Surface and Volume Phonon Polaritons in Boron Nitride Nanotubes

nanotubes (BNNTs) were found to exhibit the dispersion of volume modes ... been observed as surface phonon polaritons (SPhPs)1,4 but also as volume mo...
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Letter Cite This: J. Phys. Chem. Lett. 2019, 10, 4851−4856

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Surface and Volume Phonon Polaritons in Boron Nitride Nanotubes Cassandra Phillips,† Leonid Gilburd,† Xiaoji G. Xu,‡ and Gilbert C. Walker*,† †

Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada Department of Chemistry, Lehigh University, Bethlehem, Pennsylvania 18015, United States

‡

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S Supporting Information *

ABSTRACT: Phonon polaritons (PhPs) are quasiparticles created by coupling of photons to polar lattice vibrations. Previously, PhPs have been observed as both surface and volume confined waves. The dispersion of the polariton depends strongly on the nature of the material. Volume polaritons show asymptotic behavior near the longitudinal optical phonon frequency of the material, whereas surface polaritons instead approach the surface phonon frequency. Boron nitride nanotubes (BNNTs) were found to exhibit the dispersion of volume modes below the surface phonon frequency. However, around and above the surface phonon frequency, the behavior becomes that of a surface wave with an amplified near-field response. These findings improve our understanding of photonics within BNNTs and suggest potential applications that take advantage of the high fields and density of states in that spectral region.

P

Previously, our group has explored the nature of PhP enhancement by rough gold substrates and imaged PhP coupling using pump−probe spectroscopy.7,22 A direct model on the dispersion relationship of PhPs in BNNTs will help us understand these phenomena and facilitate future applications. In this article, we report experimental observations and analytical descriptions of PhPs in BNNTs on silicon substrates. The tubes are found to have propagation characteristics comparable to those of h-BN HPhPs but exhibit an enhanced evanescent resonance at the surface phonon mode that is not observed in h-BN. These results could be used to tailor subwavelength infrared energy guiding systems using BNNTs. BNNTs of various diameters were drop-cast onto silicon wafers cleaned in piranha solution. IR spectral data were collected on the samples using scattering-type scanning nearfield optical microscopy (sSNOM). The near-field imaging signal was collected using a phase-controlled homodyne technique with the reference phase set to alternatively π and π/2 of the laser phase. The signal homodyned at the π/2 phase provides the imaginary response of the tip−material polarization (absorption); the signal homodyned at the π phase provides the real response (reflection).23 Figure 1 shows the π/2 signal normalized to the silicon substrate π signal from a BNNT. Fringes characteristic of PhPs are observed within the tubes. The fringes are an interference pattern (standing wave) produced by the superposition of coherently excited PhPs (Figure 2) propagating and reflected from the tube terminal. The fringe spacing can be used to determine the momentum of the polariton and was obtained via two methods: by manually determining the spacing between intensity maxima in a line scan and by performing a

honon polaritons (PhPs) are quasiparticles generated by coupling of photons and phonons that can be found within a dipolar material whenever the real value of the permittivity of the material becomes strongly negative.1−4 PhPs exist between longitudinal optical (LO) and transverse optical (TO) modes within the infrared, in a spectral window called the Reststrahlen band.5 PhPs are the polar crystal dipolar lattice oscillation analogous to plasmon polaritons from electron oscillations and exhibit many of the same properties, such as a considerable reduction in the confined wavelength compared to free space.3,6,7 This confinement as a polariton has been investigated for potential uses in directed energy transfer, subdiffraction limited lensing, and various metamaterials.8−16 PhPs have been observed not only as surface phonon polaritons (SPhPs)1,4 but also as volume modes known as hyperbolic phonon polaritons (HPhPs).3,14,17 These volume modes exist under the unique hyperbolic condition where the in-plane and out-of-plane permittivities have opposite signs. Conversely, SPhPs are confined at the boundary layer of a material with the permittivity within that material being strongly negative. One major difference between HPhPs and SPhPs is the behavior of the dispersion. The HPhP dispersion asymptotically approaches the LO mode of the system, where the dielectric permittivity returns to zero, whereas surface phonons cannot exist above the surface phonon frequency (where the real part of the permittivity equals −1).6,18 Boron nitride nanotubes (BNNTs) serve as an ideal model to study the directed propagation of PhPs. BNNTs are a polymorph of hexagonal boron nitride (h-BN), functionally layered cylinders of the h-BN lattice. PhPs have previously been investigated in BN structures coupled to graphene and other van der Waals materials as well as in large metamaterial arrays.13,19−21 Confining the propagation of PhPs to one dimension allows for high directionality and control. © XXXX American Chemical Society

Received: June 24, 2019 Accepted: August 9, 2019 Published: August 9, 2019 4851

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fast Fourier transform analysis of the image and determining the spacing from the component spatial frequencies. The two methods produce results that are in good agreement with one another. No evidence of chiral PhPs is observed within our system. Chiral plasmon polaritons have previously been observed in comparable plasmonic systems.24 However, these polaritons require some degree of circular polarization in order to launch the mixed mode. The sSNOM system used in our work is optimized to probe vertical (P) polarization, so a chiral response is not expected. Momenta can be calculated using eq 1, wherein the fringe spacing is doubled in order to obtain λPhP to account for the PhP being a standing wave: q = 2π /λPhP

(1)

No analytical method has been reported previously to characterize the PhP dispersion of BNNTs. The method reported by Basov et al.3 (eq 2) can be applied to BNNTs as it is applicable to the analogous planar h-BN. This dispersion relationship describes a HPhP where the field is confined to the volume of the crystal.

Figure 1. (a) Atomic force microscopy (AFM) height image of a BNNT. The particle at the right terminus is a catalyst precursor coated in a thin layer of h-BN. (b−h) sSNOM near-field images collected at a homodyne phase of π/2. The frequencies are 1400, 1405, 1410, 1415, 1420, 1423, and 1430 cm−1. Fringe patterns characteristic of the PhP standing wave are observed. The near-field signals are normalized to the substrate reflectance signal in the π phase homodyne.

ÄÅ ÑÉÑ ij ε yz ij ε yz ÑÑ ψ ÅÅÅ q(ω) + iκ(ω) = − ÅÅÅÅarctanjjjj air zzzz + arctanjjjj s zzzz + π SÑÑÑÑ, ÑÑÖ d ÅÅÇ k ε⊥ψ { k ε⊥ψ {

ε ψ=

i ε⊥

(2)

Here, the subscripts air and s refer to the dielectric coefficients of the layer above the tube and substrate below the tube, respectively. The subscripts ∥ and ⊥ indicate the dielectric responses of BN parallel and perpendicular to the optical axis, respectively. Moreover, S is an integer that corresponds to the propagating mode of the system. Larger values of S (i.e., S > 0) have been observed in h-BN25 but were not observed in our BNNTs. BNNTs produced with a high isotopic purity may lead to sufficiently low losses that these modes become expressed. Unlike h-BN, BNNTs possess a hollow air channel within them that modifies the dielectric environment when sampling the material. We therefore adopt the Maxwell−Garnett effective medium approximation (eq 3) using ϵm and ϵi to represent the dielectric functions of the medium and inclusions, respectively, and δi to represent the volume fraction of the inclusions.

Figure 2. Schematic of PhP propagation along a BNNT. Far-field waves are injected into the tube at the tip, reflect off the tube terminals, and generate a standing wave along the BNNT.

εeff =

εm(2δi(ϵi − ϵm) + εi + 2εm) 2εm + ϵi − δi(εi − εm)

(3)

Figure 3. (a) Dispersion relationship of a BNNT with a diameter of 43 nm. (b) The volume PhP mode excitation at 1410 cm−1 plotted as a function of the tube diameter. The experimental measurements tend along the S = 0 branch of the dispersion. The subsequent higher-momentum branches are not currently observed in BNNTs. 4852

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Figure 4. (a) Effective medium-modified dielectric function for BNNTs compared with the dielectric function of h-BN in the direction perpendicular to the optical axis (ε⊥). (b) Comparison between the S = 0 branch of the analytical dispersion relationship for a h-BN flake with thickness equal to the diameter of a BNNT.

Figure 5. (a) Effective medium-modified dielectric function for BNNTs generated by eq 3 in the direction perpendicular to the optical axis (ε⊥). (b) Magnified view of the spectral window bounded by the red box in (a), surrounding the surface phonon frequency (ε⊥ = −1). The dashed line indicates the surface phonon frequency. PhPs are supported where the real portion of the dielectric function is strongly negative.

The Lorentz model was used to produce the unmodified dielectric function (methods). BNNTs and h-BN are strongly anisotropic materials, and the dielectric function in the direction parallel and perpendicular to the optical axis is modeled separately. Figure 3 shows the result of combining eqs 2 and 3 into a modified analytical dispersion relationship for a BNNT. The effective medium approximation assumes a cylindrical air channel volume fraction of 0.20 based on previous TEM studies on chemical vapor deposition grown BNNTs by our group (Figure 4).26 A good correlation is seen between the experimental data and the predicted dispersion. When BNNTs of multiple diameters are examined, the dispersion exhibits a 1/d relationship over the measured diameters d. This relationship is strongly indicative of volumetric polariton modes.27 This also shows good agreement with simulations using COMSOL Multiphysics showing the effective mediummodified dispersion relationship is a reasonable approximation for the system (Supporting Information). A key property that emerges from the effective mediummodified dielectric function is that the real part of the permittivity crosses −1 in the 1480−1490 cm−1 window (Figure 5). This crossing is characterized as the surface phonon frequency. Previous work using a plasma source to obtain a nano-Fourier-transform IR (FTIR) spectrum showed a large material response within this region that is not observed in far-field FTIR measurements (Figure 6).28,29 The far-field signal is dominated strongly by the absorption from the TO mode (1362 cm−1) and a higher frequency mode (∼1527 cm−1) of the BNNT. There is also an intermediate band observed at 1450 cm−1, appearing to be around the −2 crossing of the dielectric function. This band may be due to the

Figure 6. (a) Far-field FTIR spectrum of BNNTs in the Reststrahlen band. Peak fitting identifies a primary peak at 1370 cm−1, a secondary peak at 1530 cm−1, and an intermediate peak at 1450 cm−1. (b) Nearfield nano-FTIR spectrum in the same region, in which a strong peak at 1480 cm−1 corresponding to the surface phonon mode is observed. Part b was adapted and reprinted from ref 29. Copyright 2018 American Chemical Society.

localized PhP band.30,31 The mode at 1527 cm−1 occurs near the Re(ε) = 0 crossing of the dielectric function and thus close to the Re(ε) = 0 crossing where the LO mode is found. The LO mode is however a dark mode and cannot directly couple to free-space light. This crossing region is roughly where epsilon near zero (ENZ) and Berreman modes would be expected, and we tentatively assign the 1527 cm−1 band as one of these related modes, but this assignment is not definitive.32,33 This frequency appears constant over the tube diameters examined as evidenced by the analytical dispersion fit in Figure 3b. A change in the LO vibrational mode would be seen as a deviation from the analytical dispersion which assumes constant TO and LO frequencies. This result is consistent with ab initio and zone-folding calculations for 4853

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Figure 7. (a) Comparison of the Y component of the scattered electric field from COMSOL simulation between BNNTs and h-BN. BNNTs show a considerably enhanced local field compared to h-BN. (b) Simulation of the local field around a 45 nm BNNT at 1480 cm−1. The field decays on the order of 100 nm.

