Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Unconventional superconductivity in magic-angle graphene superlattices

Abstract

The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity—which cannot be explained by weak electron–phonon interactions—in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°—the first ‘magic’ angle—the electronic band structure of this ‘twisted bilayer graphene’ exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature–carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 1011 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Two-dimensional superconductivity in a graphene superlattice.
Figure 2: Gate-tunable superconductivity in magic-angle TBG.
Figure 3: Magnetic-field response of the superconducting states in magic-angle TBG.
Figure 4: Temperature–density phase diagrams of magic-angle TBG at different magnetic fields.
Figure 5: Quantum oscillations in magic-angle TBG at high fields.
Figure 6: Superconductivity in the strong-coupling limit.

Similar content being viewed by others

References

  1. Rajagopal, K. & Wilczek, F. in At the Frontier of Particle Physics (ed. Shifman, M. ) Vol. 3, 2061–2151 (World Scientific, 2001)

    Article  CAS  Google Scholar 

  2. v. Löhneysen, H., Rosch, A., Vojta, M. & Wölfle, P. Fermi-liquid instabilities at magnetic quantum phase transitions. Rev. Mod. Phys. 79, 1015–1075 (2007)

    Article  ADS  CAS  Google Scholar 

  3. Stormer, H. L. Nobel Lecture: The fractional quantum Hall effect. Rev. Mod. Phys. 71, 875–889 (1999)

    Article  ADS  MathSciNet  CAS  MATH  Google Scholar 

  4. Pfleiderer, C. Superconducting phases of f-electron compounds. Rev. Mod. Phys. 81, 1551–1624 (2009)

    Article  ADS  CAS  Google Scholar 

  5. Ishiguro, T ., Yamaji, K. & Saito, G. Organic superconductors 2nd edn (Springer, 1998)

  6. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006)

    Article  ADS  CAS  Google Scholar 

  7. Keimer, B., Kivelson, S. A., Norman, M. R., Uchida, S. & Zaanen, J. From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  8. Stewart, G. R. Superconductivity in iron compounds. Rev. Mod. Phys. 83, 1589–1652 (2011)

    Article  ADS  CAS  Google Scholar 

  9. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

    Article  ADS  CAS  Google Scholar 

  10. Mazurenko, A. et al. A cold-atom Fermi–Hubbard antiferromagnet. Nature 545, 462–466 (2017)

    Article  ADS  CAS  PubMed  Google Scholar 

  11. Wang, Z., Liu, C., Liu, Y. & Wang, J. High-temperature superconductivity in one-unit-cell FeSe films. J. Phys. Condens. Matter 29, 153001 (2017)

    Article  ADS  PubMed  Google Scholar 

  12. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011)

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  13. Suárez Morell, E., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010)

    Article  ADS  CAS  Google Scholar 

  14. Moon, P. & Koshino, M. Energy spectrum and quantum Hall effect in twisted bilayer graphene. Phys. Rev. B 85, 195458 (2012)

    Article  ADS  CAS  Google Scholar 

  15. Fang, S. & Kaxiras, E. Electronic structure theory of weakly interacting bilayers. Phys. Rev. B 93, 235153 (2016)

    Article  ADS  CAS  Google Scholar 

  16. Trambly de Laissardiére, G., Mayou, D. & Magaud, L. Numerical studies of confined states in rotated bilayers of graphene. Phys. Rev. B 86, 125413 (2012)

    Article  ADS  CAS  Google Scholar 

  17. Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  18. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, https://doi.org/10.1038/nature26154 (2018)

  19. Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Continuum model of the twisted graphene bilayer. Phys. Rev. B 86, 155449 (2012)

    Article  ADS  CAS  Google Scholar 

  20. Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016)

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  22. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  23. Tinkham, M. Introduction to Superconductivity (Courier Corporation, 1996)

  24. Saito, Y., Nojima, T. & Iwasa, Y. Highly crystalline 2D superconductors. Nat. Rev. Mater. 2, 16094 (2016)

    Article  ADS  CAS  Google Scholar 

  25. Mott, N. F. Metal-Insulator Transitions (Taylor and Francis, 1990)

  26. Imada, M., Fujimori, A. & Tokura, Y. Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998)

    Article  ADS  CAS  Google Scholar 

  27. Klemm, R. A. & Luther, A. Theory of the upper critical field in layered superconductors. Phys. Rev. B 12, 877–891 (1975)

    Article  ADS  Google Scholar 

  28. Goldman, A. M. in BCS: 50 Years (eds Cooper, L. N. & Feldman, D. ) 255–275 (World Scientific, 2011)

  29. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  30. Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  31. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013)

    Article  ADS  CAS  PubMed  Google Scholar 

  32. Yelland, E. A. et al. Quantum oscillations in the underdoped cuprate YBa2Cu4O8 . Phys. Rev. Lett. 100, 047003 (2008)

    Article  ADS  CAS  PubMed  Google Scholar 

  33. Bangura, A. F. et al. Small Fermi surface pockets in underdoped high temperature superconductors: observation of Shubnikov–de Haas oscillations in YBa2Cu4O8 . Phys. Rev. Lett. 100, 047004 (2008)

    Article  ADS  CAS  PubMed  Google Scholar 

  34. Jaudet, C. et al. de Haas–van Alphen oscillations in the underdoped high-temperature superconductor YBa2Cu3O6.5 . Phys. Rev. Lett. 100, 187005 (2008)

    Article  ADS  CAS  PubMed  Google Scholar 

  35. Kaul, R. K., Kim, Y. B., Sachdev, S. & Senthil, T. Algebraic charge liquids. Nat. Phys. 4, 28–31 (2008)

    Article  CAS  Google Scholar 

  36. Uemura, Y. J. Condensation, excitation, pairing, and superfluid density in high-Tc superconductors: the magnetic resonance mode as a roton analogue and a possible spin-mediated pairing. J. Phys. Condens. Matter 16, S4515–S4540 (2004)

    Article  ADS  CAS  Google Scholar 

  37. Gonzalez-Arraga, L. A., Lado, J. L., Guinea, F. & San-Jose, P. Electrically controllable magnetism in twisted bilayer graphene. Phys. Rev. Lett. 119, 107201 (2017)

    Article  ADS  PubMed  Google Scholar 

  38. Yankowitz, M . et al. Dynamic band-structure tuning of graphene moiré superlattices with pressure. Nature (in the press); preprint at https://arxiv.org/abs/1707.09054 (2017)

  39. Tsuei, C. C. & Kirtley, J. R. Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969 (2000)

    Article  ADS  CAS  Google Scholar 

  40. Nandkishore, R., Levitov, L. S. & Chubukov, A. V. Chiral superconductivity from repulsive interactions in doped graphene. Nat. Phys. 8, 158–163 (2012)

    Article  CAS  Google Scholar 

  41. Uchoa, B. & Castro Neto, A. H. Superconducting states of pure and doped graphene. Phys. Rev. Lett. 98, 146801 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  42. Hosseini, M. V. & Zareyan, M. Unconventional superconducting states of interlayer pairing in bilayer and trilayer graphene. Phys. Rev. B 86, 214503 (2012)

    Article  ADS  CAS  Google Scholar 

  43. Balents, L. Spin liquids in frustrated magnets. Nature 464, 199–208 (2010)

    Article  ADS  CAS  PubMed  Google Scholar 

  44. Ku, M. J. H., Sommer, A. T., Cheuk, L. W. & Zwierlein, M. W. Revealing the superfluid lambda transition in the universal thermodynamics of a unitary fermi gas. Science 335, 563–567 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  45. Qian, T. et al. Absence of a Holelike Fermi surface for the iron-based K0.8Fe1.7Se2 superconductor revealed by angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 106, 187001 (2011)

    Article  ADS  CAS  PubMed  Google Scholar 

  46. Hashimoto, T. et al. Sharp peak of the zero-temperature penetration depth at optimal composition in BaFe2(As1−xPx)2 . Science 336, 1554–1557 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  47. Saito, Y., Kasahara, Y., Ye, J., Iwasa, Y. & Nojima, T. Metallic ground state in an ion-gated two-dimensional superconductor. Science 350, 409–413 (2015)

    Article  ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  48. Ye, J. T. et al. Superconducting dome in a gate-tuned band insulator. Science 338, 1193–1196 (2012)

    Article  ADS  CAS  PubMed  Google Scholar 

  49. Peelaers, H. & Van de Walle, C. G. Effects of strain on band structure and effective masses in MoS2 . Phys. Rev. B 86, 241401(R) (2012)

    Article  ADS  CAS  Google Scholar 

  50. Caviglia, A. D. et al. Electric field control of the LaAlO3/SrTiO3 interface ground state. Nature 456, 624–627 (2008)

    Article  ADS  CAS  PubMed  Google Scholar 

  51. McCollam, A. et al. Quantum oscillations and subband properties of the two-dimensional electron gas at the LaAlO3/SrTiO3 interface. APL Mater. 2, 022102 (2014)

    Article  ADS  CAS  Google Scholar 

  52. Ueno, K. et al. Electric-field-induced superconductivity in an insulator. Nat. Mater. 7, 855–858 (2008)

    Article  ADS  CAS  PubMed  Google Scholar 

  53. Weller, T. E., Ellerby, M., Saxena, S. S., Smith, R. P. & Skipper, N. T. Superconductivity in the intercalated graphite compounds C6Yb and C6Ca. Nat. Phys. 1, 39–41 (2005)

    Article  CAS  Google Scholar 

  54. Valla, T. et al. Anisotropic electron-phonon coupling and dynamical nesting on the graphene sheets in superconducting CaC6 using angle-resolved photoemission spectroscopy. Phys. Rev. Lett. 102, 107007 (2009)

