- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Letter
  • Open Access

Probing superconductivity with tunneling spectroscopy in rhombohedral graphene

Denis Sedov and Mathias S. Scheurer

PDF

Phys. Rev. B 113, L140503 – Published 28 April, 2026

DOI: https://doi.org/10.1103/6qg4-cfgc

Abstract

Motivated by experiments on rhombohedral tetralayer graphene showing signs of superconductivity emerging from a valley-polarized normal state, we here analyze theoretically how tunneling spectroscopy can be used to probe the superconducting order parameter of the system. To describe different pairing scenarios on equal footing, we develop a microscopic tunneling approach that can capture arbitrary, including finite-momentum, superconducting order parameters and low-symmetry normal-state Hamiltonians. Our analysis shows that the broken time-reversal symmetry in a single valley leads to unique features in the weak-tunneling regime that are different for commensurate and incommensurate Cooper pair momenta. We further uncover an unconventional spatial dependence of the Andreev conductance, allowing to distinguish between three topologically distinct classes of single-q pairing states in the system, and compute the signatures of a competing translational-symmetry breaking three-q superconductor.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (58)

  1. E. Y. Andrei and A. H. MacDonald, Graphene bilayers with a twist, Nat. Mater. 19, 1265 (2020).
  2. L. Balents, C. R. Dean, D. K. Efetov, and A. F. Young, Superconductivity and strong correlations in moiré flat bands, Nat. Phys. 16, 725 (2020).
  3. K. P. Nuckolls and A. Yazdani, A microscopic perspective on moiré materials, Nat. Rev. Mater. 9, 460 (2024).
  4. P. A. Pantaleón, A. Jimeno-Pozo, H. Sainz-Cruz, V. Phong, T. Cea, and F. Guinea, Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene, Nat. Rev. Phys. 5, 304 (2023).
  5. H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J. R. Ehrets, E. M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn, and A. F. Young, Half- and quarter-metals in rhombohedral trilayer graphene, Nature (London) 598, 429 (2021).
  6. H. Zhou, T. Xie, T. Taniguchi, K. Watanabe, and A. F. Young, Superconductivity in rhombohedral trilayer graphene, Nature (London) 598, 434 (2021).
  7. D. Wong, K. P. Nuckolls, M. Oh, B. Lian, Y. Xie, S. Jeon, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Cascade of electronic transitions in magic-angle twisted bilayer graphene, Nature (London) 582, 198 (2020).
  8. U. Zondiner, A. Rozen, D. Rodan-Legrain, Y. Cao, R. Queiroz, T. Taniguchi, K. Watanabe, Y. Oreg, F. von Oppen, A. Stern, E. Berg, P. Jarillo-Herrero, and S. Ilani, Cascade of phase transitions and Dirac revivals in magic-angle graphene, Nature (London) 582, 203 (2020).
  9. E. Morissette, J.-X. Lin, D. Sun, L. Zhang, S. Liu, D. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, J. Pollanen, M. S. Scheurer, M. Lilly, A. Mounce, and J. I. A. Li, Dirac revivals drive a resonance response in twisted bilayer graphene, Nat. Phys. 19, 1156 (2023).
  10. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature (London) 556, 43 (2018).
  11. M. Oh, K. P. Nuckolls, D. Wong, R. L. Lee, X. Liu, K. Watanabe, T. Taniguchi, and A. Yazdani, Evidence for unconventional superconductivity in twisted bilayer graphene, Nature (London) 600, 240 (2021).
  12. H. Kim, Y. Choi, C. Lewandowski, A. Thomson, Y. Zhang, R. Polski, K. Watanabe, T. Taniguchi, J. Alicea, and S. Nadj-Perge, Evidence for unconventional superconductivity in twisted trilayer graphene, Nature (London) 606, 494 (2022).
  13. E. Lake, A. S. Patri, and T. Senthil, Pairing symmetry of twisted bilayer graphene: A phenomenological synthesis, Phys. Rev. B 106, 104506 (2022).
  14. P. O. Sukhachov, F. von Oppen, and L. I. Glazman, Andreev reflection in scanning tunneling spectroscopy of unconventional superconductors, Phys. Rev. Lett. 130, 216002 (2023).
  15. H. Sainz-Cruz, P. A. Pantaleón, V. o. T. Phong, A. Jimeno-Pozo, and F. Guinea, Junctions and superconducting symmetry in twisted bilayer graphene, Phys. Rev. Lett. 131, 016003 (2023).
  16. C. Lewandowski, E. Lantagne-Hurtubise, A. Thomson, S. Nadj-Perge, and J. Alicea, Andreev reflection spectroscopy in strongly paired superconductors, Phys. Rev. B 107, L020502 (2023).
  17. P. P. Poduval and M. S. Scheurer, Vestigial singlet pairing in a fluctuating magnetic triplet superconductor and its implications for graphene superlattices, Nat. Commun. 15, 1713 (2024).
  18. M. Christos, S. Sachdev, and M. S. Scheurer, Nodal band-off-diagonal superconductivity in twisted graphene superlattices, Nat. Commun. 14, 7134 (2023).
  19. S. Van Loon and C. A. R. Sá de Melo, Topological two-band electron-hole superconductors with d-wave symmetry: Absence of Dirac quasiparticle annihilation in magic-angle twisted trilayer graphene, Phys. Rev. B 111, 064515 (2025).
  20. Y.-Z. Chou, F. Wu, J. D. Sau, and S. Das Sarma, Acoustic-phonon-mediated superconductivity in rhombohedral trilayer graphene, Phys. Rev. Lett. 127, 187001 (2021).
  21. A. Ghazaryan, T. Holder, M. Serbyn, and E. Berg, Unconventional superconductivity in systems with annular Fermi surfaces: Application to rhombohedral trilayer graphene, Phys. Rev. Lett. 127, 247001 (2021).
  22. Y.-Z. You and A. Vishwanath, Kohn-Luttinger superconductivity and intervalley coherence in rhombohedral trilayer graphene, Phys. Rev. B 105, 134524 (2022).
  23. S. Chatterjee, T. Wang, E. Berg, and M. P. Zaletel, Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene, Nat. Commun. 13, 6013 (2022).
  24. A. Ghazaryan, T. Holder, E. Berg, and M. Serbyn, Multilayer graphenes as a platform for interaction-driven physics and topological superconductivity, Phys. Rev. B 107, 104502 (2023).
  25. A. Jimeno-Pozo, H. Sainz-Cruz, T. Cea, P. A. Pantaleón, and F. Guinea, Superconductivity from electronic interactions and spin-orbit enhancement in bilayer and trilayer graphene, Phys. Rev. B 107, L161106 (2023).
  26. W. Qin, C. Huang, T. Wolf, N. Wei, I. Blinov, and A. H. MacDonald, Functional renormalization group study of superconductivity in rhombohedral trilayer graphene, Phys. Rev. Lett. 130, 146001 (2023).
  27. Z. Li, X. Kuang, A. Jimeno-Pozo, H. Sainz-Cruz, Z. Zhan, S. Yuan, and F. Guinea, Charge fluctuations, phonons, and superconductivity in multilayer graphene, Phys. Rev. B 108, 045404 (2023).
  28. A. L. Szabó and B. Roy, Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene, Phys. Rev. B 105, L081407 (2022).
  29. Z. Dong, L. Levitov, and A. V. Chubukov, Superconductivity near spin and valley orders in graphene multilayers, Phys. Rev. B 108, 134503 (2023).
  30. Z. Dong, É. Lantagne-Hurtubise, and J. Alicea, Superconductivity from spin-canting fluctuations in rhombohedral graphene, Phys. Rev. X 16, 011055 (2026) .
  31. T. Han, Z. Lu, Y. Yao, L. Shi, J. Yang, J. Seo, S. Ye, Z. Wu, M. Zhou, H. Liu, G. Shi, Z. Hua, K. Watanabe, T. Taniguchi, P. Xiong, L. Fu, and L. Ju, Signatures of chiral superconductivity in rhombohedral graphene, Nature (London) 643, 654 (2025).
  32. H. D. Scammell, J. I. A. Li, and M. S. Scheurer, Theory of zero-field superconducting diode effect in twisted trilayer graphene, 2D Mater. 9, 025027 (2022).
  33. Y.-Z. Chou, J. Zhu, and S. D. Sarma, Intravalley spin-polarized superconductivity in rhombohedral tetralayer graphene, Phys. Rev. B 111, 174523 (2025).
  34. M. Geier, M. Davydova, and L. Fu, Chiral and topological superconductivity in isospin polarized multilayer graphene, Nat. Commun. 17, 232 (2025).
  35. H. Yang and Y.-H. Zhang, Topological incommensurate Fulde-Ferrell-Larkin-Ovchinnikov superconductor and Bogoliubov Fermi surface in rhombohedral tetra-layer graphene, Phys. Rev. B, 112, L020506 (2025).
  36. Q. Qin and C. Wu, Chiral finite-momentum superconductivity in the tetralayer graphene, Chinese Phys. Lett. 43, 030708 (2026).
  37. G. Parra-Martinez, A. Jimeno-Pozo, V. Tien Phong, H. Sainz-Cruz, D. Kaplan, P. Emanuel, Y. Oreg, P. A. Pantaleon, J. A. Silva-Guillen, and F. Guinea, Band renormalization, quarter metals, and chiral superconductivity in rhombohedral tetralayer graphene, Phys. Rev. Lett. 135, 136503 (2025).
