Abstract
The recent discovery of superconductivity and magnetism in trilayer rhombohedral graphene (RG) establishes an ideal, untwisted platform to study strong correlation electronic phenomena. However, the correlated effects in multilayer RG have received limited attention, and, particularly, the evolution of the correlations with increasing layer number remains an unresolved question. Here we show the observation of layer-dependent electronic structures and correlations—under surprising liquid nitrogen temperature—in RG multilayers from 3 to 9 layers by using scanning tunnelling microscopy and spectroscopy. We explicitly determine layer-enhanced low-energy flat bands and interlayer coupling strengths. The former directly demonstrates the further flattening of low-energy bands in thicker RG, and the latter indicates the presence of varying interlayer interactions in RG multilayers. Moreover, we find significant splittings of the flat bands, ranging from ~50 meV to 80 meV, at 77 K when they are partially filled, indicating the emergence of interaction-induced strongly correlated states. Particularly, the strength of the correlated states is notably enhanced in thicker RG and reaches its maximum in the six-layer, validating directly theoretical predictions and establishing abundant new candidates for strongly correlated systems. Our results provide valuable insights into the layer dependence of the electronic properties in RG and demonstrate it as a suitable system for investigating robust and highly accessible correlated phases.
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Data availability
The data that support the findings of this study are available within the article and its Supplementary Information. Any other relevant data are available from the corresponding authors upon reasonable request.
Code availability
The code used for the modelling in this work is available from the corresponding authors upon reasonable request.
References
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Liu, X. et al. Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature 583, 221–225 (2020).
Hao, Z. et al. Electric field-tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science 371, 1133–1138 (2021).
Tong, L.-H. et al. Spectroscopic visualization of flat bands in magic-angle twisted monolayer–bilayer graphene: coexistence of localization and delocalization. Phys. Rev. Lett. 128, 126401 (2022).
Bistritzer, R. & MacDonald, A. H. Moire bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020).
Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).
Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).
Xu, S. et al. Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 619–626 (2021).
Chen, S. et al. Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene. Nat. Phys. 16, 520–525 (2020).
Chen, G. et al. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 572, 215–219 (2019).
Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Yang, J. et al. Spectroscopy signatures of electron correlations in a trilayer graphene/hBN moiré superlattice. Science 375, 6586 (2022).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Olsen, R., van Gelderen, R. & Smith, C. M. Ferromagnetism in ABC-stacked trilayer graphene. Phys. Rev. B 87, 115414 (2013).
Kopnin, N. B., Ijäs, M., Harju, A. & Heikkilä, T. T. High-temperature surface superconductivity in rhombohedral graphite. Phys. Rev. B 87, 140503(R) (2013).
Wang, H., Gao, J.-H. & Zhang, F.-C. Flat band electrons and interactions in rhombohedral trilayer graphene. Phys. Rev. B 87, 155116 (2013).
Pierucci, D. et al. Evidence for flat bands near the Fermi level in epitaxial rhombohedral multilayer graphene. ACS Nano 9, 5432–5439 (2015).
Henck, H. et al. Flat electronic bands in long sequences of rhombohedral-stacked graphene. Phys. Rev. B 97, 245421 (2018).
Zhang, F., Sahu, B., Min, H. & MacDonald, A. H. Band structure of ABC-stacked graphene trilayers. Phys. Rev. B 82, 035409 (2010).
Muten, J. H., Copeland, A. J. & McCann, E. Exchange interaction, disorder, and stacking faults in rhombohedral graphene multilayers. Phys. Rev. B 104, 035404 (2021).
Pamuk, B., Baima, J., Mauri, F. & Calandra, M. Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles. Phys. Rev. B 95, 075422 (2017).
Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F. Superconductivity in rhombohedral trilayer graphene. Nature 598, 434–438 (2021).
Zhou, H. et al. Half- and quarter-metals in rhombohedral trilayer graphene. Nature 598, 429–433 (2021).
Hagymási, I. et al. Observation of competing, correlated ground states in the flat band of rhombohedral graphite. Sci. Adv. 8, eabo6879 (2022).
Kerelsky, A. et al. Moiréless correlations in ABCA graphene. Proc. Natl Acad. Sci. USA 118, e2017366118 (2021).
Lee, Y. et al. Gate-tunable magnetism and giant magnetoresistance in suspended rhombohedral-stacked few-layer graphene. Nano Lett. 22, 5094–5099 (2022).
Liu, K. et al. Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene. Nat. Nanotechnol. 19, 188–195 (2023).
Han, T. et al. Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene. Nat. Nanotechnol. 19, 181–187 (2023).
Yin, L.-J. et al. High-magnetic-field tunneling spectra of ABC-stacked trilayer graphene on graphite. Phys. Rev. Lett. 122, 146802 (2019).