    Article  ADS  CAS  PubMed  Google Scholar 

  55. Shallcross, S., Sharma, S., Kandelaki, E. & Pankratov, O. A. Electronic structure of turbostratic graphene. Phys. Rev. B 81, 165105 (2010)

    Article  ADS  CAS  Google Scholar 

  56. Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017)

    Article  ADS  Google Scholar 

  57. Zhang, F., MacDonald, A. H. & Mele, E. J. Valley Chern numbers and boundary modes in gapped bilayer graphene. Proc. Natl Acad. Sci. USA 110, 10546–10551 (2013)

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  58. Vaezi, A., Liang, Y., Ngai, D. H., Yang, L. & Kim, E.-A. Topological edge states at a tilt boundary in gated multilayer graphene. Phys. Rev. X 3, 021018 (2013)

    Google Scholar 

  59. Ju, L. et al. Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  60. Huang, S. et al. Emergence of topologically protected helical states in minimally twisted bilayer graphene. Preprint at https://arxiv.org/abs/1802.02999 (2018)

  61. Heersche, H. B. et al. Bipolar supercurrent in graphene. Nature 446, 56–59 (2007)

    Article  ADS  CAS  PubMed  Google Scholar 

  62. Calado, V. E. et al. Ballistic Josephson junctions in edge-contacted graphene. Nat. Nanotechnol. 10, 761–764 (2015)

    Article  ADS  CAS  PubMed  Google Scholar 

  63. Bretheau, L. et al. Tunneling spectroscopy of Andreev states in graphene. Nat. Phys. 13, 756–760 (2017)

    Article  CAS  Google Scholar 

  64. Di Bernardo, A. et al. p-wave triggered superconductivity in single-layer graphene on an electron-doped oxide superconductor. Nat. Commun. 8, 14024 (2017)

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  65. Perconte, D. et al. Tunable Klein-like tunnelling of high-temperature superconducting pairs into graphene. Nat. Phys. 14, 25–29 (2018)

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We acknowledge discussions with R. Ashoori, S. Carr, R. Comin, L. Fu, P. A. Lee, L. Levitov, K. Rajagopal, S. Todadri, A. Vishwanath and M. Zwierlein. This work was primarily supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4541 and the STC Center for Integrated Quantum Materials (NSF grant number DMR-1231319) for device fabrication, transport measurements and data analysis (Y.C., P.J.-H.), and theoretical calculations (S.F.). Data analysis by V.F. was supported by AFOSR grant number FA9550-16-1-0382. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan and JSPS KAKENHI grant numbers JP15K21722 and JP25106006. This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities, supported by the NSF (DMR-0819762), and of Harvard’s Center for Nanoscale Systems, supported by the NSF (ECS-0335765). E.K. acknowledges additional support by ARO MURI award W911NF-14-0247.

Author information

Authors and Affiliations

Authors

Contributions

Y.C. fabricated samples and performed transport measurements. Y.C., V.F. and P.J.-H. performed data analysis and discussed the results. P.J.-H. supervised the project. S.F. and E.K. provided numerical calculations. K.W. and T.T. provided hexagonal boron nitride samples. Y.C., V.F. and P.J.-H. co-wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to Yuan Cao or Pablo Jarillo-Herrero.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks E. Mele, J. Robinson and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Figure 1 Evidence of phase-coherent transport in superconducting magic-angle TBG.

a, b, Differential resistance dV/dI versus bias current I and perpendicular field B, at two different charge densities n, corresponding to those in Fig. 3a. Periodic oscillations are observed in the critical current (identified approximately as the position of the bright peaks in dV/dI). c, d, Simulations intended to reproduce qualitatively the behaviour observed in a and b.

Extended Data Figure 2 Supplementary quantum oscillation data.

a, b, Quantum oscillations in device M1 (a; θ = 1.16°, data shown for Rxx) and device D1 (b; θ = 1.08°, data shown for the two-probe conductance G2). The first derivative with respect to the gate-defined charge density n has been taken in both cases to enhance the colour contrast. Both devices exhibit a Landau fan that emerges from the half-filling state −ns/2 and have a Landau level sequence of −2, −4, −6, −8, …, consistent with the results shown in Fig. 5. By comparison, the Landau fans that start from charge neutrality have a sequence of −4, −8, −12, …

Extended Data Figure 3 Low-field Hall effect in magic-angle TBG.

a, b, Low-field Hall effect for devices M1 (a) and M2 (b). The Hall density is plotted as a function of the total charge density induced by the gate (n), measured at temperatures from 0.4 K to 31.8 K. Coloured vertical bars correspond to densities of −ns, −ns/2, ns/2 and ns for the two samples. Dashed lines are the expected Hall density if the offset given in the corresponding formula is considered.

Supplementary information

Band structure twisted bilayer graphene – animation

This video shows the evolution of the band structure of twisted bilayer graphene as a function of twist angle, from 3 degrees to 0.8 degrees. (MOV 667 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cao, Y., Fatemi, V., Fang, S. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018). https://doi.org/10.1038/nature26160

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature26160

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing