Strong correlations and superconductivity in the supermoiré lattice

Nature Physics (2026)Cite this article The supermoiré lattice, arising from the interference of multiple moiré patterns, reshapes the electronic band structure of the material that hosts it by introducing new mini bands and modifying the band dispersion. Concurrently, strong electronic interactions within the flat bands induced by the moiré pattern lead to the emergence of various correlated states. However, the impact of the supermoiré lattice on the flat band system with strong interactions remains largely unexplored. Here we report the existence of the supermoiré lattice in twisted trilayer graphene with broken mirror symmetry and elucidate its role in generating mini flat bands and mini Dirac bands. We demonstrate interaction-induced symmetry-broken phases in the supermoiré mini flat bands alongside a cascade of superconductor–insulator transitions enabled by the supermoiré lattice. Our work shows that robust superconductivity can exist in twisted trilayer graphene with broken mirror symmetry and underscores the importance of the supermoiré lattice as an additional degree of freedom for tuning the electronic properties in twisted multilayer systems. It also sheds light on the correlated quantum phases such as superconductivity in the original moiré flat bands, and highlights the potential of using the supermoiré lattice to design and simulate quantum phases.This is a preview of subscription content, access via your institution Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription $32.99 / 30 days cancel any timeSubscribe to this journal Receive 12 print issues and online access $259.00 per yearonly $21.58 per issueBuy this articleUSD 39.95Prices may be subject to local taxes which are calculated during checkoutSource data are provided with this paper. These data are also available via Zenodo at https://doi.org/10.5281/zenodo.17403996 (ref. 41). All other data that support the findings of this study are available from the corresponding author upon request.Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).Article ADS Google Scholar Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).Article ADS Google Scholar Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).Article ADS Google Scholar Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).Article Google Scholar Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).Article ADS Google Scholar Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).Article ADS Google Scholar Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).Article ADS Google Scholar Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).Article ADS Google Scholar Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).Article ADS Google Scholar Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).Article ADS Google Scholar Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).Article ADS Google Scholar Zhu, Z. et al. Twisted trilayer graphene: a precisely tunable platform for correlated electrons. Phys. Rev. Lett. 125, 116404 (2020).Article ADS Google Scholar Nakatsuji, N., Kawakami, T. & Koshino, M. Multiscale lattice relaxation in general twisted trilayer graphenes. Phys. Rev. X 13, 041007 (2023).

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The National High Magnetic Field Laboratory is supported by the National Science Foundation through NSF/DMR-2128556 and the State of Florida. M.B. acknowledges support from SNSF Eccellenza grant number PCEGP2_194528, and support from the QuantERA II Programme that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement number 101017733. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant numbers 20H00354 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan.Institute of Physics, Ecole Polytechnique Fédérale de Lausanne, Lausanne, SwitzerlandZekang Zhou, Cheng Shen & Mitali BanerjeeDahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Berlin, GermanyKryštof Kolár^Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, JapanKenji WatanabeInternational Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, JapanTakashi TaniguchiNational High Magnetic Field Laboratory, Tallahassee, FL, USACyprian LewandowskiDepartment of Physics, Florida State University, Tallahassee, FL, USACyprian LewandowskiCenter for Quantum Science and Engineering, Ecole Polytechnique Fédérale de Lausanne, Lausanne, SwitzerlandMitali BanerjeeSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarSearch author on:PubMed Google ScholarM.B. supervised the project. Z.Z. fabricated the devices, performed the measurements and analysed the data, with help from C.S. C.S., K.K. and C.L. conducted the theory calculations. K.W. and T.T. provided the hBN crystals. Z.Z. wrote the paper with input from all authors.Correspondence to Mitali Banerjee.The authors declare no competing interests.Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.a–b, Rxx as function of ν and D when B = 0 T (a) and B = 1 T (b) at T = 240 mK. Superconductivity appears on both the hole-doped side and electron-doped side. Correlated states appear at moiré filling ν = 1, ± 2, 3. The result is symmetric with respect to the displacement field, reflecting the device’s mirror symmetry. c-d, Landau fan diagram of Rxx (c) and Rxy (d) at D = 0 V/nm. e, The states shown in (c) and (d). Landau levels originating from ν = ± 4, 0 and ν = 1, ± 2, 3 are visible, as indicated by the black and red lines, while those from the Dirac band are shown in pink. The red lines mark the most robust Landau levels stemming from each correlated state at ν and have a slope of C = 2 + 4 − ν in the fan diagram. Dirac Landau levels contribute CDirac = 2, and Cflat = 2 + 4 − ν originates from symmetry-broken Chern insulators in flat bands, similar to those observed in TBG.a, Rxx and Rxy as a function of B and n when D = − 0.193 V/nm. The right figure extracted the states by black lines, and the red lines mark 1, 1/2, 1/3… quantum flux of the supermoiré lattice. Landau levels stemming from different supermoiré minibands are visible. b, the same measurement as a with fixing top gate voltage Vtg = 11 V and varying Vbg to change carrier density. Four sets of Landau levels can be seen and the distance between each is nsm. (T = 11 mK).a, Longitudinal conductance as a function of n and B at T = 15 K. The conductance shows peaks at the fractional quantum flux of the supermoiré lattice, suggesting the Brown-Zak oscillation. b, Line cut of conductance at a fixed carrier density from a.The longitudinal resistance Rxx is plotted as a function of carrier density for a fixed top gate voltage of Vtg = 11 V under different magnetic fields. Red lines serve as guides to the eye, indicating the expected positions of resistance peaks. The spacing between successive red lines corresponds to nsm = 0.468 × 1012 cm−2. The first resistance peak consistently aligns with the corresponding red guiding line. The second resistance peak shows a slight deviation from the red line; however, at B = 0.15 T and B = 0.25 T, it aligns well with the guiding lines. The third and fourth resistance peaks exhibit small deviations from the red lines.a–p, The single particle electronic structure of the TTG is tracked as a function of interlayer potential difference ΔU and interlayer tunnelling between layer 2 and layer 3. The band color indicates the extent of state polarization on the bottom layer (layer 3). In the weak tunnelling regime, the Dirac band exists and the relative fermi surface between mini bands and Dirac band can be adjusted by the displacement field. a-d show the band structure at ΔU = 0 meV. e-h show the band structure at ΔU = 10 meV. i-l show the band structure at ΔU = 20 meV. m-p show the band structure at ΔU = 30 meV.a–b, n − D mapping of Rxx and Rxy when B = 1 T. Same as in Fig. 2e,f, vertical features are flat band Landau levels, and ‘S’ shape features are the transition lines of nearby Dirac Landau levels. However, compared with the results measured at B = 0.5 T, the distance between different vertical features equals eB/h, which means the four-fold degeneracy of flat band Landau levels is lifted. c-e, Zoom-in of Rxx (c) and Rxy (d). The degeneracy of Dirac band Landau levels is also lifted. There are four Dirac Landau level transition lines near CNP, between which NDirac equals 1, 0, − 1. At a fixed n, the number of total filled Landau levels Ntotal = nh/eB and the filled flat band Landau levels Nflat = Ntotal − NDirac can be extracted. e, Figure shows (NDirac, Nflat) in the n − D mapping. (T = 240 mK).a, the corresponding Landau fan diagram of Rxy of the Rxx shown in Fig. 3a. b, Line cut of Rxy at a carrier density of n = 4.26 × 1012 cm−2. Rxy shows almost quantized resistance values of h/e2, h/2e2, h/6e2, and h/10e2, attributed to the Dirac Landau levels. When the Fermi level lies within the gap of the flat band, the transport is solely governed by the Dirac band, which transitions into Dirac Landau levels in the presence of a magnetic field. c-d, n − D mapping of Rxx and Rxy at B = 1 T for electron densities near the full filling of the top moiré lattice. The black solid lines indicate the full filling of the top moiré lattice. It is evident that the position of this full filling shifts as a function of the displacement field. This shift arises from the relative band shift between the Dirac band and the flat band. When the displacement field becomes sufficiently large (in our case, D > 0.3 V/nm), the Dirac band hybridizes with the flat band. As a result, Rxy no longer exhibits characteristics associated with the Dirac band. The purple lines mark the strong states appearing at n12 + nsm, which occur when the Fermi level lies within the gap of both the Dirac and flat bands. Additionally, the red dashed line highlights a gapped state induced by the supermoiré lattice. Between the red and black lines, three more states marked by yellow, green, and cyan lines are observed. These are attributed to isospin symmetry breaking within the supermoiré miniband.Landau fan diagram of Rxx and Rxy at D = 0.145 V/nm. All the observed features in the Landau fan are illustrated. The black dashed lines represent Landau levels originating from the full filling of the top moiré lattice (n12). The red dashed line marks the gapped state induced by the supermoiré lattice. The pink line indicates the transition between different Dirac Landau level regimes and above this line, two Dirac Landau levels are filled; below it, due to a change in degeneracy, six Dirac Landau levels are filled. Additionally, three states highlighted by yellow, green, and cyan lines are observed, with spacings nsm/4. These are isospin symmetry broken states within the supermoiré mini band.n − D mapping of Rxx on the hole-doped side. The red dashed lines mark the half filling \((\frac{1}{2}* {n}_{12})\) and full filling (n12) states of the top moiré lattice. The green dashed lines are the guiding lines for the other resistive states appearing in the superconducting regime. And the distance between is \(\frac{1}{2}* {n}_{sm}\). Similar to Fig. 4a, the nature of these states depends on the relative strength between interaction effects and the supermoiré potential.a, n − D mapping of Rxx at T = 240 mK. b–e, dVxx/dI versus Idc and n at different displacement fields. At a very large negative displacement field (b), superconductivity shows a single superconducting dome with the maximum critical current around 100 nA. As the displacement field increases, superconductivity weakens, and the maximum critical current decreases. More interestingly, the superconductor is gradually diced into small superconducting domes. At D = 0 V/nm, the critical current shows a kink in the superconducting dome as marked by the green dashed line where the carrier density is \(\frac{1}{2}* {n}_{12}+{n}_{sm}\). This shows that the supermoiré lattice starts mediating the superconductivity. At higher displacement fields, there are critical current kinks features appearing as marked by green dashed lines in d, e, and f. The carrier density at these green lines corresponds to the half filling of supermoiré minibands. This indicates the appearance of symmetry-broken phases in mini flat bands. (T = 240 mK).Supplementary Figs. 1–7.Source data.Source data.Source data.Source data.Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.Reprints and permissionsZhou, Z., Shen, C., Kolár^, K. et al. Strong correlations and superconductivity in the supermoiré lattice. Nat. Phys. (2026). https://doi.org/10.1038/s41567-025-03131-0Download citationReceived: 19 December 2024Accepted: 07 November 2025Published: 20 January 2026Version of record: 20 January 2026DOI: https://doi.org/10.1038/s41567-025-03131-0Anyone you share the following link with will be able to read this content:Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative