Abstract
Moiré superlattices have led to observations of exotic emergent electronic properties such as superconductivity and strong correlated states in small-rotation-angle twisted bilayer graphene (tBLG)1,2. Recently, these findings have inspired the search for new properties in moiré plasmons. Although plasmon propagation in the tBLG basal plane has been studied by near-field nano-imaging techniques3,4,5,6,7, the general electromagnetic character and properties of these plasmons remain elusive. Here we report the direct observation of two new plasmon modes in macroscopic tBLG with a highly ordered moiré superlattice. Using spiral structured nanoribbons of tBLG, we identify signatures of chiral plasmons that arise owing to the uncompensated Berry flux of the electron gas under optical pumping. The salient features of these chiral plasmons are shown through their dependence on optical pumping intensity and electron fillings, in conjunction with distinct resonance splitting and Faraday rotation coinciding with the spectral window of maximal Berry flux. Moreover, we also identify a slow plasmonic mode around 0.4 electronvolts, which stems from the interband transitions between the nested subbands in lattice-relaxed AB-stacked domains. This mode may open up opportunities for strong light–matter interactions within the highly sought after mid-wave infrared spectral window8. Our results unveil the new electromagnetic dynamics of small-angle tBLG and exemplify it as a unique quantum optical platform.
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Data availability
The data that support Figs. 1–5 and the Extended Data figures can be found in the source data. Source data are provided with this paper.
Code availability
The codes that were used in this study are available from the corresponding authors upon reasonable request.
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Acknowledgements
This project was primarily supported by the National Key R&D Program of China (2018YFA0307300, 2018YFA0209100 and 2017YFA0206301), the National Natural Science Foundation of China (61934004 and 62005119), the Program for High-Level Entrepreneurial and Innovative Talent Introduction of Jiangsu Province, the Strategic Priority Research Program of the Chinese Academy of Sciences (grant no. XDB30000000) and the Fundamental Research Funds for the Central Universities. X.L acknowledges the Shenzhen Science and Technology Program (No. (2021)105). L.S. acknowledges financial support from the National Natural Science Foundation of China (NSAF, U1930402) and computational resources from the Beijing Computational Science Research Center. We also thank the NJU micro-fabrication and integration centre for support.
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X.W. conceived the project. T.H., B.Z. and J.W. fabricated and measured the samples. X.T. carried out the electron beam lithography. C.S. and X.L. grew the graphene single crystals. H.W. and L.S. performed the FDTD calculations. K.K., S.H.P., T.L., Z.L., T.Y. and Z.Z. performed the band structure and random phase approximation calculation. B.Z. helped perform scanning electron microscopy and contributed to the data processing. X.W. and T.H. analysed the data and wrote the manuscript. X.W., Y.S., T.L. and X.L. supervised the research. All authors discussed the results obtained.
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Extended data figures and tables
Extended Data Fig. 1 Raman spectra of tBLG samples.
R’ peaks are observed in all samples from 0.8 to 21.8 degree.
Extended Data Fig. 2 Comparison between highly ordered and regular tBLGs.
a, Optical photo image of the 2.88°tBLG sample showing in Fig. 1b after nano-ribbon fabrication. b, Extinction spectra of the marked regions A (blue) B (red) C (green) D (yellow) in (a). c, Raman spectra of the marked regions A B C D in (a). The regions A and B (C and D) are regular (highly ordered) tBLG defined due to the absence (presence) of R’ Raman peak. The non-trivial plasmon mode can be only observed in samples with R’ peak, indicating the key roles played by ordered moiré superlattice.
Extended Data Fig. 3 Characterization of twisted bilayer graphene.
a, Optical microscope image of a tBLG sample after fabricating nanoribbons. The nano-ribbon region and fully etched background region are marked by dotted and dashed boxes, respectively. Scale bar 100 μm. b, c, Raman position (b) and area (c) mapping of 2D peak of the sample in (a).
Extended Data Fig. 4 Band structure and RPA calculation.
a, Calculated band structure of tBLG modeled by a continuum model. b, Corresponding low energy band structure in (a). The red, black and blue arrows indicate interband transition between multiple van Hove singularities with energy of 0.08 eV, 0.11 eV and 0.16 eV. c, d, Calculated longitude (c) and transverse (d) optical conductivity of tBLG. Grey and red curves represent imaginary and real part, respectively.
Extended Data Fig. 5 Plasmon mode in AB stacked bilayer graphene.
a, Extinction spectra of AB stacked bilayer graphene. Graphene flake is patterned to spiral nanoribbon arrays whose width ranges from 100 to 200 nm. The three branches of mid-energy plasmon are marked. The dashed lines indicate silica SO phonon and graphene optical phonon, respectively. b, Plasmon peak (peak 1 of the 200 nm sample) intensity as a function of the polarization detection angle. c, SEM image of a typical spiral nanoribbon made of AB stacked graphene. Scale bar 200 nm.
Extended Data Fig. 6 Schematic of experimental setup for magnetic field-free Faraday effect measurements.
The incident IR source is linearly polarized, aligning with the short axes of the spiral ribbons, and a polarization analyzer is placed in front of the detector. Measuring the transmitted signal intensity while rotating the analyzer thus allows us to determine the polarization rotation.
Extended Data Fig. 7 Extinction spectra of CBP in counter clockwise and clockwise spiral ribbons.
Opposite Faraday rotation angles are observed due to the Berry curvature is opposite for K and K’ valleys. Switching the sign of valley polarization by mirroring the spiral direction should reverse the sign of Faraday rotation.
Extended Data Fig. 8 Loss function calculation with Fermi energy at 0.05 eV (n = 2 × 1012 cm−2).
The dotted black line illustrates the quasi-flat dispersion of γ-mode.
Extended Data Fig. 9 Plasmon mode in 7.3° tBLG.
a, Extinction spectra of tBLG ribbons on SiO2 substrate with different ribbon widths. b, Enlarged extinction spectra of tBLG ribbons in the black dashed box. Blue curves are measured results. Red chain lines are best Fano fitting curves. c, Plasmon frequency as a function of wave vector for peaks in (a). The results show damped γ-mode.
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Huang, T., Tu, X., Shen, C. et al. Observation of chiral and slow plasmons in twisted bilayer graphene. Nature 605, 63–68 (2022). https://doi.org/10.1038/s41586-022-04520-8
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DOI: https://doi.org/10.1038/s41586-022-04520-8
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