Yin, L.-J. et al. Observation of chirality transition of quasiparticles at stacking solitons in trilayer graphene. Phys. Rev. B 95, 081402(R) (2017).
Xu, R. et al. Direct probing of the stacking order and electronic spectrum of rhombohedral trilayer graphene with scanning tunneling microscopy. Phys. Rev. B 91, 035410 (2015).
Yin, L.-J. et al. Imaging of nearly flat band induced atomic-scale negative differential conductivity in ABC-stacked trilayer graphene. Phys. Rev. B 102, 241403(R) (2020).
Yin, L.-J. et al. Imaging Friedel oscillations in rhombohedral trilayer graphene. Phys. Rev. B 107, L041404 (2023).
Slizovskiy, S., McCann, E., Koshino, M. & Fal’ko, V. I. Films of rhombohedral graphite as two-dimensional topological semimetals. Commun. Phys. 2, 164 (2019).
McCann, E. & Koshino, M. The electronic properties of bilayer graphene. Rep. Prog. Phys. 76, 056503 (2013).
Sun, D. et al. Spectroscopic measurement of interlayer screening in multilayer epitaxial graphene. Phys. Rev. Lett. 104, 136802 (2010).
Ohta, T. et al. Interlayer interaction and electronic screening in multilayer graphene investigated with angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 98, 206802 (2007).
Ohta, T., Bostwick, A., Seyller, T., Horn, K. & Rotenberg, E. Controlling the electronic structure of bilayer graphene. Science 313, 951–954 (2006).
Ghahari, F. et al. An on/off Berry phase switch in circular graphene resonators. Science 356, 845–849 (2017).
Zhang, J., Jiang, Y.-P., Ma, X.-C. & Xue, Q.-K. Berry-phase switch in electrostatically confined topological surface states. Phys. Rev. Lett. 128, 126402 (2022).
Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).
Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).
Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019).
Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174–1180 (2019).
Shi, Y. et al. Electronic phase separation in multilayer rhombohedral graphite. Nature 584, 210–214 (2020).
Lee, Y. et al. Competition between spontaneous symmetry breaking and single-particle gaps in trilayer graphene. Nat. Commun. 5, 5656 (2014).
Myhro, K. et al. Large tunable intrinsic gap in rhombohedral-stacked tetralayer graphene at half filling. 2D Mater. 5, 045013 (2018).
Huang, C. et al. Spin and orbital metallic magnetism in rhombohedral trilayer graphene. Phys. Rev. B 107, L121405 (2023).
Acknowledgements
This work was supported by the National Natural Science Foundation of China (grant numbers 12174095 (L.-J.Y.), 12174096 (Z.Q.), 62101185 (Y.T.), 12204164 (Li Zhang), 12304217 (S.Z.), 11904076 (W.-X.W.), 12474166 (L.-J.Y.), 12425405 (L.H.), 12404198 (Y.-N.R.) and 51972106 (Lijie Zhang)), the Natural Science Foundation of Hunan Province, China (grant number 2021JJ20026 (L.-J.Y.)), and the Strategic Priority Research Program of Chinese Academy of Sciences (grant number XDB30000000 (Z.Q.)). L.-J.Y. also acknowledges support from the Science and Technology Innovation Program of Hunan Province, China (grant number 2021RC3037), and the Natural Science Foundation of Chongqing, China (cstc2021jcyj-msxmX0381). We acknowledge the financial support from the Fundamental Research Funds for the Central Universities of China.
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Y.Z. and Y.-Y.Z. fabricated the samples with the help of W.-Y.L., R.-J.Z. and S.-M.X. Y.Z., Y.-Y.Z. and L.-H.T. conducted the electrode fabrications and AFM characterizations with the help of Y.T., Y.W., X.Z., X.L., Y.H. and L.L. Y.Z., Y.-Y.Z. and L.-J.Y. performed the STM experiments and analysed the data. T.C., Q.T., C.Z., Y.-N.R., Li Zhang, Lijie Zhang and L.H. assisted with STM measurements. S.Z. performed the mean-field calculations. H.C. performed the tight-binding calculations. W.-X.W., Z.Q. and L.-J.Y. supervised the experiments. L.-J.Y. designed the project. Y.Z., Y.-Y.Z., S.Z. and L.-J.Y. wrote the paper with inputs from all the other authors.
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Zhang, Y., Zhou, YY., Zhang, S. et al. Layer-dependent evolution of electronic structures and correlations in rhombohedral multilayer graphene. Nat. Nanotechnol. 20, 222–228 (2025). https://doi.org/10.1038/s41565-024-01822-y
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DOI: https://doi.org/10.1038/s41565-024-01822-y