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Observation of interband collective excitations in twisted bilayer graphene

Abstract

The single-particle and many-body properties of twisted bilayer graphene (TBG) can be dramatically different from those of a single graphene layer, particularly when the two layers are rotated relative to each other by a small angle (θ ≈ 1°), owing to the moiré potential induced by the twist. Here we probe the collective excitations of TBG with a spatial resolution of 20 nm, by applying mid-infrared near-field optical microscopy. We find a propagating plasmon mode in charge-neutral TBG for θ = 1.1−1.7°, which is different from the intraband plasmon in single-layer graphene. We interpret it as an interband plasmon associated with the optical transitions between minibands originating from the moiré superlattice. The details of the plasmon dispersion are directly related to the motion of electrons in the moiré superlattice and offer an insight into the physical properties of TBG, such as band nesting between the flat band and remote band, local interlayer coupling, and losses. We find a strongly reduced interlayer coupling in the regions with AA stacking, pointing at screening due to electron–electron interactions. Optical nano-imaging of TBG allows the spatial probing of interaction effects at the nanoscale and potentially elucidates the contribution of collective excitations to many-body ground states.

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Fig. 1: Collective excitations in TBG.
Fig. 2: Controlling the wavelength of interband plasmons.
Fig. 3: Extracting the optical conductivity from the plasmon dispersion.
Fig. 4: Electronic band structure and optical conductivity of TBG for θ = 1.35°.
Fig. 5: Calculated properties of the relevant interband transition as functions of tunnelling amplitude in the AA regions.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank F. Vialla for providing the illustration in Fig. 1a. We acknowledge A. H. MacDonald, F. Guinea, T. Stauber, F. Mauri, R. K. Kumar and A. Tomadin for useful discussions. F.H.L.K. acknowledges support from the ERC TOPONANOP (grant agreement no. 726001), the government of Spain (PID2019-106875GB-I00; Severo Ochoa CEX2019-000910-S), Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya (CERCA, AGAUR, SGR 1656). Furthermore, the research leading to these results has received funding from the European Union’s Horizon 2020 under grant agreement no. 881603 (Graphene flagship Core3). N.C.H.H., I.T., P.S., D.B.-R., H.H.S., D.K.E. and F.H.L.K. acknowledge financial support from the Spanish Ministry of Economy and Competitiveness through the ‘Severo Ochoa’ program for Centres of Excellence in R&D (SEV-2015-0522), from Fundació Privada Cellex and Fundació Privada Mir-Puig, and from Generalitat de Catalunya through the CERCA program. N.C.H.H. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 665884. I.T. acknowledges funding from the Spanish Ministry of Science, Innovation and Universities (MCIU) and State Research Agency (AEI) via the Juan de la Cierva fellowship no. FJC2018-037098-I. D.B.-R. acknowledges funding from the ‘Secretaria d’Universitats i Recerca de la Generalitat de Catalunya i del Fons Social Europeu’. H.H.S. acknowledges funding under the Marie Skłodowska-Curie grant agreement no. 843830. D.K.E. acknowledges support from the Horizon 2020 programme under grant agreement no. 820378, Project 2D·SIPC and the La Caixa Foundation. P.N. and M.P. have been supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 785219, GrapheneCore2. Work at MIT has been primarily supported by the National Science Foundation (award DMR-1809802), the Center for Integrated Quantum Materials under NSF grant DMR-1231319, and the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF9643 to P.J.-H. for device fabrication, transport measurements and data analysis. This work was performed in part at the Harvard University Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Coordinated Infrastructure Network (NNCI), which is supported by the National Science Foundation under NSF ECCS award no. 1541959. D.R.-L. acknowledges partial support from Fundacio Bancaria ‘la Caixa’ (LCF/BQ/AN15/10380011). S.F. was supported by the STC Center for Integrated Quantum Materials, NSF grant no. DMR-1231319. S.C. and E.K. were supported by ARO MURI Award W911NF-14-0247. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, and the CREST (JPMJCR15F3), JST.

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Contributions

F.H.L.K. and P.J.-H. designed the experiment. N.C.H.H. performed the near-field measurements with assistance from D.B.-R. and H.H.S. D.R.-L., Y.C. and P.S. fabricated the devices and performed transport measurements under the supervision of P.J.-H. and D.K.E. N.C.H.H. and I.T. performed the data analysis. I.T. and P.N. developed the theory part with inputs from M.P. and F.H.L.K. S.C. and S.F. provided the band structures based on ab initio k·p perturbation theory under the supervision of E.K. K.W. and T.T. provided the hBN crystals. F.H.L.K., M.P. and P.J.-H. supervised the project. I.T., N.C.H.H., M.P. and F.H.L.K. wrote the manuscript with input from all the authors.

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Correspondence to Pablo Jarillo-Herrero, Marco Polini or Frank H. L. Koppens.

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Supplementary Information

Supplementary Notes 1–11.

Source data

Source Data Fig. 2

All non-analytical elements in Fig. 2g.

Source Data Fig. 3

All non-analytical elements in Fig. 3b,c.

Source Data Fig. 4

All non-analytical elements in Fig. 4.

Source Data Fig. 5

All non-analytical elements in Fig. 5.

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Hesp, N.C.H., Torre, I., Rodan-Legrain, D. et al. Observation of interband collective excitations in twisted bilayer graphene. Nat. Phys. 17, 1162–1168 (2021). https://doi.org/10.1038/s41567-021-01327-8

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