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Published November 15, 2023 | in press
Journal Article Open

Imaging inter-valley coherent order in magic-angle twisted trilayer graphene


Magic-angle twisted trilayer graphene (MATTG) exhibits a range of strongly correlated electronic phases that spontaneously break its underlying symmetries1,2. Here we investigate the correlated phases of MATTG using scanning tunnelling microscopy and identify marked signatures of interaction-driven spatial symmetry breaking. In low-strain samples, over a filling range of about two to three electrons or holes per moiré unit cell, we observe atomic-scale reconstruction of the graphene lattice that accompanies a correlated gap in the tunnelling spectrum. This short-scale restructuring appears as a Kekulé supercell—implying spontaneous inter-valley coherence between electrons—and persists in a wide range of magnetic fields and temperatures that coincide with the development of the gap. Large-scale maps covering several moiré unit cells further reveal a slow evolution of the Kekulé pattern, indicating that atomic-scale reconstruction coexists with translation symmetry breaking at a much longer moiré scale. We use auto-correlation and Fourier analyses to extract the intrinsic periodicity of these phases and find that they are consistent with the theoretically proposed incommensurate Kekulé spiral order3,4. Moreover, we find that the wavelength characterizing moiré-scale modulations monotonically decreases with hole doping away from half-filling of the bands and depends weakly on the magnetic field. Our results provide essential insights into the nature of the correlated phases of MATTG in the presence of strain and indicate that superconductivity can emerge from an inter-valley coherent parent state.

Copyright and License

© The Author(s), under exclusive licence to Springer Nature Limited 2023.


We thank N. Bultinck, S. Parameswaran, A. Pasupathy, A. Vishwanath, S. Todadri and A. Yazdani for the discussions. We are grateful in particular to T. Soejima and M. Zaletel for pointing out subtleties regarding the extraction of q_(IKS) through Fourier analysis. This work has been primarily supported by the National Science Foundation (grant no. DMR-2005129); the Office of Naval Research (grant no. N142112635); and the Army Research Office (grant award W911NF17-1-0323). S.N.-P. acknowledges support from the Sloan Foundation. J.A. and S.N.-P. also acknowledge support from the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation (grant no. GBMF1250); É.L.-H. and C.L. acknowledge support from the EPiQS Initiative of the Gordon and Betty Moore Foundation (grant no. GBMF8682) (at Caltech). C.L. acknowledges start-up funds from the Florida State University and the National High Magnetic Field Laboratory. The National High Magnetic Field Laboratory is supported by the National Science Foundation through NSF/DMR-1644779 and the state of Florida. A.T. and J.A. are grateful for the support of the Walter Burke Institute for Theoretical Physics at Caltech. H.K. acknowledges support from the Kwanjeong fellowship. L.K. acknowledges support from an IQIM-AWS Quantum postdoctoral fellowship. The primary support for sample fabrication efforts at UCSB was provided by the US Department of Energy (award no. DE-SC0020305). This work used facilities supported by the UC Santa Barbara NSF Quantum Foundry funded by the Q-AMASE-i programme under award DMR-1906325.


These authors contributed equally: Hyunjin Kim, Youngjoon Choi.

H.K. and Y.C. fabricated samples with the help of Y.Z., H.Z. and L.H. and performed STM measurements. H.K., Y.C. and S.N.-P. analysed the data with the help of L.K. and E.B. É.L.-H., C.L. and A.T. provided the theoretical analysis supervised by J.A. S.N.-P. supervised the project. K.W. and T.T. provided the hBN crystals and A.F.Y. supervised the device fabrication efforts. H.K., Y.C., É.L.-H., C.L., A.T., J.A. and S.N.-P. wrote the paper with input from other authors.

Data Availability

The raw data shown in the main figures are available at Zenodo (https://doi.org/10.5281/zenodo.8317363). Other data that support the findings of this study are available from the corresponding authors upon reasonable request.

Code Availability

The code that supports the findings of this study is available from the corresponding authors upon reasonable request.

Conflict of Interest

The authors declare no competing interests.


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Additional details

November 16, 2023
November 16, 2023