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Tunable Phonon Polaritons in Atomically Thin van der Waals Crystals of Boron Nitride

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Science  07 Mar 2014:
Vol. 343, Issue 6175, pp. 1125-1129
DOI: 10.1126/science.1246833

Nanoimaged Polaritons

Engineered heterostructures consisting of thin, weakly bound layers can exhibit many attractive electronic properties. Dai et al. (p. 1125) used infrared nanoimaging on the surface of hexagonal boron nitride crystals to detect phonon polaritons, collective modes that originate in the coupling of photons to optical phonons. The findings reveal the dependence of the polariton wavelength and dispersion on the thickness of the material down to just a few atomic layers.

Abstract

van der Waals heterostructures assembled from atomically thin crystalline layers of diverse two-dimensional solids are emerging as a new paradigm in the physics of materials. We used infrared nanoimaging to study the properties of surface phonon polaritons in a representative van der Waals crystal, hexagonal boron nitride. We launched, detected, and imaged the polaritonic waves in real space and altered their wavelength by varying the number of crystal layers in our specimens. The measured dispersion of polaritonic waves was shown to be governed by the crystal thickness according to a scaling law that persists down to a few atomic layers. Our results are likely to hold true in other polar van der Waals crystals and may lead to new functionalities.

Layered van der Waals (vdW) crystals consist of individual atomic planes weakly coupled by vdW interaction, similar to graphene monolayers in bulk graphite (13). These materials can harbor superconductivity (2) and ferromagnetism (4) with high transition temperatures, emit light (5, 6), and exhibit topologically protected surface states (7), among many other effects (8). An ambitious practical goal (9) is to exploit atomic planes of vdW crystals as building blocks of more complex artificially stacked structures where each such block will deliver layer-specific attributes for the purpose of their combined functionality (3). We explored the behavior of phonon polaritons in hexagonal boron nitride (hBN), a representative vdW crystal. The phonon polaritons are collective modes that originate from coupling of photons with optical phonons (10) in polar crystals. They have been investigated in the context of energy transfer (11, 12), coherent control of the lattice (13), ultramicroscopy (14, 15), “superlensing” (16), and metamaterials (17, 18). Tunable phonon polaritons that we discovered in hBN by direct infrared (IR) nanoimaging set the stage for the implementation of these appealing concepts in vdW heterostructures. Polaritonic effects reported here are likely generic to other polar vdW solids because these materials commonly show optical phonons. hBN stands out in this class of materials thanks to its light constituent elements, which yield particularly strong phonon resonances that span a broad region of the technologically important IR band.

IR nanoimaging and Fourier transform IR nano-spectroscopy (nano-FTIR) experiments were performed at UCSD by using a scattering-type scanning near-field optical microscope (s-SNOM) (19). The physics of polariton imaging using s-SNOM is akin to nanoimaging of surface plasmons (20, 21) (Fig. 1A). In short, we illuminated the metalized tip of an atomic force microscope (AFM) with an IR beam. We used quantum cascade lasers (QCLs) with tunable frequency ω = 1/λIR, where λIR is IR beam wavelength and a broad-band difference frequency generation (DFG) laser system (22). Our AFM tip with curvature radius a ≈ 25 nm is polarized by the incident IR beam. The light momenta imparted by the tip extend to the typical range of momenta supporting phonon polaritons in hBN (Fig. 2E). Therefore, the strong electric field between the tip and the sample provides the necessary momentum to launch polariton waves of wavelength λp that propagate radially outward from the tip along the hBN surface. AFM tips exploited in our nanospectroscopy instrument are commonly referred to as optical antennas (23): an analogy that is particularly relevant to describe the surface wave launching function of the tip. Upon reaching the sample edge, polaritonic waves are reflected back, forming a standing wave between the tip and hBN edge. As the tip is scanned toward the edge, the scattering signal collected from underneath the tip reveals oscillations with the period of λp/2.

