)-(7×7) grows as an amorphous layer and, from an average thickness of about 1.5 nm (at 120 K) up to 2 nm, this amorphous state fully turns into the crystalline fcc phase.10 Based on these experimental findings, it can be expected that the selfassembled Pb nanorods show a defect scattering that is low enough to enable the study of phonon effects. The positions of the nanorods are stochastically distributed on the Si surface. So the dipolar far field interaction is averaged out and the nanorods behave as individual particles26 because also the plasmonic near-field interaction has negligible influence as the distances between the nanowires are in the micrometer range.27 IR spectroscopic measurements were performed in transmittance geometry at normal incidence of light. A polarizer was placed into the optical path in front of the sample and the electrical field is used as linearly polarized parallel to the long axis of the nanowires. IR spectra were acquired


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with a resolution of 16 cm-1 and 200 scans for each spectrum. The transmittance spectrum of the clean and annealed Si(557) was used as a reference with the same temperature as that of the Pbwire sample. For the temperature dependent measurements, the thermal drift of the vertical sample position was determined to be about 1.5 mm from RT to 25 K. Within that spatial shift, the lateral sample homogeneity was demonstrated by the laterally low deviation of the extinction at resonance (below 0.3% at constant temperature) and by the absence of shifts of the resonance frequency. The average nanowire length in an ensemble depends on the nucleation density that is defined at the very beginning stage of a nucleation process.28 Jałochowski and Bauer reported on the inverse dependency of the average length 𝐿 on the nucleation density 𝑛x and on the influence of diffusion barriers for lead nanorods.19,21 For the general case, for example J.R. Venables explains in detail how 𝑛x depends on experimental parameters temperature, flux (evaporation rate), and surface properties like diffusion barriers and surface coverage.29 With such knowledge and careful sample temperature control it is possible to grow arrays with a narrow 𝐿 distribution for a certain amount of deposited Pb in the following given in ML.30 The continuous change of the average length with Pb coverage was already shown in the IR study of resonances of Pb nanowires on a vicinal Si(335)/Au surface by Klevenz et al..20 In that publication the preparation procedure was not optimized for lateral homogeneity. In contrast, the samples discussed here consist of a much more homogeneous L distribution over macroscopic distances. Because of the nearly one-dimensional diffusion parallel to the step edges of the Si(557) template at RT, the nanowires are formed perfectly parallel on nearly the entire silicon-wafer piece (5 mm × 18 mm). The nanowires are self-assembled in a manner that their long axis is parallel to the Sistep edges (parallel to the 110 direction of the Si (111) plane). Figure 1a shows an ex-situ


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scanning electron microscopy (SEM) image of a nanowire ensemble. The image taken four days after sample removal from UHV shows a nanowire density of 5.95×10! cm-2. It is important to note here that the Pb nanowire structures turned out to be rather stable in air, since measurements of the plasmon resonance indicate only marginal change after several days in air.30 The inset of Figure 1a exhibits a typical ex-situ atomic force microscopy (AFM) image of a nanowire with sharp tip-ends and triangular cross section. As reported in ref 19, this kind of nanowire has two main facets of the Pb bulk crystal: 111 and 100 .

Figure 1. (a) Ex-situ SEM image of a Pb nanowire ensemble for 3 ML of Pb on Si(557). Inset: AFM picture of a typical nanowire, performed in contact mode, scanning perpendicular to the long axis of the nanowires. (b) Length distribution of nanowires estimated from (a). The average length is 585 nm.


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From the length distribution (for 3 ML with the average value 𝐿 ≈ 585 nm, the average height

ℎ ≈ 15 nm, and the average width

𝑤 ≈ 100 nm) a distribution of resonance

frequencies follows, which gives rise to an inhomogeneous broadening of the plasmonic resonance that we consider in our spectral analysis by the convolution of the extinction cross section (the sum of eq 2 and 3) with a Gaussian distribution of resonance frequencies. In the following it is assumed that (after preparation) this inhomogeneous broadening is temperatureindependent in the temperature range from 25 K to RT because after deposition the Pb wires are very stable in their shape and size. Geometrical information is provided in Table 1.

