Abstract
Phonon engineering at gigahertz frequencies forms the foundation of microwave acoustic filters1, acousto-optic modulators2 and quantum transducers3,4. Terahertz phonon engineering could lead to acoustic filters and modulators at higher bandwidth and speed, as well as quantum circuits operating at higher temperatures. Despite their potential, methods for engineering terahertz phonons have been limited due to the challenges of achieving the required material control at subnanometre precision and efficient phonon coupling at terahertz frequencies. Here we demonstrate the efficient generation, detection and manipulation of terahertz phonons through precise integration of atomically thin layers in van der Waals heterostructures. We used few-layer graphene as an ultrabroadband phonon transducer that converts femtosecond near-infrared pulses to acoustic-phonon pulses with spectral content up to 3 THz. A monolayer WSe2 is used as a sensor. The high-fidelity readout was enabled by the exciton–phonon coupling and strong light–matter interactions. By combining these capabilities in a single heterostructure and detecting responses to incident mechanical waves, we performed terahertz phononic spectroscopy. Using this platform, we demonstrate high-Q terahertz phononic cavities and show that a WSe2 monolayer embedded in hexagonal boron nitride can efficiently block the transmission of terahertz phonons. By comparing our measurements to a nanomechanical model, we obtained the force constants at the heterointerfaces. Our results could enable terahertz phononic metamaterials for ultrabroadband acoustic filters and modulators and could open new routes for thermal engineering.
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The data that support the findings of this study are available from the corresponding authors upon request.
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Acknowledgements
The pump–probe spectroscopy, data analysis and DFT and DFPT calculations were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (DE-AC02-05CH11231 within the Nanomachine Program). The monolayer exfoliation and heterostructure stacking were supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (DE-AC02-05CH11231 within the van der Waals Heterostructure Program, KCWF16). Fabrication of the suspended devices was supported by the US Army Research Office (Multidisciplinary University Research Initiative Award W911NF-17-1-0312). S.C. acknowledges support from the Kavli ENSI Heising-Simons Junior Fellowship. W.K., M.H.N. and S.G.L. acknowledge the Texas Advanced Computing Center at the University of Texas at Austin for providing high-performance computing resources. This research also used resources of the National Energy Research Scientific Computing Center, a US Department of Energy, Office of Science User Facility at Lawrence Berkeley National Laboratory, operated under contract DE-AC02-05CH11231. K.W. and T.T. acknowledge support from the Japan Society for the Promotion of Science (KAKENHI grants 21H05233 and 23H02052) and the World Premier International Research Center Initiative, Ministry of Education, Culture, Sports, Science and Technology, Japan.
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Y.Y. and F.W. conceived the project. F.W., M.F.C. and S.G.L. supervised the project. Y.Y. and C.U. performed the pump–probe measurements. Z.L., Y.Y., R.Q., W.Z., S.C. and Q.F. fabricated and characterized the samples. Y.Y. and Z.L. performed the one-dimensional mass–spring simulations. W.K. and M.H.N. performed the DFT-based simulations. K.W. and T.T. grew the hBN crystals. All authors discussed the results and contributed to the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 Fast hot-carrier relaxation in FLG.
a, A near-infrared (NIR) pump-probe spectrum measured in an hBN/WSe2/hBN/FLG heterostructure at 77 K. The pump pulse was at \({E}_{\mathrm{pump}}=1.409\,\mathrm{eV}\) and right-circularly polarized (\({\sigma }^{+}\)). A broadband probe pulse (\({E}_{\text{probe}}=\mathrm{1.55\mbox{--}1.91}\,\text{eV}\)) with the same polarization (\({\sigma }^{+}\)) measures the pump-induced change of the heterostructure reflectance. b, A horizontal line cut at \(E=1.714\,\mathrm{eV}\) shows the optical AC Stark shift at time zero (\(\Delta t=0\)), which follows the pump pulse intensity envelope (FWHM of 230 fs). c, A pump-probe spectrum measured with a left-circularly polarized (\({\sigma }^{-}\)) probe pulse, where the optical a.c. Stark shift signal is absent. The color scale is saturated at the ±30% of the maximum level in a. d, A horizontal line cut at \(E=1.60\,\mathrm{eV}\) shows that the hot-carrier-induced broadband reflectance change of FLG appears and disappears in 370 fs (FWHM).
Extended Data Fig. 2 Phonon-induced exciton energy shift.
a, Pump-probe spectra (\(\Delta R/R\)) measured in an hBN/WSe2/hBN/3LG heterostructure (\({d}_{\text{t-hBN}}=41.0\,\text{nm}\) and \({d}_{\text{b-hBN}}=24.6\,\text{nm}\)) at 77 K. The pump fluence was 250 μJ/cm2. b, Vertical line cuts at t1 = 6.0 ps, t2 = 7.0 ps, and t3 = 7.5 ps are shown in blue circles. The data at \({t}_{1}\) and \({t}_{2}\) are vertically shifted for clarity. By performing transfer-matrix calculations including pump-induced exciton energy shift (\(\Delta E={E}_{\text{pump on}}-{E}_{\text{pump off}}\)), line broadening (\(\Delta \Gamma ={\Gamma }_{\text{pump on}}-{\Gamma }_{\text{pump off}}\)), and oscillator strength change (\(\Delta A={A}_{\text{pump on}}-{A}_{\text{pump off}}\)) as fitting parameters, the fit results (orange lines) and corresponding energy shift values are shown. The exciton energy shift between \({t}_{2}\) and \({t}_{3}\) is |ΔE3 − ΔE2| = 335 μeV.
