Abstract
Magic-angle twisted multilayer graphene stands out as a highly tunable class of moiré materials that exhibit strong electronic correlations and robust superconductivity1,2,3,4. However, understanding the relationships between the low-temperature superconducting phase and the preceding correlated parent states remains a challenge. Here we use scanning tunnelling microscopy (STM) and spectroscopy to track the formation sequence of correlated phases established by the interplay of dynamic correlations, intervalley coherence and superconductivity in magic-angle twisted trilayer graphene (MATTG). We discover the existence of two well-resolved gaps pinned at the Fermi level within the superconducting doping range. Although the outer gap, previously associated with the pseudogap phase5,6, persists at high temperatures and magnetic fields, the newly revealed inner gap is more fragile, in line with previous transport experiments1,2,4. Andreev reflection spectroscopy taken at the same location confirms a clear trend that closely follows the doping behaviour of the inner gap and not the outer one. Moreover, spectroscopy taken at nanoscale domain boundaries further corroborates the contrasting behaviour of the two gaps, with the inner gap remaining resilient to structural variations. By comparing our results with recent topological heavy fermion (THF) models that include dynamical correlations7,8, we find that the outer gap probably arises from a splitting of the Abrikosov–Suhl–Kondo resonance9,10 owing to the breaking of the valley symmetry. Our results indicate an intricate yet tractable hierarchy of correlated phases in twisted multilayer graphene.
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Data availability
The raw data shown in the main figures are available at Zenodo (https://doi.org/10.5281/zenodo.17884628) (ref. 61). Other data and code that support the findings of this study are available from the corresponding authors on reasonable request.
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Acknowledgements
We thank J. Alicea, C. Lewandowski, É. Lantagne-Hurtubise, A. Thomson, M. Randeria, S. Biswas, Z.-d. Song, Y.-j. Wang and G.-D. Zhou for fruitful discussion. This work has been primarily supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-2317110), the Gordon and Betty Moore Foundation, grant DOI 10.37807/GBMF12967 and by the Office of Naval Research (grant no. N142112635). H.K. acknowledges support from the Kwanjeong Fellowship and the Eddleman Quantum Institute Fellowship. L.K. acknowledges support from an IQIM-AWS Quantum postdoctoral fellowship. We gratefully acknowledge the critical support and infrastructure provided for this work by The Kavli Nanoscience Institute at Caltech. Work at UCSB was supported by the U.S. Department of Energy (award no. DE-SC0020305) and by the Gordon and Betty Moore Foundation under award GBMF9471. This work used facilities supported by the UC Santa Barbara NSF Quantum Foundry financed through the Q-AMASE-i programme under award DMR-1906325. B.A.B. was supported by the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the Princeton theory programme, the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant no. GBMF11070), the Office of Naval Research (ONR grant no. N00014-20-1-2303), the Global Collaborative Network Grant at Princeton University, the Simons Investigators grant no. 404513, the BSF Israel US foundation no. 2018226, the NSF-MERSEC (grant no. MERSEC DMR 2011750), the Simons Collaboration on New Frontiers in Superconductivity and the Schmidt Foundation at Princeton University. H.H. and D.C. were supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 101020833). G.R., L.C., R.V., G.S. and T.W. acknowledge support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through QUAST FOR 5249 (project no. 449872909, projects P4 and P5). G.S. and L.C. were supported by the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter ct.qmat - EXC 2147 (project no. 390858490). G.R., L.C. and T.W. acknowledge support from the Cluster of Excellence ‘CUI: Advanced Imaging of Matter’ - EXC 2056 (project no. 390715994) and SPP 2244 (WE 5342/5-1 project no. 422707584). L.C. gratefully acknowledges the scientific support and HPC resources provided by the Erlangen National High Performance Computing Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the NHR project b158cb. G.R. gratefully acknowledges the computing time granted by the Resource Allocation Board and provided on the supercomputers Lise and Emmy at NHR@ZIB and NHR@Göttingen as part of the NHR infrastructure (project ID hhp00061).