Table 1. Representative geometrical data obtained from AFM measurements under ambient conditions (immediately after the transfer of samples to air). For 5 ML no AFM date had been taken because of experimental problems. For 3 ML, the length is in accordance to the SEM result. Also listed are the results from the further analysis of the total scattering rate 𝜔τ which was obtained from spectral fits. Applying eq 5 and 6 delivers the electronic surface + defect scattering rate 𝜔τ,s + 𝜔τ,d , the wire-height dependent Debye temperature 𝜃D , and the 𝜏0 parameter. For 10 ML the bulk value of 𝜃D = 88 K leads to a perfect fit. More details of the fit are described in the text. For the accuracy of the fit parameters, see Supporting Information. Average Pb coverage

Length (nm)

Width (nm)

Height (nm)

𝜔τ,s + 𝜔τ,d (cm-1)

𝜃D (K)

𝜏0 (fs)

2 ML

170 ± 30

30 ± 6

5±1

1450

43

37

3 ML

585 ± 20

90 ± 6

15 ± 1

1380

55

47

1050

58

50

670

88

76

5 ML 10 ML

1126 ± 100

144 ± 12

24 ± 2


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4. RESULTS The relative transmittance of Pb nanowires for parallel-polarized IR radiation features resonant antenna-like excitations,20,26,27,30,31 as presented in Figure 2. Figure 2a shows the development of the resonance feature with increasing Pb coverage that has lead to longer, broader, and thicker wires. In Figure 2b the spectral changes of the antenna feature with temperature are shown for two wire sizes. Upon cooling, the maximum extinction (minimum transmittance) at resonance clearly increases (decreases), for 3 ML of lead by about 7.5% in transmittance (corresponding to 1.4 times larger extinction). This increase in extinction upon cooling indicates remarkably lower intrinsic damping because of less scattering events of electrons with phonons at lower temperatures. It is also found for the other Pb coverage, as shown in Figure 2b for 10 ML, but less pronounced because of the bigger contribution of radiation damping 𝜔2 𝑡 that is proportional to the antenna volume (see above). The tendency towards a higher extinction for a lower temperature is similar to the findings for gold nano-bipyramides in the visible range.32 Also a small red-shift of the transmission minimum (extinction maximum, at ca. 2020 cm-1) is observed upon cooling but more clearly as for the gold-bipyramide array in ref 32.

5. DISCUSSION The transmittance spectra have been fitted with the extinction model defined in eq 2 and 3 (see fit spectra as black lines in Figure 2a and further details in the Supporting Information). The fits were done for a temperature independent Gaussian broadening Δ𝜔 that turns out to be about 120 cm-1 for 3 ML, which is in accordance to the measured length distribution of the wires (Figure 1b). For 2 ML, 5 ML and 10 ML the Gaussian broadening is 59 cm-1, 180 cm-1, and


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320 cm-1, respectively. The increase of the values with the coverage indicates the statistical nature of the growth process.

Figure 2. (a) Relative IR transmittance for selected Pb coverages at RT. (b) Typical temperaturedependent behavior found for plasmonic resonances of lead nanowires for two selected coverages. Notice the different ordinate scales for 3 and 10 ML. The electric polarization of the incident IR light is parallel to the Si-step edges. The thin black lines are the fit curves to which the parameters of Table 1 belong. The fit range did not include the noisy part of the spectrum.

In Figure 3 the best-fit parameters for the resonance frequency (Figure 3a), the temperature dependent transmission at resonance (at maximum extinction = minimum transmittance, as measured and from fit spectra, Figure 3b), and the best-fit values for the electronic scattering rates (Figure 3c) are shown. The three panels of Figure 3 demonstrate the monotonous decrease of the transmittance and of fit parameters with temperature. The extinction change of the plasmonic resonance for the different Pb coverages goes linearly with temperature down to the


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range where 𝑇 ≈ 𝜃D . (For bulk lead we use the value 𝜃D = 88 K, derived assuming a temperature independent 𝜃D .33 There are various other literature data that scatter around this value by ca. 10%.) We explain the linear extinction change as follows: Above 𝜃D , the phonon contribution to intrinsic electronic damping should increase linearly with 𝑇 (as follows from eq 6) and so behaves the plasmonic absorption contribution (see eq 3) to extinction. A linear slope with temperature is directly seen also for the electronic scattering rates in Figure 3c. However, these curves show different offsets at low temperatures for the different wire heights. Because all the wires are too thick for quantum-size effects of electrons10 and related changes of electronelectron scattering, and since bulk electron-electron scattering at temperatures above a few K at IR energies is negligibly small,32,34 the differently pronounced diffuse scattering of electrons at the lead surface, the lead-silicon interface, and at defects should be the main reason for the offsets.10 The higher values for the thinner wires indicate the increasing importance of surface and interface scattering for the thinner wires. It is important to note, first, that the scattering rate of the thickest Pb layer is much lower than the bulk value, which indicates the high crystalline quality of these wires. Second, the comparison to IR data for ultrathin Pb layers on Si(111)10 reveals a surprisingly well accordance of the scattering rate of the thickest layer (5 nm) of ref

10

to the result for the 5 nm thick wire of this study for the same temperature. A closer look at the temperature dependence of 𝜔τ for the different wire types discovers that the slope of the various curves is also different. In fact, modeling the curves with the help of eq 5 and 6, using the bulk values 𝜃D = 88 K for the thickest layer, fitting 𝜃D for the thinner layers (with the surface scattering + defect rate, 𝜔τ,s + 𝜔τ,d , as one temperature independent parameter), and taking into account that 𝜏! ~𝜃D finally yields lower Debye temperatures for the thinner layers, see Table 1.


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Figure 3. (a) Resonance frequency from spectral fits. (b) Change of relative transmittance at resonance frequency with temperature for various Pb coverages. (c) Electronic scattering rate from spectral fits (circles) compared to the scattering rate according to eq 5 and 6 for 𝜔τ,s , 𝜃D , and 𝜏0 as given in Table 1 (full black lines) (c). Further details on the fits are explained in the Supporting Information. For 5 ML data are missing because of a faulty function of the sample cooling. There are two data points added to panel (c). The triangle is the bulk scattering rate at room temperature for polycrystalline lead in the IR and the black dot indicates the scattering rate of a 5 nm thick lead layer grown on Si(111).10 The value for the 5 nm thick layer was determined by IR transmittance spectroscopy at 120 K. It perfectly matches the scattering rate obtained in this study for wires of the same thickness at the same temperature.


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The lowest Debye temperatures are in accord to the values obtained for the Pb(111) surface from the studies of the Debye-Waller effect in electron diffraction for various electron energies (and thus various mean free path) in lead by G.A. Somorjai, e.g. ref

35

. A recent electron

diffraction study of flat Pb(111) islands revealed a surface Debye temperature of 37±6 K.36 This value is in very good accordance to our result for the thinnest wires. With decreasing thickness, the increasing surface phonon contribution lowers the Debye temperature because the phonons on surfaces are softer compared to the bulk because of the fewer neighbor atoms. This softening might be further increased by dislocations near the interface to the substrate. The lowered Debye temperature is important. First, it demonstrates that the increase in intrinsic scattering with temperature might be bigger for smaller nanoparticles. Second, in view of the Lindemann's criterion 37 for the melting temperature proportional to 𝜃D2 , such smaller particles melt at much lower temperatures than the big bulky ones. Another consequence of the temperature dependent electron-phonon interaction certainly is the slight reduction of the resonance frequency with decreasing temperature (Figure 3a). First, we have to point out that this decrease is a robust fit result and stays the same for the Larmor time parameter t variable with temperature or fixed for a certain thickness, see Supporting Information. (One should notice that the tiny wires scatter the light only a little bit.) Second, one also has to consider that 𝑛host is decreasing for a silicon substrate by about 1% in the IR if the temperature is lowered from 300 K to 100 K.38 This would mean an increase in resonance frequency.7,39 Third, the length change for a temperature difference of 300 K is below the error in length and would also shift the plasmonic resonance to higher frequencies. Therefore, the


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observed decrease in resonance frequency certainly is related to the renormalization effect of the plasma frequency, i.e. due to the electron-phonon interaction.

6. CONCLUSIONS The precise analysis of the temperature dependence of the fundamental plasmonic resonance of single-crystalline lead nanowires has demonstrated that the electron-phonon interaction strongly influences the plasmonic behavior. At lower temperatures at which the phononic ground is relevant, single crystalline particles show much stronger resonances than at room temperature. For the lead nanorods, a shift of the resonance frequency to lower values with decreasing temperature is found which can be related to the temperature dependence of the renormalized plasma frequency of lead. This temperature dependence is a result of the electron-phonon interaction. Furthermore, because of this interaction, the differences between bulk and surface (and interface) phonon properties of nanoparticles give rise to further modification of the plasmonic resonances and their thermal change. The thinner the particles are the more relevant is the deviation from bulk material properties. Our results make obvious the important connection of plasmonic behavior of nanoparticles to solid-state physics and surface science.

ASSOCIATED CONTENT Supporting Information. Details on the fit procedure and simulated spectra for a 15 nm high cuboid based on bulk data. AUTHOR INFORMATION Corresponding Author


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* E-mail: [email protected]. Tel.: +49 6221 54 9863 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. ǁ

These authors contributed equally.

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT The work was partially done within the DFG project PU193/9. The authors thank Dr. Tadaaki Nagao (NIMS, Tsukuba) for the provision of the silicon (557) wafer and his valuable advice for the sample preparation. J.V. acknowledges support by the Heidelberg Graduate School of Fundamental Physics.

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For Table of Contents Use Only

How Intrinsic Phonons Manifest in Infrared Plasmonic Resonances of Crystalline Lead Nanowires Jochen Vogt, Chung Vu Hoang, Christian Huck, Frank Neubrech, and Annemarie Pucci


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How Intrinsic Phonons Manifest in Infrared Plasmonic Resonances of

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