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Terahertz photocurrent probe of quantum geometry and interactions in magic-angle twisted bilayer graphene

Nature Materials volume 24, pages 1034–1041 (2025)Cite this article

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Abstract

Moiré materials represent strongly interacting electron systems bridging topological and correlated physics. Despite notable advances, decoding wavefunction properties underlying the quantum geometry remains challenging. Here we utilize polarization-resolved photocurrent measurements to probe magic-angle twisted bilayer graphene, leveraging its sensitivity to the Berry connection that encompasses quantum ‘textures’ of electron wavefunctions. Using terahertz light resonant with optical transitions of its flat bands, we observe bulk photocurrents driven by broken symmetries and reveal the interplay between electron interactions and quantum geometry. We observe inversion-breaking gapped states undetectable through quantum transport, sharp changes in the polarization axes caused by interaction-induced band renormalization and recurring photocurrent patterns at integer filling factors of the moiré unit cell that track the evolution of quantum geometry through the cascade of phase transitions. The large and tunable terahertz response intrinsic to flat-band systems offers direct insights into the quantum geometry of interacting electrons and paves the way for innovative terahertz quantum technologies.

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Fig. 1: Polarization-dependent THz photocurrents in TBG.
Fig. 2: ν dependence of α in TBG.
Fig. 3: Hartree-interaction-induced THz photocurrents.
Fig. 4: Temperature dependence of photoresponse and α.
Fig. 5: Photocurrent cascade in commensurate TBG aligned to hBN with a supermoiré potential.

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Data availability

The data that support the plots within this paper are available via Zenodo at https://doi.org/10.5281/zenodo.14882592 (ref. 56). Additional data including those from the Supplementary Information are available from the corresponding authors upon request.

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Acknowledgements

R.B. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 847517. J.B. acknowledges support from the European Union’s Horizon Europe programme under grant agreement no. 101105218. K.N. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 713729. S.C. acknowledges funding by the Departament de Recerca i Universitats de la Generalitat de Catalunya (no. 2021 SGR 01443). E.K. acknowledges funding under the Marie Skłodowska-Curie Fellowship project SuperTera. IMDEA Nanociencia acknowledges support from the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (no. CEX2020-001039-S/AEI/10.13039/501100011033). P.A.P. and F.G. acknowledge funding from the European Commission, within the Graphene Flagship Core 3 via grant no. 881603 and from grant no. NMAT2D (Comunidad de Madrid, Spain), SprQuMat, from NOVMOMAT, project PID2022-142162NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by FEDER, UE, as well as financial support through the (MAD2D-CM)-MRR MATERIALES AVANZADOS-IMDEA-NC. Z.Z. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 101034431. S.B.-P. acknowledges support from the ‘Presencia de la Agencia Estatal de Investigación’ within the ‘Convocatoria de tramitación anticipada, correspondente al año 2020, de las ayudas para contractos predoctorales (ref. no. PRE2020-094404) para la formación de doctores contemplada en el Subprograma Estatal de Fromación del Programa Estatal de Promoción del Talento y su Empleabilidad en I+D+i, en el marco del Plan Estatal de Investigacón Científica y Técnica de Innovación 2017–2020, cofinanciado por el Fondo Social Europeo’. E.I. and C.S. acknowledge funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 881603 (Graphene Flagship) and from the European Research Council (ERC) under grant agreement no. 820254, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1–390534769 and the FLAG-ERA grant PhotoTBG–471733165. H.A. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 665884. K.W. and T.T. acknowledge support from JSPS KAKENHI (grant nos. 20H00354 and 23H02052) and World Premier International Research Center Initiative (WPI), MEXT, Japan. J.C.W.S. acknowledges support from the Singapore Ministry of Education under its Academic Research Fund Tier 2 grant no. MOE-T2EP50222-0011 and Tier 3 grant no. MOE-MOET32023-0003 Quantum Geometric Advantage. G.R. acknowledges support from the Simons Foundation, the ARO MURI grant no. W911NF-16-1-0361 and the Institute of Quantum Information and Matter. C.L. was supported by 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-2128556 and the State of Florida. P.J.-H. acknowledges support from the National Science Foundation (no. DMR-1809802), the STC Center for Integrated Quantum Materials (NSF grant no. DMR1231319), the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF9463, the Ramon Areces Foundation and the ICFO Distinguished Visiting Professor program. P.J.-H. acknowledges funding for his sabbatical by CEX2019-000910-S [MCIN/AEI/10.13039/501100011033] Fundacio Cellex, Fundacio Mir-Puig, and Generalitat de Catalunya through CERCA. This material is based on work supported by the Air Force Office of Scientific Research under award no. FA8655-23-17047. Any opinions findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Air Force. F.H.L.K. acknowledges support from the ERC TOPONANOP under grant agreement no. 726001, the Gordon and Betty Moore Foundation through grant no. GBMF12212 and the Government of Spain (nos. FIS2016-81044; PID2019-106875GB-100; and Severo Ochoa CEX2019-000910-S [MCIN/AEI/10.13039/501100011033], PCI2021-122020-2A and PDC2022-133844-100 funded by MCIN/AEI/10.13039/501100011033). This work was also supported by the European Union NextGenerationEU/PRTR (PRTR-C17.I1) and EXQIRAL 101131579, Fundació Cellex, Fundació Mir-Puig and Generalitat de Catalunya (CERCA, AGAUR, 2021 SGR 014431656). Views and opinions expressed are those of the author(s) only and do not necessarily reflect those of the European Union Research Executive Agency. Neither the European Union nor the granting authority can be held responsible for them. Additionally, the research leading to these results received funding from European Union’s Horizon 2020 programme under grant agreement nos. 881603 (Graphene Flagship Core 3) and 820378 (Quantum Flagship). This material is based on work supported by the Air Force Office of Scientific Research under award no. FA8655-23-1-7047. R.K.K. acknowledges funding by MCIN/AEI/10.13039/501100011033 and by the ‘European Union NextGenerationEU/PRTR’ PCI2021-122020-2A within the FLAG-ERA grant (PhotoTBG), by ICFO, RWTH Aachen and ETHZ/Department of Physics, and support from the Ramon y Cajal grant no. RYC2022-036118-I funded by MICIU/AEI/10.13039/501100011033 and by ‘ESF+’.

Author information

Author notes

  1. These authors contributed equally: Geng Li, Riccardo Bertini, Swati Chaudhary.

Authors and Affiliations

  1. ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels (Barcelona), Spain

    Roshan Krishna Kumar, Geng Li, Riccardo Bertini, Krystian Nowakowski, Sebastian Castilla, Hitesh Agarwal, Sergi Batlle-Porro, Matteo Ceccanti, Antoine Reserbat-Plantey, Giulia Piccinini, Julien Barrier, Ekaterina Khestanova, Petr Stepanov & Frank H. L. Koppens

  2. Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology (BIST), Campus UAB, Bellaterra, Spain

    Roshan Krishna Kumar

  3. Department of Physics, The University of Texas, Austin, TX, USA

    Swati Chaudhary

  4. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Swati Chaudhary, Jeong Min Park & Pablo Jarillo-Herrero

  5. IMDEA Nanociencia, Madrid, Spain

    Zhen Zhan, Pierre A. Pantaleón & Francisco Guinea

  6. JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen, Germany

    Eike Icking & Christoph Stampfer

  7. Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich, Germany

    Eike Icking & Christoph Stampfer

  8. Université Côte d’Azur, CNRS, CRHEA, Sophia-Antipolis, France

    Antoine Reserbat-Plantey

  9. Research Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  10. Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  11. Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA, USA

    Gil Refael & Cyprian Lewandowski

  12. Donostia International Physics Center, San Sebastian, Spain

    Francisco Guinea

  13. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Justin C. W. Song

  14. Department of Physics and Astronomy, University of Notre Dame, Notre Dame, IN, USA

    Petr Stepanov

  15. Stavropoulos Center for Complex Quantum Matter, University of Notre Dame, Notre Dame, IN, USA

    Petr Stepanov

  16. National High Magnetic Field Laboratory, Tallahassee, FL, USA

    Cyprian Lewandowski

  17. Department of Physics, Florida State University, Tallahassee, FL, USA

    Cyprian Lewandowski

  18. ICREA—Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain

    Frank H. L. Koppens

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  1. Roshan Krishna Kumar
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Contributions

R.K.K., K.N. and F.H.L.K. conceived the experiments. R.K.K. and R.B. performed the photocurrent measurements and analysed the data with support from K.N. G.L. fabricated the D0.94, D1.12 and D1.5 devices, and performed quantum transport measurements in these devices. P.S. fabricated the D1.03 device. S.C. performed the calculations and provided theoretical support regarding the shift current. J.M.P. fabricated the D1.02 device supported by P.J.-H. S.C. performed the numerical simulations. Z.Z. and P.A.P. performed the tight-binding calculations of TBG on hBN with support from F.G. R.K.K., R.B., H.A. and A.R.-P. built the cryogenic THz photocurrent setup in which the measurements were performed. S.B.-P. and J.B. performed the supporting photocurrent measurements. M.C. provided the fabrication support and technical expertise. E.I. fabricated the bilayer graphene devices supported by C.S. G.P. fabricated the monolayer graphene devices. E.K. provided technical assistance with the THz measurements. T.T. and K.W. provided the high-quality hBN crystals. G.R. provided theoretical support. J.C.W.S., C.L. and F.H.L.K. supervised the project. R.K.K., R.B., C.L. and F.H.L.K. wrote the manuscript with input from all authors.

Corresponding authors

Correspondence to Roshan Krishna Kumar or Frank H. L. Koppens.

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Nature Materials thanks Fan Zhang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Sections 1–13, Figs. 1–16 and References.

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Krishna Kumar, R., Li, G., Bertini, R. et al. Terahertz photocurrent probe of quantum geometry and interactions in magic-angle twisted bilayer graphene. Nat. Mater. 24, 1034–1041 (2025). https://doi.org/10.1038/s41563-025-02180-3

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