Insights into hyperbolic phonon polaritons in \nh−BN\n using Raman scattering from encapsulated transition metal dichalcogenide layers

Abstract

New techniques for probing hyperbolic phonon polaritons (HPP) in 2D materials will support the development of the emerging technologies in this field. Previous reports have shown that it is possible for WSe2 monolayers in contact with the hexagonal boron nitride (hBN) to generate HPP in the hBN via Raman scattering. In this paper, we set out new results on HPP Raman scattering induced in hBN by WSe2 and MoSe2 monolayers including new resonances at which the Raman scattering is enhanced. Analysis of the observed Raman lineshapes demonstrates that Raman scattering allows HPP with wavevectors with magnitudes significantly in excess of 15000 cm-1 to be probed. We present evidence that the Raman scattering can probe HPP with frequencies less than the expected lower bound on the Reststrahlen band suggesting new HPP physics still waits to be discovered. Intro The unique properties of hyperbolic phonon polaritons (HPPs)1–4 are leading to their exploitation in a range of important applications5,6. For instance, in the production of a new class of mid-infrared sources7 which, whilst thermally excited, produce radiation which is narrowband8 and spatially coherent9,10. Work on related sources indicates that it should be possible to combine these properties with high modulation frequencies; up to 10 MHz11. Another field in which HPPs are being exploited is MIR integrated nanophotonics for applications in surface-enhanced infrared spectroscopy12 as well as sub-diffraction imaging6,13. A recent highlight in this field has been the creation of reconfigurable waveguides and lenses for hyperbolic phonon polaritons14,15 using phase change materials. Hyperbolic phonon polaritons allow subwavelength volume confinement6,16,17 of mid-infrared radiation by as much as a factor of 86. This confinement is not only being exploited for miniaturisation but also allows the concentration of electromagnetic energy, allowing for strong coupling18,19 and nonlinear effects20–22. By analogy with plasmonics, which are more lossy than HPP23, an even wider range of HPP applications, e.g. biosensors24 and improving signal to noise photodetectors7,8, are likely to emerge soon. The two main techniques used to study HPP are FTIR spectroscopy25 and scattering-type scanning near-field optical microscopy (s-SNOM)26–28. FTIR is simpler however it either requires specially prepared microfabricated structures5 or prism coupling5,29 to access the large wavevector HPP. The former is not suitable for probing HPP in devices and the latter limits the wavevector that can be accessed. s-SNOM26–28 allows HPPs to be imaged in real space with impressive resolution and thus access to wavevectors of the order of ~ 1000 times the free space wavevector27,28. However, this technique is complex and requires physical contact with the sample. A HPP measurement method based upon the conversion of MIR to visible radiation would enable a wide range of new opportunities. The relative maturity of visible photonics means that such a method is likely to be much simpler. It should allow high-resolution (0.5 μm) imaging without the need for a near-field probe and because many of the key HPP are wide band gap materials it should allow imaging of sub-surface HPP. Due to the much shorter wavelength of visible light such a method might allow access to even larger wavevector HPPs. Actually, it has already been shown that transition metal dichalcogenide (TMD) layers allow the probing of HPPs via Raman scattering of visible radiation30–32. However, no one has explored what information about HPP can be obtained from the Raman spectra. In this paper we present significant new results on HPP Raman scattering in TMDs. These include new resonances at which the HPP Raman features are enhanced in WSe2 monolayers and the first measurements of HPP Raman features in Mo based TMDs. Based upon these new results we discuss the mechanism for HPP Raman scattering; the fact that it can access much higher wavevector HPP than IR based techniques; and what Raman scattering of HPP might bring to the field of HPP technologies. Main Body Figure 1a) shows a Raman spectrum of the encapsulated WSe2 monolayer taken with an excitation energy of 1.866 eV. The observed Raman features can be separated into one-phonon peaks (E′′TO(M) at 196 cm-1; E′′TO(K) at 209 cm-1; E′TO(M) at 229 cm-1; E′(Γ)/A1′(Γ) at 250 cm-1; A′′2(M)/ E′LO(K) at 258 cm-1.) and two-phonon peaks (range of shifts up to 500 cm-1) and two features at around 730-850 cm-1 and 1000-1080 cm-1. Further discussion of the WSe2 phonon Raman peaks and their attribution can be found in literature31,33–36. The 730-850 cm-1 and 1000-1080 cm-1 features have previously been associated with scattering of excitons in the monolayer by hBN HPP (lower shift feature) and a combination of a hBN HPP and a monolayer A1′ phonon (upper shift feature). This hypothesis is strongly supported by the facts that no Raman scattering is observed at comparable Raman shifts31,32 in samples where WSe2 monolayers are not in intimate contact with hBN and the only peak observed in Raman spectra of hBN30,32,37 is at 1380 cm-1. The peaks at smaller Raman shifts, which only involve phonons, are characteristically narrower with widths of the order of 0.25 meV (2 cm-1), whereas the HPP related features are significantly broader, at 10 meV (80 cm-1). The Raman features can also be observed in Figure 1b) and c) where we present colourmaps of the resonance Raman spectra of an encapsulated WSe2 monolayer. All the features show clear resonance behaviour in the colourmaps. For instance the Raman peak at 250 cm-1, assigned to the degenerate A1′/E’ phonons35,38, has four resonances; when the incoming and scattered photons are resonant with the A1s and A2s bright excitonic states. As previously reported, the 730-850 cm-1 features shows a clear outgoing resonance with the A1s state and incoming resonance with the A2s state31,32. As also previously reported, the 1000-1080 cm-1 shows a strong resonance at ~1.865 eV which is both an outgoing resonance with the A1s and an incoming resonance with the A2s, i.e. a double resonance. In addition, the same features have at least two other resonances at higher laser energies which have not been reported before. The clearest of these is an outgoing resonance associated with the A2s exciton. There is also a weaker resonance, approximately 20 meV higher in energy corresponding to the A3s exciton. As more clearly shown in Figure 1b), the features at the outgoing resonances show a characteristic behaviour in which the higher shift scattering is resonant at higher laser energies. This is particularly visible from 1.95 to 2 eV. This is clear proof that the two broad features, with Raman shifts centred at approximately 800 and 1050 cm-1, can be associated with a band of excitations rather than a single underlying excitation. Figure 1: a) An individual Raman spectrum from the hBN encapsulated WSe2 sample with an excitation energy of 1.866 eV. The first two parts of the spectrum are scaled by a factor of 120 and 40 for visibility. b) and c) show colourmaps of the resonance behaviour of the 800 and 1050 cm-1 hBN Raman features b) presents the full spectral width including lower Raman shift features from the WSe2 phonons, such as the strong 250 cm-1 A1′(Γ)/E’(Γ) peak, as well as the higher shift hBN modes. c) Presents a zoom of the higher shift part of the spectra presented in b) with the colours adjusted to show a narrower range of intensities. The colour indicates the intensity of the Raman scattering in logarithmic scale, with blue corresponding to lowest and red to highest intensity. The energies of the incoming and outgoing Raman resonances (solid and dashed lines) associated with the A1s, A2s and A3s excitonic states are shown with red, white and pink lines respectively. The green lines correspond to the resonance conditions for the lowest energy unbound electron hole pair (UBP). The signal around 1.87 eV between the 800 and 1050 cm-1 peaks and shifts above 1100 cm-1 are from photoluminescence from the A1s exciton, which follows the A1s outgoing resonance. In order to better understand the resonance behaviour and to determine the energy of the excitonic states involved, resonance profiles of the Raman scattering were determined for the two features as presented in Figure 2. As each feature is associated with a band of excitations, the extracted resonance profile changes at different Raman shifts across the feature. For both of these hBN features, 3 resonance profiles were determined; each by integrating the Raman scattering for a 5 cm-1 band around a centre Raman shift. This process is described in the supplementary section S139. The resonance profiles presented in Figure 2 clearly show the A1s outgoing and A2s incoming resonances previously observed30–32, as well as the new higher energy resonances. Interestingly there is no statistically significant Raman scattering associated with the hBN related features at the A1s incoming resonance. However, the significant additional noise due to the strong A1s luminescence means the upper limit on any scattering at these laser energies is comparable with the strength of the Raman scattering at the highest energy resonances. In the case of the 730-850 cm-1 feature, shown in Figure 2a), the A1s outgoing resonance near 1.83 eV shifts to lower energy, as expected, for the lower centre Raman shifts. The two higher energy resonances above 1.95 eV show the same behaviour indicating they are also both outgoing resonances. For the 1000-1080 cm-1 feature profiles shown in Figure 2b), the A1s outgoing and A2s incoming resonances fall at the same energy, creating a double resonance with the measured Raman scattering two orders of magnitude greater than that of the Raman feature at 730-850 cm-1. The resonance profiles were all fitted using the standard third-order perturbation theory prediction for Raman scattering39 that assumes that the exciton