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Efficient Fizeau drag from Dirac electrons in monolayer graphene


Fizeau demonstrated in 1850 that the speed of light can be modified when it is propagating in moving media1. However, such control of the light speed has not been achieved efficiently with a fast-moving electron media by passing an electrical current. Because the strong electromagnetic coupling between the electron and light leads to the collective excitation of plasmon polaritons, it is hypothesized that Fizeau drag in electron flow systems manifests as a plasmonic Doppler effect. Experimental observation of the plasmonic Doppler effect in electronic systems has been challenge because the plasmon propagation speed is much faster than the electron drift velocity in conventional noble metals. Here we report direct observation of Fizeau drag of plasmon polaritons in strongly biased monolayer graphene by exploiting the high electron mobility and the slow plasmon propagation of massless Dirac electrons. The large bias current in graphene creates a fast-drifting Dirac electron medium hosting the plasmon polariton. This results in non-reciprocal plasmon propagation, where plasmons moving with the drifting electron media propagate at an enhanced speed. We measure the Doppler-shifted plasmon wavelength using cryogenic near-field infrared nanoscopy, which directly images the plasmon polariton mode in the biased graphene at low temperature. We observe a plasmon wavelength difference of up to 3.6 per cent between a plasmon moving with and a plasmon moving against the drifting electron media. Our findings on the plasmonic Doppler effect provide opportunities for electrical control of non-reciprocal surface plasmon polaritons in non-equilibrium systems.

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Fig. 1: Schematic view of the Doppler effect in a graphene device.
Fig. 2: Near-field signal of the propagating plasmons under different driving currents.
Fig. 3: Gating dependence of graphene plasmon wavelength.
Fig. 4: Graphene plasmon dispersion and Doppler-induced wavelength shift.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.


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The device fabrication and characterization and theoretical analysis of the work is supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division of the US Department of Energy under contract number DE-AC02-05CH11231 (sp2-Bonded Materials Program KC2207). The cryogenic near-field nanoscopy measurement was supported by the NSF award 1808635. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST.

Author information

Authors and Affiliations



F.W. conceived the research. W.Z. and S.Z. carried out the near-field optical measurements. W.Z., S.Z., Sheng Wang, S.Y. and F.W. performed the data analysis. W.Z., S.Z., H.L., Shaoxin Wang, M.I.B.U, S.K., Y.J. and X.X. fabricated the graphene devices. K.W. and T.T. grew the hexagonal boron nitride crystals. All authors discussed the results and wrote the manuscript.

Corresponding author

Correspondence to Feng Wang.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Jiahua Duan, Joel Cox and Hugen Yan for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Graphene channel current at discrete bias voltages in the two-terminal device.

Measurements taken at 25 K at a carrier density of 7.0 × 1012 cm−2.

Extended Data Fig. 2 Near-field signal of the propagating plasmon on the left side of the gold nanobar.

a, b, Illustration of plasmon propagation under negative (a) and positive (b) current flows. c, e, g, Near-field data at −0.4 mA and + 0.4 mA (c), −1.2 mA and + 1.2 mA (e) and −1.9 mA and +1.7 mA (g). d, f, h, The corresponding line profiles for c, e, g, respectively, averaged over the 30 scans. The gold nanobar is located on the right and the graphene plasmons propagate from the right to the left.

Extended Data Fig. 3 Near-field signal of the propagating plasmon on the right side of the gold nanobar.

a, b, Illustration of plasmon propagation under negative (a) and positive (b) current flows. c, e, Near-field data at −0.4 mA and +0.4 mA (c) and −1.2 mA and +1.2 mA (e). d, f, The corresponding line profiles c, e, respectively, averaged over the 30 scans. The gold nanobar is located on the left and the graphene plasmons propagate from the left to the right.

Extended Data Fig. 4 Comparison of the Doppler effect between theory and experiment at different carrier drift velocities in the second device.

The width of the graphene channel is w = 2.5 μm and the carrier density is estimated to be |n| = 7.0 × 1012 cm−2.

Extended Data Fig. 5 Breakdown of device under high positive backgate voltages.

The ultrahigh backgate voltage at the positive side triggers a series of gas ionization in high vacuum and damages the sample.

Extended Data Fig. 6 Filtered optical image to enhance the contrast between hBN and graphene.

The alignment angle between the hBN and graphene is around 0.93° and corresponds to a moiré period of around 10.3 nm, which is calculated from the carrier density (ns ≈ 3.98 × 1012 cm−2) at the small resistance peak in our device.The white line indicates the straight graphene edge and the yellow line shows the top hBN edge.

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Zhao, W., Zhao, S., Li, H. et al. Efficient Fizeau drag from Dirac electrons in monolayer graphene. Nature 594, 517–521 (2021).

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