  38. C. Yoon, T. Xu, Y. Barlas, and F. Zhang, Quarter metal superconductivity, Phys. Rev. Lett. 136, 026603 (2026).
  39. M. Christos, P. M. Bonetti, and M. S. Scheurer, Finite-momentum pairing and superlattice superconductivity in valley-imbalanced rhombohedral graphene, arXiv:2503.15471.
  40. A. Jahin and S.-Z. Lin, Enhanced Kohn-Luttinger topological superconductivity in bands with nontrivial geometry, Phys. Rev. B 113, 014504 (2026).
  41. J. May-Mann, T. Helbig, and T. Devakul, How pairing mechanism dictates topology in valley-polarized superconductors with Berry curvature, npj Quantum Mater. (2026).
  42. M. Kim, A. Timmel, L. Ju, and X.-G. Wen, Topological chiral superconductivity beyond pairing in a Fermi liquid, Phys. Rev. B 111, 014508 (2025).
  43. S. Banerjee and M. S. Scheurer, Enhanced superconducting diode effect due to coexisting phases, Phys. Rev. Lett. 132, 046003 (2024).
  44. P. H. Wilhelm, A. M. Läuchli, and M. S. Scheurer, Ideal Chern bands with strong short-range repulsion: Applications to correlated metals, superconductivity, and topological order, Phys. Rev. Res. 6, 043240 (2024).
  45. J. C. Cuevas, A. Martín-Rodero, and A. L. Yeyati, Hamiltonian approach to the transport properties of superconducting quantum point contacts, Phys. Rev. B 54, 7366 (1996).
  46. F. Zhang, B. Sahu, H. Min, and A. H. MacDonald, Band structure of ABC-stacked graphene trilayers, Phys. Rev. B 82, 035409 (2010).
  47. M. Koshino and E. McCann, Trigonal warping and Berry's phase Nπ in ABC-stacked multilayer graphene, Phys. Rev. B 80, 165409 (2009).
  48. See Supplemental Material at http://link.aps.org/supplemental/10.1103/6qg4-cfgc for a detailed derivation of the tunneling current; symmetry analysis of the Andreev current; details on the different contributions to the Berry curvature of the superconductor; additional results for the finite-momentum single-q and three-q pairing states; discussion of a 1D toy model with a pair density wave.
  49. We here neglect an additional reflection symmetry σv for simplicity of the discussion.
  50. J. M. B. L. Dos Santos, N. M. R. Peres, and A. H. C. Neto, Graphene bilayer with a twist: Electronic structure, Phys. Rev. Lett. 99, 256802 (2007).
  51. R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proc. Natl. Acad. Sci. USA 108, 12233 (2011).
  52. K. P. Nuckolls, R. L. Lee, et al., Quantum textures of the many-body wavefunctions in magic-angle graphene, Nature (London) 620, 525 (2023).
  53. Y.-C. Tsui, M. He, Y. Hu, E. Lake, T. Wang, K. Watanabe, T. Taniguchi, M. P. Zaletel, and A. Yazdani, Direct observation of a magnetic-field-induced Wigner crystal, Nature (London) 628, 287 (2024).
  54. S. Turkel, J. Swann, Z. Zhu, M. Christos, K. Watanabe, T. Taniguchi, S. Sachdev, M. S. Scheurer, E. Kaxiras, C. R. Dean, and A. N. Pasupathy, Orderly disorder in magic-angle twisted trilayer graphene, Science 376, 193 (2022).
  55. Y. Liu, Z. Li, S. Jiang, M. Li, Y. Gu, K. Liu, Q. Shen, L. Liu, X. Liu, D. Guan, Y. Li, H. Zheng, C. Liu, K. Watanabe, T. Taniguchi, J. Jia, T. Li, G. Chen, J. Liu, C. Li, et al., Electronic correlations in rhombohedral graphene at atomic scale, Phys. Rev. Lett. 135 156401 (2025).
  56. R. Xu, L.-J. Yin, J.-B. Qiao, K.-K. Bai, J.-C. Nie, and L. He, Direct probing of the stacking order and electronic spectrum of rhombohedral trilayer graphene with scanning tunneling microscopy, Phys. Rev. B 91, 035410 (2015).
  57. L.-J. Yin, Y.-Y. Zhou, L.-H. Tong, L.-J. Shi, Z. Qin, and L. He, Imaging Friedel oscillations in rhombohedral trilayer graphene, Phys. Rev. B 107, L041404 (2023).
  58. Y. Liu, A. Gupta, Y. Choi, Y. Vituri, H. Stoyanov, J. Xiao, Y. Wang, H. Zhou, B. Barick, T. Taniguchi, K. Watanabe, B. Yan, E. Berg, A. F. Young, H. Beidenkopf, and N. Avraham, Visualizing incommensurate inter-valley coherent states in rhombohedral trilayer graphene, arXiv:2411.11163.

Outline

Information

Phys. Rev. B 113, L140503– Published 28 April, 2026
  • Received 1 April 2025
  • Revised 18 March 2026
  • Accepted 2 April 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation