Abstract
Thermally excited electrons and holes form a quantum-critical Dirac fluid in ultraclean graphene and their electrodynamic responses are described by a universal hydrodynamic theory. The hydrodynamic Dirac fluid can host intriguing collective excitations distinctively different from those in a Fermi liquid1,2,3,4. Here we report the observation of the hydrodynamic plasmon and energy wave in ultraclean graphene. We use the on-chip terahertz (THz) spectroscopy technique to measure the THz absorption spectra of a graphene microribbon as well as the propagation of the energy wave in graphene close to charge neutrality. We observe a prominent high-frequency hydrodynamic bipolar-plasmon resonance and a weaker low-frequency energy-wave resonance of the Dirac fluid in ultraclean graphene. The hydrodynamic bipolar plasmon is characterized by the antiphase oscillation of massless electrons and holes in graphene. The hydrodynamic energy wave is an electron-hole sound mode with both charge carriers oscillating in phase and moving together. The spatial–temporal imaging technique shows that the energy wave propagates at a characteristic speed of \({V}_{{\rm{F}}}/\sqrt{{\rm{2}}}\) near the charge neutrality2,3,4. Our observations open new opportunities to explore collective hydrodynamic excitations in graphene systems.
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The data that support the findings of this study are available from the corresponding author on request. Source data are provided with this paper.
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Acknowledgements
The on-chip terahertz spectroscopy and theoretical analysis of the work was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division under contract number DE-AC02-05CH11231 within the vdW heterostructure Program (KCWF16). The device fabrication is supported by the Army Research Office award W911NF2110176. S.C. acknowledges support from Kavli ENSI Heising-Simons Junior Fellowship. K.W. and T.T. acknowledge support from the Element Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST.
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F.W. conceived the research. W.Z. carried out the on-chip THz measurements. S.W. and Z.Z. fabricated the graphene devices. W.Z., S.W., S.C. and F.W. performed the data analysis. K.W. and T.T. grew the hBN crystals. F.W., W.Z., S.C. and A.Z. wrote the manuscript.
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Extended data figures and tables
Extended Data Fig. 1 On-chip THz spectroscopy on graphene microribbon.
a, Optical micrograph of the device close to the sample region. b, Cross-sectional schematics of the sample under study. The graphene microribbon of 2 μm width and 20 μm length is encapsulated by hBN flakes. The doping level of the microribbon is controlled through a few-layer MoS2 back gate for its minimal absorption in the THz frequency range. c, Illustration of the collective motion of electrons and holes in hydrodynamic bipolar plasmon and demon.
Extended Data Fig. 2 Optical micrograph of the graphene microribbon device for hydrodynamic plasmon and demon measurements.
The waveguide consists of two parallel gold traces of 20 μm width separated by a 15-μm gap. The gap is tapered and narrowed down near the sample to enhance the sample–waveguide coupling.
Extended Data Fig. 3 Temperature difference of the absorption spectra, \({{\boldsymbol{A}}}_{{{\boldsymbol{V}}}_{{\bf{G}}},{{\boldsymbol{T}}}_{{\bf{e}}}}\,-{{\boldsymbol{A}}}_{{{\boldsymbol{V}}}_{{\bf{G}}},{{\boldsymbol{T}}}_{{\bf{0}}}}\), obtained by the double-modulation measurement.
The absorption shows a symmetric profile with respect to VG = −0.1 V, the back-gate voltage associated with the charge-neutrality point.
Extended Data Fig. 4 Determination of ACNP and background subtraction for the absorption spectra.
a, The measured spectrum (solid curve) is fitted to a two-Lorentzian model, in which L1 and L2 represent the fitted absorption spectra at the charge-neutrality point and VG, respectively. b, The global background absorption spectra obtained by averaging the fitted ACNP over a broad range of gate voltages from 0.1 V to 0.8 V. c, Measured \({{A}_{{V}_{{\rm{G}}}}-A}_{{\rm{CNP}}}\) at various gate voltages. d, \({A}_{{V}_{{\rm{G}}}}\) obtained by subtracting the global absorption background associated with ACNP.
Extended Data Fig. 5 Field response of the nanogap.
Schematic top view (a) and side view (b) of the model used in the FDTD simulations. c, Field amplitude collected at the monitor position. d, Linecut of the field amplitude at 0.1 THz.
Extended Data Fig. 6 Linear fit of the phase term along the propagation direction for different carrier densities.
From top to bottom, the frequency changes from 0.03 THz to 0.1 THz. q(f) corresponds to the phase-accumulation slope.
Extended Data Fig. 7 Exponential fit of the amplitude decay, q′(f), along the propagation direction at different carrier densities.
The y axis is plotted in logarithmic scale.
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Zhao, W., Wang, S., Chen, S. et al. Observation of hydrodynamic plasmons and energy waves in graphene. Nature 614, 688–693 (2023). https://doi.org/10.1038/s41586-022-05619-8
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DOI: https://doi.org/10.1038/s41586-022-05619-8
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