Fig. 1 Real-space imaging of surface phonon polaritons on hBN.

(A) Schematics. Arrows denote the incident and back-scattered IR light. Concentric yellow circles illustrate the phonon polariton waves launched by the AFM tip and reflected by the two edges of a tapered hBN crystal. (B and D to F) IR near-field images of the normalized amplitude s(ω) defined in the text and taken at different IR frequencies [hBN thickness in (B) to (F) d = 256 nm]. (C) Simulation of the phonon polariton interference pattern (19). (G) Phonon polaritons probed in three-layer (left) and four-layer (right) hBN crystals. White dashed line tracks the hBN edges according to the AFM topography. Scale bars indicate 800 nm.

Fig. 2 The surface phonon polariton dispersion and nano-FTIR spectra.

(A) Schematics of a nano-FTIR line scan across the hBN crystal. Arrows denote the incident and back-scattered IR beam spanning 1350 to 1600 cm−1. Polaritonic waves are launched (green) by AFM tip and then reflected (orange) by hBN edge at L = 0. (B) Polaritonic features detected in a single line scan in (A). The normalized scattering amplitude spectra s(ω) is plotted in the false color scale. White dashed line at L = 0 marks the edge of the hBN crystal (thickness d = 134 nm). Triangles, fringe maxima extracted from monochromatic imaging similar to Fig. 1. (C) Nano-FTIR spectra at three representative locations along the line scan marked in (B). The peaks marked by the arrows correspond to the dominant polariton interference fringe. (D) Phonon polariton features as probed via line scans for ultrathin hBN crystals with d = 3.8 nm (left) and d = 8.8 nm (right). (E) The dispersion relation of phonon polaritons in hBN. Triangles indicate data from monochromatic imaging in Fig. 1; dots, the nano-FTIR results from (B). The data are superimposed on a false-color plot of calculated Im rp (19); the black dashed lines are from Eq. 1. The straight line on the left represents the light line. (F) Nano-FTIR spectrum s(ω) for the hBN crystal (Fig. 1, A to F) taken away from the sample edges. The solid (green) part of the data corresponds to hBN’s hyperbolic region where Embedded Image< 0.

Representative nanoimaging data are displayed in Fig. 1, B and D to F, where we plot the normalized near-field amplitude s(ω) = shBN(ω)/sAu(ω) at several IR frequencies in the 1550- to 1580-cm−1 range. Here, shBN(ω) and sAu(ω) are the scattering amplitudes for, respectively, the sample and the reference (Au-coated wafer) (19). The amplitudes were demodulated at the third or the fourth harmonic of the tapping frequency to isolate the genuine near-field signal (23). The images in Fig. 1, B to F, were taken for a tapered hBN crystal of thickness d = 256 nm. They reveal a hatched pattern of periodic maxima, fringes, of s(ω) running parallel to the edges, with the “hot spots” located where two or more fringes intersect. We observed similar fringe patterns in other hBN samples, including those that are only a few atomic layers thick (Fig. 1G). Such patterns are readily accounted for (Fig. 1C) within a phenomenological theory that considers reflections from the tapered edges (19).

Data in Fig. 1 allow one to obtain the polariton wavelength λp simply by doubling the fringe period, and the corresponding momentum can be calculated as q = 2π/λp. We used two approaches to determine the dispersion relation q = q(ω) of the polaritons. One method (15, 20, 21) is to analyze the periodicity of fringes at discrete frequencies of the IR source (Fig. 1, B and D to G). We have complemented this procedure with a technique capable of capturing the entire dispersion in the course of one single scan of our nanoscope. We executed this line scan on an hBN crystal with a large surface area to ensure that the L = 0 boundary is the principal reflector for the tip-launched polaritons (Fig. 2A). Such a line scan (Fig. 2, A, B, and D) is composed of a series of broad-band nano-FTIR spectra taken at every pixel. Starting in the region of unobscured SiO2 substrate (L < 0) and continuing through the hBN crystal (L > 0), we combined the spectra from all pixels along the line scan and thus obtained a two-dimensional map s(L, ω), shown in Fig. 2B. In the plot, we observed a series of resonances that systematically vary with frequency ω and the distance from the sample edge L. The nano-FTIR spectra from three representative positions are shown in Fig. 2C. Each of the frames in Fig. 2C and each pixel in Fig. 2B unveil phonon polaritons in the frequency domain. The momentum q corresponding to each ω in this map can be found from the fringe periodicity along the ω = constant cut. Therefore, a single line scan is sufficient to extract the complete dispersion profile of any surface mode.

