Abstract
Graphene moiré superlattices display electronic flat bands. At integer fillings of these flat bands, energy gaps due to strong electron–electron interactions are generally observed. However, the presence of other correlation-driven phases in twisted graphitic systems at non-integer fillings is unclear. Here, we report the existence of three-fold rotational (C3) symmetry breaking in twisted double bilayer graphene. Using spectroscopic imaging over large and uniform areas to characterize the direction and degree of C3 symmetry breaking, we find it to be prominent only at energies corresponding to the flat bands and nearly absent in the remote bands. We demonstrate that the magnitude of the rotational symmetry breaking does not depend on the degree of the heterostrain or the displacement field, being instead a manifestation of an interaction-driven electronic nematic phase. We show that the nematic phase is a primary order that arises from the normal metal state over a wide range of doping away from charge neutrality. Our modelling suggests that the nematic instability is not associated with the local scale of the graphene lattice, but is an emergent phenomenon at the scale of the moiré lattice.
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Data availability
All data that support the plots in this paper are available from the corresponding author upon reasonable request. Source data are provided with this paper.
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All relevant source code is available from the corresponding author upon reasonable request.
References
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).
Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys. 15, 1174–1180 (2019).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Urgell, C., Watanabe, K., Taniguchi, T., Zhang, G. & Bachtold, A. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 20–23 (2019).
Jiang, Y. et al. Charge order and broken rotational symmetry in magic-angle twisted bilayer graphene. Nature 573, 91–95 (2019).
Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).
Liu, X. et al. Spin-polarized correlated insulator and superconductor in twisted double bilayer graphene. Nature 583, 221–225 (2020).
Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature https://doi.org/10.1038/s41586-020-2260-6 (2020).
He, M. et al. Tunable correlation-driven symmetry breaking in twisted double bilayer graphene. Nat. Phys. 17, 26–30 (2021).
Liu, X. et al. Spectroscopy of a tunable moiré system with a correlated and topological flat band. Nat. Commun. 12, 2732 (2021).
Zhang, C. et al. Visualizing delocalized correlated electronic states in twisted double bilayer graphene. Nat. Commun. 12, 2516 (2021).
Chen, G. et al. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 572, 215–219 (2019).
Lyu, B. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Williams, R. Liquid crystals in an electric field. Nature 199, 273–274 (1963).
Fradkin, E., Kivelson, S. A., Lawler, M. J. & Mackenzie, A. P. Nematic Fermi fluids in condensed matter physics. Annu. Rev. Condens. Matter Phys. 1, 153–178 (2010).
Fernandes, R. M., Chubukov, A. V. & Schmalian, J. What drives nematic order in iron-based superconductors? Nat. Phys. 10, 97–104 (2014).
Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).
Kerelsky, A. et al. Moiréless correlations in ABCA graphene. Proc. Natl Acad. Sci. USA 118, e2017366118 (2020).
Edelberg, D., Kumar, H., Shenoy, V., Ochoa, H. & Pasupathy, A. N. Tunable strain soliton networks confine electrons in van der Waals materials. Nat. Phys. 16, 1097–1102 (2020).
Haddadi, F., Wu, Q., Kruchkov, A. J. & Yazyev, O. V. Moiré flat bands in twisted double bilayer graphene. Nano Lett. 20, 2410–2415 (2020).
Koshino, M. Band structure and topological properties of twisted double bilayer graphene. Phys. Rev. B 99, 235406 (2019).
Samajdar, R. & Scheurer, M. S. Microscopic pairing mechanism, order parameter, and disorder sensitivity in moiré superlattices: applications to twisted double-bilayer graphene. Phys. Rev. B 102, 064501 (2020).
Yankowitz, M. et al. Band structure mapping of bilayer graphene via quasiparticle scattering quasiparticle scattering. APL Mater. 2, 092503 (2014).
Fernandes, R. M. & Venderbos, J. W. F. Nematicity with a twist: rotational symmetry breaking in a moiré superlattice. Sci. Adv. 6, eaba8834 (2020).
Bi, Z., Yuan, N. F. Q. & Fu, L. Designing flat bands by strain. Phys. Rev. B 100, 035448 (2019).
Scheurer, M. S. & Samajdar, R. Pairing in graphene-based moiré superlattices. Phys. Rev. Res. 2, 033062 (2020).
Venderbos, J. W. F. & Fernandes, R. M. Correlations and electronic order in a two-orbital honeycomb lattice model for twisted bilayer graphene. Phys. Rev. B 98, 245103 (2018).
Dodaro, J. F., Kivelson, S. A., Schattner, Y., Sun, X. Q. & Wang, C. Phases of a phenomenological model of twisted bilayer graphene. Phys. Rev. B 98, 075154 (2018).
Isobe, H., Yuan, N. F. Q. & Fu, L. Unconventional superconductivity and density waves In twisted bilayer graphene. Phys. Rev. X 8, 041041 (2018).
Kozii, V., Isobe, H., Venderbos, J. W. F. & Fu, L. Nematic superconductivity stabilized by density wave fluctuations: possible application to twisted bilayer graphene. Phys. Rev. B 99, 144507 (2019).
Chichinadze, D. V., Classen, L. & Chubukov, A. V. Nematic superconductivity in twisted bilayer graphene. Phys. Rev. B 101, 224513 (2020).
Kennes, D. M., Lischner, J. & Karrasch, C. Strong correlations and d + id superconductivity in twisted bilayer graphene. Phys. Rev. B 98, 241407 (2018).
Soejim, T., Parker, D. E., Bultinck, N., Hauschild, J. & Zaletel, M. P. Efficient simulation of moire materials using the density matrix renormalization group. Phys. Rev. B 102, 205111 (2020).
Kang, J. & Vafek, O. Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer fillingin magic-angle twisted bilayer graphene. Phys. Rev. B 102, 035161 (2020).
Samajdar, R. et al. Electric-field-tunable electronic nematic order in twisted double-bilayer graphene. 2D Mater. 8, 3 (2021).
Klebl, L., Kennes, D. M. & Honerkamp, C. Functional renormalization group for a large moiré unit cell. Phys. Rev. B 102, 085109 (2020).
Girit, Ç. Ö. & Zettl, A. Soldering to a single atomic layer. Appl. Phys. Lett. 91, 193512 (2007).
Acknowledgements
S.T. and A.N.P. acknowledge funding from Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award no. DE-SC0019443. STM equipment support (A.N.P.) and 2D sample synthesis (Y.S.) were provided by the Air Force Office of Scientific Research via grant no. FA9550-16-1-0601. C.R.-V. acknowledges funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie grant agreement no. 844271. A.R. acknowledges funding by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT1249-19) and the Flatiron Institute, a division of the Simons Foundation. L.K., D.M.K. and A.R. acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) under Germany’s Excellence Strategy-Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1-390534769 and Advanced Imaging of Matter (AIM) EXC 2056−390715994 and funding by the Deutsche Forschungsgemeinschaft (DFG) under RTG 1995, within the Priority Program SPP 2244 ‘2DMP’ and GRK 2247. A.R. acknowledges support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. H.O. is supported by the NSF MRSEC programme grant no. DMR-1420634. Tight-binding and fRG simulations were performed with computing resources granted by RWTH Aachen University under projects rwth0496 and rwth0589. R.S. and M.S.S. acknowledge support from the National Science Foundation under grant no. DMR-2002850. R.M.F. was supported by the DOE-BES under award no. DE-SC0020045. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001), JSPS KAKENHI (grant no. JP20H00354) and the CREST (grant no. JPMJCR15F3) JST.
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C.R.-V. and S.T. performed the STM measurements. Y.S. fabricated the samples for STM measurements. C.R.-V. and S.T. performed experimental data analysis. K.W. and T.T. provided hBN crystals. L.K., L.X. and D.M.K. performed tight-binding calculations. S.T., R.S., M.S.S., J.W.F.V., H.O. and R.M.F. performed continuum-model calculations. R.M.F., A.R. and A.N.P. gave advice. C.R.-V. and S.T. wrote the manuscript with assistance from all authors.
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Rubio-Verdú, C., Turkel, S., Song, Y. et al. Moiré nematic phase in twisted double bilayer graphene. Nat. Phys. 18, 196–202 (2022). https://doi.org/10.1038/s41567-021-01438-2
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DOI: https://doi.org/10.1038/s41567-021-01438-2
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