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H.K. fabricated samples with the help of Y.C., Y.Z. and L.H. under the supervision of S.N.-P. and performed STM measurements. H.K. and S.N.-P. analysed the data with the help of L.K. and E.B. T.T. and K.W. synthesized hexagonal boron nitride crystals. A.F.Y. supervised nanofabrication efforts at UCSB. L.C. and G.R. performed the DMFT calculations and analysed the results with D.C., H.H., G.S., R.V., T.W. and B.A.B. D.C. and H.H. performed iterative perturbation theory calculations under the supervision of B.A.B. H.K. and S.N.-P. wrote the manuscript with input from the other authors. S.N.-P. supervised the project.
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Extended data figures and tables
Extended Data Fig. 1 Temperature-dependent evolution of MATBG sample.
a–d, VGate-dependent dI/dV spectroscopy measured on MATBG device at an area with local twist angle θ = 1.02° for temperature T = 2 K (a), T = 7 K (b), T = 9.5 K (c) and T = 20 K (d). e,f, Temperature-dependent spectrum taken from a–d at filling factors ν = −1.3 (e) and ν = 0 (f). The dashed line is the convolution of 2-K data with Fermi–Dirac distribution function at each temperature. g–i, Temperature-dependent spectrum taken at different parts of the same MATBG sample for which the local twist angle is θ = 1.07° at filling factors ν = 0 (g), ν = −1.3 (h) and ν = 4.0 (i).
Extended Data Fig. 2 VBias-dependent mapping of the lattice tripling order on MATTG.
a,b, Real-space dI/dV map at VGate = −8.5 V at VBias = 0.4 mV (a) and 2.2 mV (b). The two real-space maps show perfectly inverted Kekulé pattern. c, Conductance at VGate = −8.5 V corresponding to a filling factor of ν = −2.35 measured on the AAA site on the moiré lattice averaged over a 3 × 3-nm region. Green (blue) dashed line corresponds to VBias at which a (b) is measured. d, Phase of the local IKS order parameter as a function of VBias. Local order parameter decomposition is performed by taking the real-space dI/dV map for each VBias and linear transformation of FT Kekulé peaks. e, Intensity of the local IKS order parameter as a function of VBias.
Extended Data Fig. 3 VGate switching of dI/dV spectrum owing to intervalley coherence reconstruction.
a, VGate-dependent dI/dV spectroscopy focusing on the hole-doping side, in which we observe correlated gap. Red (green) dashed line indicates VBias at which c (d) is taken. b, Tip height as a function of VGate recorded for this figure. Tunnelling current feedback is turned ON, which gives smooth increasing background in height. c, Tunnelling dI/dV as a function of VGate for fixed VBias = −3 mV after 5 mins of taking data in a. The position of the dI/dV peak in VGate matches the VGate at which switching happens in a around −8.5 V, indicating that certain switching behaviours seen in VGate-dependent spectroscopies are reproducible over measurements taken at different times. d, Tunnelling dI/dV as a function of VGate for fixed VBias = 3 mV after 2 mins of taking data in c.
Extended Data Fig. 4 Tip–sample distance-dependent dI/dV spectrum tracking the evolution of Andreev reflection signal.
a, Point-contact dI/dV spectra taken as the tip approaches the sample. b, VGate-dependent point-contact dI/dV spectroscopy taken on MATTG device #1 at twist angle θ = 1.61°. Andreev reflection signal is visible between filling factor ν = −2 to −3. c,d, dI/dV map measured on the same region with different STM tip feedback conditions. VBias = 100 mV and Iset = 1 nA for c and VBias = 100 mV and Iset = 20 pA for d. Tip–sample distance is shorter by 0.9 nm for c compared with d.
Extended Data Fig. 5 Intensity of FT Kekulé peak from real-space dI/dV map adjacent to the MATTG stripe domain boundary.
a, 35 × 35-nm real-space dI/dV map containing regions on the domain boundary and outside the domain boundary. Blue arrow indicates real-space trajectory at which the data in c are extracted. b, Local IKS bond order parameter phase extracted from a by taking a 2 × 2-nm window and decomposing Kekulé FT peaks into IKS order parameters. c, Intensity of FT Kekulé peak normalized by FT graphene peak extracted in real space as we move towards the stripe domain boundary. d, Intensity of FT Kekulé peak normalized by FT graphene peak measured at the centre of the domain boundary as a function of VGate.
Extended Data Fig. 6 Onset temperature of inner gap signal in tunnelling dI/dV and PCS in MATTG device #1.
a, Tunnelling dI/dV spectra at fixed VGate = −8.6 V measured as a function of temperature on the AAA site. b, Temperature dependence of point-contact dI/dV spectra at VGate = −10 V.
Extended Data Fig. 7 Two-gap dI/dV spectrum characterized on MATTG device #2 θ = 1.38°.
a, VGate-dependent dI/dV spectrum taken at T = 400 mK on the AAA site featuring correlated gaps on the electron-doped side. b,c, VGate-dependent dI/dV spectrum focusing between ν = 2 to 3 at out-of-plane magnetic field 0 T (b) and 600 mT (c). d, Intensity of the peaks at Kekulé reciprocal lattice vector normalized by the intensity of the peaks at graphene reciprocal lattice vector as a function of VGate. VBias at which the real-space dI/dV map is taken is chosen to be at the coherence peak of the gap. e, Tunnelling dI/dV spectrum as a function of temperature at fixed VGate = 10.7 V. f,g, Point-contact dI/dV spectrum showing weak Andreev reflection signal on the electron side.
Extended Data Fig. 8 Local doping of the correlated gaps owing to work function mismatching STM tips.
a,b, VGate-dependent dI/dV spectrum on area θ = 1.51° with STM tips no local doping (a) and local hole doping (b). Cascade features are moved to positive VGate for hole-doping STM tips. c,d, VGate-dependent dI/dV spectrum on area θ = 1.38° with STM tips no local doping (c) and local electron doping (d). The outer gap is moved to negative VGate for electron-doping STM tips, whereas minimal shift is observed for the inner gap.
Extended Data Fig. 9 Observation of zero energy resonance in several samples.
a,b, VGate-dependent dI/dV spectrum taken from an old MATTG device, which is device #3 with twist angle θ = 1.51° at T = 0.4 K (a) and T = 7 K (b) highlighting diminishing zero-bias feature at 7 K. c, Linecut taken from a, where three clear peaks coexist at the same doping, at which the Kondo resonance is pinned to the Fermi level, compared with split flat band peaks that shift with doping. d,e, VGate-dependent dI/dV spectrum on area θ = 1.51° at T = 2 K (d) and T = 10 K (e) highlighting diminishing zero-bias feature at 10 K. f, VGate-dependent dI/dV spectrum on area θ = 1.43° at T = 2 K showing zero-bias peak along with split flat band peak on both positive and negative energies. g, VGate-dependent dI/dV spectrum on MATBG device with θ = 0.97° at T = 2 K showing zero-bias peak along with split flat band peak on both positive and negative energies.
Extended Data Fig. 10 Filling-dependent size evolution of the inner and outer gaps measured in different spatial positions in MATTG device #1.
a, Extracted from Fig. 3a. The outer gap is marked in red and the inner gap is marked in blue. When the inner gap is merged with the outer gap, we mark that filling factor range as ‘Single-gap regime’. b, Same dataset as Fig. 4g. c, Outer and inner gaps are extracted from dI/dV spectra taken at region with 1.62° twist angle. Panels a–c are located within a 1.0 × 1.0-μm area. d–f, Outer and inner gaps are extracted from dI/dV spectra taken at region with 1.56° (d), 1.57° (e) and 1.55° (f) twist angle. Panels d–f are measured in an area that is moved 2.6 μm in the +y direction from the area in which panels a–c are measured.
Extended Data Fig. 11 Temperature dependence of Kondo resonance height and width in MATTG.
a, dI/dV spectra focusing on the Kondo resonance on MATTG device #2 for filling factor ν = 1.2 at several temperatures. Black arrows indicate the positions of the resonance peaks. b, Full width at half maximum of the resonance extracted from a, obtained by Lorentzian fits after subtracting a smooth background. Dashed red line is a formula derived from previous literature62 assuming single Kondo impurity. c, dI/dV spectra focusing on the Kondo resonance on MATTG device #3 for filling factor ν = −1.63 at several temperatures. d, Full width at half maximum of the resonance extracted from c, obtained by Lorentzian fits after subtracting a smooth background. Dashed red line is a formula derived from previous literature62 assuming single Kondo impurity.
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Kim, H., Rai, G., Crippa, L. et al. Resolving intervalley gaps and many-body resonances in moiré superconductors. Nature (2026). https://doi.org/10.1038/s41586-025-10067-1
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DOI: https://doi.org/10.1038/s41586-025-10067-1