The two approaches for mapping the surface wave dispersion produced consistent results (triangles in Fig. 2B were obtained from monochromic imaging). The broad-band line scan data (dots in Fig. 2E) allowed us to probe the dispersion in the ω − q parameter space (1430 to 1530 cm−1) that cannot be investigated through the single-frequency imaging because of unavailability of proper QCLs. The experimental data for phonon polariton dispersion in Fig. 2E are in excellent agreement with the modeling results. Briefly, the surface polaritons correspond to the divergences of the reflectivity rp(q + iκ, ω) of the system at complex momenta q + iκ (10). For λp « λIR, we derived the analytical formula for polariton dispersion (19):Embedded Image (1)where εa(ω), Embedded Image, ε(ω), and εs(ω) are the dielectric functions of air, hBN (for directions perpendicular and parallel to the c axis), and SiO2 substrate, respectively. The propagating modes correspond only to those integer l (if any) for which the loss factor γ = ακ/q is positive and less than unity. Parameter α = ± is the sign of the group velocity dω/dq (19). An instructive way to visualize both the dispersion and the damping is via a false-color plot of Im rp(q, ω) (19, 24) at real q and ω (Fig. 2E). Our data line up with the topmost of these curves, which corresponds to the principal l = 0 branch (19) in Eq. 1.

Additional insights into the photonic and polaritonic properties of hBN were obtained by analyzing the frequency dependence of the nano-FTIR spectra. We collected the spectrum in Fig. 2F far away from the hBN edges, where the surface waves are damped and the scattering amplitude signal is solely governed by the local interaction with the phonon resonances (25). Two of these resonances centered around 770 and 1370 cm−1 are due to the c axis and the in-plane phonon modes of hBN, respectively (26, 27). The hump-dip feature around 1100 cm−1 originates from the SiO2 substrate (28): a consequence of a partial transparency of our specimen. The quantitative relation between this spectrum, the reflectivity rp(q, ω), and the fundamental phonon modes can be established by numerical modeling of the tip-sample interaction (19). The right plot of Fig. 2F indicates that our model captures the gross features of the data. Moreover, the hBN is an example of a natural hyperbolic material (29): a crystal possessing the in-plane and out-of-plane components of the dielectric tensor having the opposite signs so that Embedded Image< 0. Hyperbolic regions are marked in green in Fig. 2F.

The layered nature of vdW materials, including hBN, facilitates the control of both the wavelength and the amplitude of polaritonic waves by varying the thickness d of the specimens. Representative line profiles (Fig. 3A) for specimens with d in the range of 150 to 250 nm were taken normal to the crystal edge at L = 0. The thickness was measured simultaneously with the scattering amplitude through the AFM topography. All fringe profiles share the same line form with a prominent peak close to the edge followed by weaker peaks that are gradually suppressed away from the edge. The oscillation period, equal to λp/2 (arrows in Fig. 3A), systematically decreases as the samples become thinner. This scaling extends down to a few atomic layers (Fig. 3, B and C).

Fig. 3 The evolution of the phonon polariton wavelength and amplitude with the thickness of hBN crystals.

(A) Line profiles of the scattering amplitude s(ω) at 1560 cm−1 for hBN crystals with d = 154, 237, and 256 nm. Arrows indicate the polariton wavelength. (B) Near-field image and (C) phonon polariton line profiles for few-layer hBN crystals. White dashed line in (B) tracks the sample boundary; scale bar in (B), 400 nm. (D) Calculated dispersion relation of the l = 0 branch of the phonon polaritons in hBN for various crystal thicknesses d. TO and LO frequencies are marked with blue dashed lines. (E) Dots, wavelengths of phonon polaritons probed at 1560 cm−1 for crystals with different thicknesses d; red line, calculated thickness-dependence relation. (Inset) Thickness-dependence relation probed at 1400 cm−1 for ultrathin hBN crystals. See (19) for details. (F) Calculated loss factor for phonon polaritons.

The measured polariton wavelength (Fig. 3E) agrees with the theoretical predictions (Fig. 3D). For λp smaller than about one-half of λIR = 7.1 μm, the polariton wavelength scales linearly with the crystal thickness d, in agreement with Eq. 1; at larger λp, the linear law shows signs of saturation, also in accord with our model (Fig. 3E inset). Experimentally, the phonon polaritons display thickness-tunability persisting down to three atomic layers (Fig. 3, B and C). We detected polaritons in even thinner samples (bilayer and monolayer hBN). However, the quantitative analysis of these latter data is complicated because of the increasing role of the substrate in the polaritonic response that calls for further experiments on suspended membranes.

Similar to surface plasmons, the phonon polaritons allow one to confine and control electromagnetic energy at the nanoscale (30). In fact, the line form in Fig. 3A strongly resembles plasmonic standing waves in graphene (20, 21). The confinement factor λIRp reaches 25 in hBN, comparable to that of plasmons in graphene (20, 21). Yet these compact polaritons in hBN are able to travel at least 5 to 10 μm, compared with less than 0.5 μm for graphene plasmons. The corresponding loss factor γ = ακ/q is around 0.055, much smaller than a typical γ in graphene. The low damping of polaritons in our insulating samples is consistent with the absence of the electronic losses, the dominant damping channel in plasmonics. The observed losses can likely be further suppressed by improving the crystallographic order of the crystals.

Data in Figs. 1 to 3 show that phonon polaritons of the desired wavelength and confinement can be engineered by varying the number of atomic layers in hBN by, for example, exfoliation techniques. Thus, hBN and likely other polar layered materials can be integrated into vdW hetrostructures (3) to serve not only as electrically insulating spacers but also as waveguides for weakly damped polaritons capable of traveling over considerable distances. Additionally, the hyperbolic response of few-layer hBN is appealing in the context of unique nanophotonics characteristics of this class of solids (29).

Supplementary Materials

www.sciencemag.org/content/343/6175/1125/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S5

References (3142)

References and Notes

  1. Materials and methods are available as supplementary materials on Science Online.
  2. Acknowledgments: Work at UCSD was supported by U.S. Department of Energy–Office of Basic Energy Sciences (DOE-BES). The development of nano-FTIR at UCSD is supported by Office of Naval Research (ONR), DOE, Air Force Office of Scientific Research (AFOSR), and NSF. M.M.F. is supported by ONR. P.J.-H. acknowledges support from AFOSR grant number FA9550-11-1-0225. A.S.R. acknowledges DOE grant DE-FG02-08ER46512 and ONR grant MURI N00014-09-1-1063. M.T. and G.D. are supported by NASA. A.H.C.N. acknowledges a National Research Foundation–Competitive Research Programme award (R-144-000-295-281). A.Z., W.G., and W.R. acknowledge support from the Director, Office of Energy Research, BES, Materials Sciences and Engineering Division, of the U.S. DOE under contract no. DE-AC02- 05CH11231, which provided for preparation and characterization of the BN, and from the ONR, which provided for substrate transfer technique. F.K. is a cofounder of Neaspec, producer of the s-SNOM apparatus used in this study.
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