Extended Data Fig. 3 Saturation of phonon amplitude at high pump fluence.
a, The pump-induced FLG absorption signal of device 3 at \(\Delta t=0\) (similar to that shown in Extended Data Fig. 1d) at pump fluence of 450 μJ/cm2 and 1210 μJ/cm2 show a roughly linear increase of the FLG absorption as a function of pump fluence (weak saturation). b, The peak-to-peak amplitude of the first phonon pulse at Δt = 6.2 ps at pump fluence of 450 μJ/cm2 and 1210 μJ/cm2 show strong saturation at the high pump fluence. The sublinear dependence in a implies that not all pump power is absorbed by FLG, and the stronger sublinear dependence in b implies that not all absorbed power is converted to phonon amplitudes at high pump fluence.
Extended Data Fig. 4 Temperature-dependent phonon oscillation decay.
Phonon oscillations of device 3 at 77 K (a, b) and at 300 K (c, d) with similar pump fluences (300-400 μJ/cm2, lower than the saturation regime). Hann filters are used to remove the d.c. component. Note that the absolute pump fluences cannot be directly compared due to the different local field strengths at the FLG location at these two temperatures. The phonon amplitude lifetimes are calculated by the procedure described in section 4 of Supplementary Information.
Extended Data Fig. 5 Frequency-dependent phonon loss due to surface roughness.
a, For device 3 (WSe2/hBN/5LG, dhBN = 19.6 nm), the fraction of specular reflection after a round trip, \(p\), is plotted as a function of phonon frequency. The gray-filled circles are obtained from the Fourier analysis of phonon pulses. This behavior can be modeled by including both the intrinsic hBN phonon loss and an additional surface-roughness-induced loss. Based on the model described by J. M. Ziman38, the fraction of specular reflection can be expressed as \(p\left(\lambda \right)=\exp \left(-16{{\rm{\pi }}}^{3}{\eta }^{2}/{\lambda }^{2}\right)\), where \(\lambda \) is the phonon wavelength and \(\eta \) is the root-mean-square deviation of the interfacial height from a reference plane. The colored lines show calculated \(p\left(\lambda \right)\) with various \(\eta \) values. It indicates that the surface roughness is below 0.3 Å in device 3. b, For device 1 (WSe2/hBN/3LG, dhBN = 80.2 nm), the fraction of specular reflection after a round trip is plotted in gray-filled circles. The brown line shows the best-fit result with a roughness value of η = 0.91 Å.
Extended Data Fig. 6 1D nanomechanical simulation of devices 1, 3, and 4.
a, Phonon oscillation data (gray line) and the simulation result (brown line) using \({K}_{\text{gh}}=7.3\times {10}^{19}\,\text{N}\,{\text{m}}^{-3}\) and \({K}_{\text{hw}}=3.8\times {10}^{19}\,{\text{N m}}^{-3}\) for device 1. b, Phonon oscillation data (gray line) and the simulation result (brown line) using \({K}_{\text{gh}}=8.8\times {10}^{19}\,\text{N}\,{\text{m}}^{-3}\) and \({K}_{\text{hw}}=4.6\times {10}^{19}\,\text{N}\,{\text{m}}^{-3}\) for device 3. c, Phonon oscillation data (gray line) and the simulation result (brown line) using \({K}_{\text{gh}}=8.1\times {10}^{19}\,\text{N}\,{\text{m}}^{-3}\) and \({K}_{\text{hw}}=4.0\times {10}^{19}\,\text{N}\,{\text{m}}^{-3}\) for device 4. On average, the heterolayer force constant values are \({K}_{\text{gh}}=(8.1\pm 0.4)\times {10}^{19}\,\text{N}\,{\text{m}}^{-3}\) and \({K}_{\text{hw}}=(4.0\pm 0.3)\times {10}^{19}\,\text{N}\,{\text{m}}^{-3}\) across the three devices.
Extended Data Fig. 8 Simulated atomic structure of heterointerface.
a, Simulated atomic structure of the graphene-hBN heterobilayer. b, Simulated atomic structure of the hBN-WSe2 heterobilayer.
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Supplementary Information
Supplementary sections 1–6, Figs. 1–3, Tables 1–4 and references.
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Yoon, Y., Lu, Z., Uzundal, C. et al. Terahertz phonon engineering with van der Waals heterostructures. Nature (2024). https://doi.org/10.1038/s41586-024-07604-9
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DOI: https://doi.org/10.1038/s41586-024-07604-9
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