Resolving intervalley gaps and many-body resonances in moiré superconductors

Kim, Hyunjin; Rai, Gautam; Crippa, Lorenzo; Călugăru, Dumitru; Hu, Haoyu; Choi, Youngjoon; Kong, Lingyuan; Baum, Eli; Zhang, Yiran; Holleis, Ludwig; Watanabe, Kenji; Taniguchi, Takashi; Young, Andrea F.; Bernevig, B. Andrei; Valentí, Roser; Sangiovanni, Giorgio; Wehling, Tim; Nadj-Perge, Stevan

doi:10.1038/s41586-025-10067-1

Published February 19, 2026 | Version Supplemental material

Journal Article Open

Resolving intervalley gaps and many-body resonances in moiré superconductors

1. California Institute of Technology
2. Universität Hamburg
3. University of Würzburg
4. Princeton University
5. University of California, Santa Barbara
6. National Institute for Materials Science
7. Donostia International Physics Center
8. Ikerbasque
9. Goethe University Frankfurt

Magic-angle twisted multilayer graphene stands out as a highly tunable class of moiré materials that exhibit strong electronic correlations and robust superconductivity. 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 phase, persists at high temperatures and magnetic fields, the newly revealed inner gap is more fragile, in line with previous transport experiments. 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 correlations, we find that the outer gap probably arises from a splitting of the Abrikosov–Suhl–Kondo resonance owing to the breaking of the valley symmetry. Our results indicate an intricate yet tractable hierarchy of correlated phases in twisted multilayer graphene.

Copyright and License (English)

Acknowledgement (English)

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.

Funding (English)

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).

Contributions (English)

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.

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.