Abstract
In systems with multiple energy bands, the interplay between electrons with different effective masses drives correlated phenomena that do not occur in single-band systems. Magic-angle twisted trilayer graphene is a tunable platform for exploring such effects, hosting both heavy electrons in its flat bands and delocalized light Dirac electrons in dispersive bands. Superconductivity in this system spans a wider range of phase space than moiré materials without dispersive bands, suggesting that interband interactions influence the stabilization of correlated phases. Here we investigate the interplay between the light and heavy electrons in magic-angle twisted trilayer graphene by performing local compressibility measurements with a scanning single-electron-transistor microscope. We establish that weak incompressibility features near several integer moiré band fillings host a finite population of light Dirac electrons at the Fermi level, despite a gap opening in the flat band sector. At higher magnetic field near charge neutrality, we find a phase transition sequence that is robust over nearly 10 μm but exhibits complex spatial dependence. Calculations establish that the Dirac sector can be viewed as flavour analogous to the spin and valley degrees of freedom.
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Data availability
Source data are provided with this paper. All other data that support the findings of this Article are available from the corresponding authors upon request.
Code availability
The codes that support the findings of this study are available from the corresponding authors upon reasonable request.
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Acknowledgements
We acknowledge discussions with A. Stern. We thank A. Vishwanath, E. Khalaf, D. Parker, P. Ledwith and J. Wang for collaboration on related projects. This work was sponsored by the Army Research Office under award number W911NF-21-2-0147 and by the Gordon and Betty Moore Foundation EPiQS initiative through Grant GBMF 9468. Help with transport measurements and data analysis were supported by the National Science Foundation (DMR-1809802), and the STC Center for Integrated Quantum Materials (NSF grant number DMR-1231319). P.J.-H. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF9463, the CIFAR Quantum Materials Program and the Fundación Ramón Areces. A.T.P. acknowledges support from the Department of Defense through the National Defense Science and Engineering Graduate Fellowship (NDSEG) Program. Y.X. acknowledges partial support from the Harvard Quantum Initiative in Science and Engineering. During the revision of this work, Y.X. was supported by the NSF CAREER DMR-2339623 and Robert A. Welch Foundation grant number C-2219 and A.Y. was partly supported by the Gordon and Betty Moore Foundation through Grant GBMF12762. Y.X, A.T.P. and A.Y. acknowledge support from the Harvard Quantum Initiative Seed Fund. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant numbers 21H05233 and 23H02052), the CREST (grant number JPMJCR24A5), JST and World Premier International Research Center Initiative (WPI), MEXT, Japan. This work was performed, in part, at the Center for Nanoscale Systems (CNS), a member of the National Nanotechnology Infrastructure Network, which is supported by the NSF under award number ECS-0335765. CNS is part of Harvard University.
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A.T.P., Y.X., J.M.P., P.J.-H. and A.Y. designed the experiment. A.T.P., Y.X. and Z.C. performed the scanning SET experiment and the temperature-dependent transport measurements and analysed the data with input from A.Y. J.M.P. and P.J.-H. designed and provided the samples and contributed to the analysis of the results. Y.X., A.T.P. and Z.C. carried out the simulation of the compressibility. K.W. and T.T. provided hBN crystals. All authors participated in discussions and in writing of the paper.
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Extended data
Extended Data Fig. 1 Device and transport characterization.
a, Left panel: Optical microscope image of the device. The black points marked 1 (1.53°) and 2 (1.58°) are the approximate locations at which the compressibility measurements were carried out. Vxx denotes contacts used for the transport measurements. Right panel: topographic image obtained by measuring the electrostatic potential of the device using the scanning SET. b, Temperature-dependent longitudinal resistance Rxx measured between contacts marked by Vxx in a, showing superconductivity for both electron and hole dopings.
Extended Data Fig. 2 Experimentally determined Hofstadter energy spectrum obtained from a second location.
The location is marked 2 in Extended Data Fig 1 and the local twist angle θ is around 1.58°. Orange and blue dots correspond to contributions from the Dirac and flat bands, respectively.
Extended Data Fig. 3 Negligible role of quantum capacitance on the density shifts.
a-d, Locations of the incompressibility peaks as a function of the magnetic field (blue circles) and the corresponding linear fit (red line) at integer fillings. e-h, Fit residual from a-d, demonstrating a universal finite density shift near zero magnetic field. i-l, Change of chemical potentials associated with the incompressible peaks at integer fillings as a function of magnetic field.
Extended Data Fig. 4 Spatial dependence of localized states at different tip-sample voltages.
a-c, Position-dependent of the localized states associated with the (C, ν) = (2, −2) Chern insulators at 2T measured with three different tip-sample voltages Vt-s = +1.35V (a), +0.45V (b) and −0.65V (c). The insets sketch the density profiles observed in the data, demonstrating their tunability by Vt-s. The density modulation used is about δn~5.7x108 cm−2.
Extended Data Fig. 5 Simulation results from a non-interacting phenomenological model.
a, Inverse compressibility as a function of Landau level fillings and magnetic fields, computed from the linearly-dispersive energy spectrum shown in Fig. 3b. b, The corresponding energy gaps from the same calculation as (a) and their comparison with the experiments. Despite its simplicity, our non-interacting phenomelogical model not only captures the locations at which integer quantum Hall states are interrupted, but also produces gap values in close agreement with the experiment.
Extended Data Fig. 6 Role of Coulomb interaction in driving the phase transition near the CNP.
a-c, Simulated inverse compressibility using the mean-field model described in the text (see also Methods section) at three representative U/W values.
Extended Data Fig. 7 Phase transitions near charge neutrality measured at a second location.
a, Local compressibility of MATTG in the vicinity of charge neutrality plotted as a function of Landau level filling factor νLL and magnetic field. b, Simulated inverse compressibility using the mean-field model described in the text (see also Methods section). nD represents the number of Landau levels that are partially or fully populated with carriers.
Source data
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Pierce, A.T., Xie, Y., Park, J.M. et al. Tunable interplay between light and heavy electrons in twisted trilayer graphene. Nat. Phys. 21, 1237–1242 (2025). https://doi.org/10.1038/s41567-025-02956-z
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DOI: https://doi.org/10.1038/s41567-025-02956-z
