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Moiré nematic phase in twisted double bilayer graphene

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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Fig. 1: LDOS in twisted double bilayer graphene.
Fig. 2: Broken C3 symmetry.
Fig. 3: Manifestations of long-range nematic order in TDBG.
Fig. 4: Moiré nematic order.

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.

Code availability

All relevant source code is available from the corresponding author upon reasonable request.

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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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Authors

Contributions

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.

Corresponding author

Correspondence to Abhay N. Pasupathy.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Guy Trambly de Laissardière and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–8 and Discussion.

Source data

Source Data Fig. 1

Source data for plots in Fig. 1c–e.

Source Data Fig. 2

Source data for plots in Fig. 2c,d.

Source Data Fig. 3

Source data for plots in Fig. 3c,d.

Source Data Fig. 4

Source data for plots in Fig. 4e.

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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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