Article | Published:

Unconventional superconductivity in magic-angle graphene superlattices

Nature volume 556, pages 4350 (05 April 2018) | Download Citation

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.

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References

  1. 1.

    & in At the Frontier of Particle Physics (ed. ) Vol. 3, 2061–2151 (World Scientific, 2001)

  2. 2.

    v. , , & Fermi-liquid instabilities at magnetic quantum phase transitions. Rev. Mod. Phys. 79, 1015–1075 (2007)

  3. 3.

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

  4. 4.

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

  5. 5.

    ., & Organic superconductors 2nd edn (Springer, 1998)

  6. 6.

    , & Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006)

  7. 7.

    , , , & From quantum matter to high-temperature superconductivity in copper oxides. Nature 518, 179–186 (2015)

  8. 8.

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

  9. 9.

    , & Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

  10. 10.

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

  11. 11.

    , , & High-temperature superconductivity in one-unit-cell FeSe films. J. Phys. Condens. Matter 29, 153001 (2017)

  12. 12.

    & Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011)

  13. 13.

    , , , & Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010)

  14. 14.

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

  15. 15.

    & Electronic structure theory of weakly interacting bilayers. Phys. Rev. B 93, 235153 (2016)

  16. 16.

    , & Numerical studies of confined states in rotated bilayers of graphene. Phys. Rev. B 86, 125413 (2012)

  17. 17.

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

  18. 18.

    et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, (2018)

  19. 19.

    , & Continuum model of the twisted graphene bilayer. Phys. Rev. B 86, 155449 (2012)

  20. 20.

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

  21. 21.

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

  22. 22.

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

  23. 23.

    Introduction to Superconductivity (Courier Corporation, 1996)

  24. 24.

    , & Highly crystalline 2D superconductors. Nat. Rev. Mater. 2, 16094 (2016)

  25. 25.

    Metal-Insulator Transitions (Taylor and Francis, 1990)

  26. 26.

    , & Metal-insulator transitions. Rev. Mod. Phys. 70, 1039–1263 (1998)

  27. 27.

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

  28. 28.

    in BCS: 50 Years (eds & ) 255–275 (World Scientific, 2011)

  29. 29.

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

  30. 30.

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

  31. 31.

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

  32. 32.

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

  33. 33.

    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)

  34. 34.

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

  35. 35.

    , , & Algebraic charge liquids. Nat. Phys. 4, 28–31 (2008)

  36. 36.

    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)

  37. 37.

    , , & Electrically controllable magnetism in twisted bilayer graphene. Phys. Rev. Lett. 119, 107201 (2017)

  38. 38.

    . et al. Dynamic band-structure tuning of graphene moiré superlattices with pressure. Nature (in the press); preprint at (2017)

  39. 39.

    & Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969 (2000)

  40. 40.

    , & Chiral superconductivity from repulsive interactions in doped graphene. Nat. Phys. 8, 158–163 (2012)

  41. 41.

    & Superconducting states of pure and doped graphene. Phys. Rev. Lett. 98, 146801 (2007)

  42. 42.

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

  43. 43.

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

  44. 44.

    , , & Revealing the superfluid lambda transition in the universal thermodynamics of a unitary fermi gas. Science 335, 563–567 (2012)

  45. 45.

    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)

  46. 46.

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

  47. 47.

    , , , & Metallic ground state in an ion-gated two-dimensional superconductor. Science 350, 409–413 (2015)

  48. 48.

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

  49. 49.

    & Effects of strain on band structure and effective masses in MoS2. Phys. Rev. B 86, 241401(R) (2012)

  50. 50.

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

  51. 51.

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

  52. 52.

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

  53. 53.

    , , , & Superconductivity in the intercalated graphite compounds C6Yb and C6Ca. Nat. Phys. 1, 39–41 (2005)

  54. 54.

    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)

  55. 55.

    , , & Electronic structure of turbostratic graphene. Phys. Rev. B 81, 165105 (2010)

  56. 56.

    & Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017)

  57. 57.

    , & Valley Chern numbers and boundary modes in gapped bilayer graphene. Proc. Natl Acad. Sci. USA 110, 10546–10551 (2013)

  58. 58.

    , , , & Topological edge states at a tilt boundary in gated multilayer graphene. Phys. Rev. X 3, 021018 (2013)

  59. 59.

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

  60. 60.

    et al. Emergence of topologically protected helical states in minimally twisted bilayer graphene. Preprint at (2018)

  61. 61.

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

  62. 62.

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

  63. 63.

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

  64. 64.

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

  65. 65.

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

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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.

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Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Yuan Cao
    • , Valla Fatemi
    •  & Pablo Jarillo-Herrero
  2. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    • Shiang Fang
    •  & Efthimios Kaxiras
  3. National Institute for Materials Science, Namiki 1-1, Tsukuba, Ibaraki 305-0044, Japan

    • Kenji Watanabe
    •  & Takashi Taniguchi
  4. John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA

    • Efthimios Kaxiras

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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.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Yuan Cao or Pablo Jarillo-Herrero.

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.

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Videos

  1. 1.

    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.

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https://doi.org/10.1038/nature26160

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