states which might, for example, provide a way to do near-field surface chemistry at the surface phonon frequency.

single-walled BNNTs which show the scaling of phonon frequencies as a function of tube diameter stagnates above around 2 nm.27 It should also be noted that different data sets appear to show different ratios between the intermediate band and the TO mode. The near-field enhancement at 1480 cm−1 is due to the presence of a localized surface phonon mode around the ε = −εm crossing, where −εm is the dielectric of the surrounding medium (Figure 7). These modes are evanescent in nature and decay exponentially away from the surface.34,35 This property exists as a function of the material geometry, with the resonance condition for a cylinder being located at ε = −1 due to the interface with air.36−38 This results in a surface phonon mode that is independent of cylinder length and diameter. There are theoretical predictions of surface phonon modes that are strongly dependent on the cylinder aspect ratio, but we do not observe this relationship in our current study.39 The HPhP dispersion in h-BN, a planar material, does not exhibit this surface phonon. The analytical dispersion relationship (eq 2) serves as an accurate description when coupled with an effective medium approximation to account for the air channel. In h-BN, PhP standing waves continue to be observed up to the LO mode frequency. For BNNTs in the region past the surface phonon mode, standing waves indicative of PhPs are not observed (Figure 8). Surface PhPs exhibit a cutoff frequency at the

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EXPERIMENTAL METHODS Scattering-Type Scanning near-Field Optical Microscopy. A quantum cascade laser (Daylight Solutions) provides a continuous wave mid-IR signal with a frequency range of 1300−1440 cm−1. A modified AFM (Multimode AFM, Bruker Nano) allows for the laser to be focused onto a metal-coated AFM tip using a parabolic reflector. Light scattered off the tip is recollected using the same parabolic reflector and homodyned interferometrically with a reference laser field from the same source. A mercury cadmium telluride detector (Kolmar Technologies) converts the optical intensity into an electrical signal which is demodulated based on the tapping frequency using a HF2LI lock-in amplifier (Zurich Instruments). The effects of background scattering are suppressed by demodulating to the third harmonic of the tapping frequency. The out-of-phase (π/2) homodyne condition is set by minimizing the near-field signal from the substrate.40 Sample Synthesis and Preparation. Multiwall BNNTs were synthesized using a high-temperature chemical vapor deposition (CVD) technique in an induction furnace. More details may be found in the literature.41 Magnesium oxide, tin(II) oxide, or iron(II) oxide and boron powders were combined at a weight ratio of 7:150:30, placed in a BN crucible, and heated to approximately 1450 °C under flow of argon carrying gas and ammonia reactive gas.

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Figure 8. Near-field signal for the nanotube in Figure 1 at 1500 cm−1, taken at the π/2 phase homodyne. As it is a region where the dielectric function of BNNTs is past the surface phonon frequency (where ε = −1), no standing wave PhPs are supported.

COMPUTATIONAL METHODS The dispersion relationship of the BNNTs was calculated using MATLAB. The permittivities ε∥ and ε⊥ were described using a Lorentz model 2 2 ωLO, ji zyz μ − ωTO, μ zz, εμ = ε∞, μjjjj1 + 2 2 j ωTO, μ − ω − iω Γμ zz{ k

surface phonon mode, where volume PhPs approach the LO mode frequency. The observed PhPs appear to have the dispersion of a volume PhP but the cutoff frequency of surface PhPs. In essence, BNNT PhPs exhibit the properties of surface waves at higher frequencies and volume waves at lower frequencies. In conclusion, we have shown that PhP modes in BNNTs can be surface- or volume-confined waves. Tubes exhibit the dispersion relationship of a volume hyperbolic mode as well as the localized field enhancement at the surface phonon frequency of a surface mode due to their geometry. These unique properties improve our understanding of PhPs and offer waves to create strong local fields and high densities of

μ = ⊥, ∥

where ε∞ is the high-frequency permittivity, ωTO and ωLO are the TO and LO phonon frequencies, respectively, and Γ is the damping constant. For the dielectric function perpendicular to the optical axis, the TO frequency is taken to be 1362 cm−1, and the LO is associated with the ε = 0 crossing at 1527 cm−1, respectively, based on FTIR measurements on CVD-grown BNNTs, and they are consistent with the literature.28 The damping constant Γ was chosen to be 4 cm−1, in line with observations for h-BN.3 The values for the dielectric function 4854

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(6) Maier, S. A. Plasmonics: Fundamentals and Applications, 2007 ed.; Springer: New York, 2007; DOI: 10.1007/0-387-37825-1. (7) Xu, X. G.; Ghamsari, B. G.; Jiang, J.-H.; Gilburd, L.; Andreev, G. O.; Zhi, C.; Bando, Y.; Golberg, D.; Berini, P.; Walker, G. C. OneDimensional Surface Phonon Polaritons in Boron Nitride Nanotubes. Nat. Commun. 2014, 5, 4782. (8) Shen, S.; Narayanaswamy, A.; Chen, G. Surface Phonon Polaritons Mediated Energy Transfer between Nanoscale Gaps. Nano Lett. 2009, 9, 2909−2913. (9) Taubner, T.; Korobkin, D.; Urzhumov, Y.; Shvets, G.; Hillenbrand, R. Near-Field Microscopy Through a SiC Superlens. Science 2006, 313, 1595. (10) Poddubny, A.; Iorsh, I.; Belov, P.; Kivshar, Y. Hyperbolic Metamaterials. Nat. Photonics 2013, 7, 948−957. (11) Schuller, J. A.; Zia, R.; Taubner, T.; Brongersma, M. L. Dielectric Metamaterials Based on Electric and Magnetic Resonances of Silicon Carbide Particles. Phys. Rev. Lett. 2007, 99, 107401. (12) Zapata-Rodríguez, C. J.; Miret, J. J.; Vuković, S.; Belić, M. R. Engineered Surface Waves in Hyperbolic Metamaterials. Opt. Express 2013, 21, 19113−19127. (13) Brar, V. W.; Jang, M. S.; Sherrott, M.; Kim, S.; Lopez, J. J.; Kim, L. B.; Choi, M.; Atwater, H. Hybrid Surface-Phonon-Plasmon Polariton Modes in Graphene/Monolayer h-BN Heterostructures. Nano Lett. 2014, 14, 3876−3880. (14) Li, P.; Lewin, M.; Kretinin, A. V.; Caldwell, J. D.; Novoselov, K. S.; Taniguchi, T.; Watanabe, K.; Gaussmann, F.; Taubner, T. Hyperbolic Phonon-Polaritons in Boron Nitride for near-Field Optical Imaging and Focusing. Nat. Commun. 2015, 6, 7507. (15) Berte, R.; Gubbin, C. R.; Wheeler, V. D.; Giles, A. J.; Giannini, V.; Maier, S. A.; De Liberato, S.; Caldwell, J. D. Sub-Nanometer Thin Oxide Film Sensing with Localized Surface Phonon Polaritons. ACS Photonics 2018, 5, 2807−2815. (16) Wang, T.; Li, P.; Chigrin, D. N.; Giles, A. J.; Bezares, F. J.; Glembocki, O. J.; Caldwell, J. D.; Taubner, T. Phonon-Polaritonic Bowtie Nanoantennas: Controlling Infrared Thermal Radiation at the Nanoscale. ACS Photonics 2017, 4, 1753−1760. (17) Shi, Z.; Bechtel, H. A.; Berweger, S.; Sun, Y.; Zeng, B.; Jin, C.; Chang, H.; Martin, M. C.; Raschke, M. B.; Wang, F. Amplitude- and Phase-Resolved Nanospectral Imaging of Phonon Polaritons in Hexagonal Boron Nitride. ACS Photonics 2015, 2, 790−796. (18) Basov, D. N.; Fogler, M. M.; Abajo, F. J. G. de. Polaritons in van Der Waals Materials. Science 2016, 354, aag1992. (19) Xu, X. G.; Jiang, J.-H.; Gilburd, L.; Rensing, R. G.; Burch, K. S.; Zhi, C.; Bando, Y.; Golberg, D.; Walker, G. C. Mid-Infrared Polaritonic Coupling between Boron Nitride Nanotubes and Graphene. ACS Nano 2014, 8, 11305−11312. (20) Woessner, A.; Lundeberg, M. B.; Gao, Y.; Principi, A.; AlonsoGonzález, P.; Carrega, M.; Watanabe, K.; Taniguchi, T.; Vignale, G.; Polini, M.; et al. Highly Confined Low-Loss Plasmons in Graphene− Boron Nitride Heterostructures. Nat. Mater. 2015, 14, 421−425. (21) Brown, L. V.; Davanco, M.; Sun, Z.; Kretinin, A.; Chen, Y.; Matson, J. R.; Vurgaftman, I.; Sharac, N.; Giles, A. J.; Fogler, M. M.; et al. Nanoscale Mapping and Spectroscopy of Nonradiative Hyperbolic Modes in Hexagonal Boron Nitride Nanostructures. Nano Lett. 2018, 18, 1628−1636. (22) Gilburd, L.; Xu, X. G.; Bando, Y.; Golberg, D.; Walker, G. C. Near-Field Infrared Pump−Probe Imaging of Surface Phonon Coupling in Boron Nitride Nanotubes. J. Phys. Chem. Lett. 2016, 7, 289−294. (23) Xu, X. G.; Tanur, A. E.; Walker, G. C. Phase Controlled Homodyne Infrared Near-Field Microscopy and Spectroscopy Reveal Inhomogeneity within and among Individual Boron Nitride Nanotubes. J. Phys. Chem. A 2013, 117, 3348−3354. (24) Zhang, S.; Wei, H.; Bao, K.; Håkanson, U.; Halas, N. J.; Nordlander, P.; Xu, H. Chiral Surface Plasmon Polaritons on Metallic Nanowires. Phys. Rev. Lett. 2011, 107, 096801. (25) Giles, A. J.; Dai, S.; Vurgaftman, I.; Hoffman, T.; Liu, S.; Lindsay, L.; Ellis, C. T.; Assefa, N.; Chatzakis, I.; Reinecke, T. L.; et al.

parallel to the optical axis as well as the high-frequency permittivities were taken from analysis of h-BN.42 To obtain the final effective values for the dielectric function, the values of ε∥ and ε⊥ were inserted into the Maxwell−Garnett approximation (eq 3). The effective medium approximation assumes an air channel volume fraction of 0.20.26 Finally, the effective medium dielectric functions were combined in the analytical dispersion relationship (eq 2) to produce the final dispersion simulation. Finite element method simulations were performed using the commercial software package COMSOL. Calculations on the scattered field were performed on a 2D cut along a cylindrical structure with a platinum sphere included to model the behavior of the AFM probe. The values used were the same as the parameters above in MATLAB with no consideration given to the effective medium approximation. For the scattered field for h-BN, identical parameters were used from previous studies on phonon polaritons within h-BN.3

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.9b01829. Numerical realization of dispersion relationship by finite element method simulations using COMSOL, figures of scattered field generated using COMSOL (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Xiaoji G. Xu: 0000-0003-0847-5871 Gilbert C. Walker: 0000-0002-5248-5498 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Funding for this work was provided through the Natural Sciences and Engineering Research Council of Canada (NSERC) as well as the Canada Foundation for Innovation (CFI). We thank an anonymous reviewer for their helpful comments.

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