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Superconductivity and strong correlations in moiré flat bands

Nature Physics volume 16, pages 725–733 (2020)Cite this article

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Abstract

Strongly correlated systems can give rise to spectacular phenomenology, from high-temperature superconductivity to the emergence of states of matter characterized by long-range quantum entanglement. Low-density flat-band systems play a vital role because the energy range of the band is so narrow that the Coulomb interactions dominate over kinetic energy, putting these materials in the strongly-correlated regime. Experimentally, when a band is narrow in both energy and momentum, its filling may be tuned in situ across the whole range, from empty to full. Recently, one particular flat-band system—that of van der Waals heterostructures, such as twisted bilayer graphene—has exhibited strongly correlated states and superconductivity, but it is still not clear to what extent the two are linked. Here, we review the status and prospects for flat-band engineering in van der Waals heterostructures and explore how both phenomena emerge from the moiré flat bands.

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Fig. 1: Three classes of flat bands in van der Waals heterostructures.
Fig. 2: Correlation-driven phases in Hofstadter flat bands.
Fig. 3: Substrate tuning of electronic structure in twisted bilayer graphene.
Fig. 4: Superconductivity in twisted bilayer graphene.
Fig. 5: Proliferation of zero-field narrow-band systems.

References

  1. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-Dimensional Magnetotransport in the Extreme Quantum Limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

    ADS  Google Scholar 

  2. Wen, X.-G. Topological orders and edge excitations in fractional quantum Hall states. Adv. Phys 44, 405–473 (1995).

    ADS  Google Scholar 

  3. Bednorz, J. G. & Müller, K. A. Possible highTc superconductivity in the Ba-La-Cu-O system. Z. Phys. B 64, 189–193 (1986).

    ADS  Google Scholar 

  4. Fradkin, E. & Kivelson, S. A. Ineluctable complexity. Nat. Phys 8, 864–866 (2012).

    Google Scholar 

  5. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol 5, 722–726 (2010).

    ADS  Google Scholar 

  6. Wang, L. et al. One-Dimensional Electrical Contact to a Two-Dimensional Material. Science 342, 614–617 (2013).

    ADS  Google Scholar 

  7. Kim, K. et al. van der Waals Heterostructures with High Accuracy Rotational Alignment. Nano Lett. 16, 1989–1995 (2016).

    ADS  Google Scholar 

  8. Hofstadter, D. R. Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239–2249 (1976).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  11. Hunt, B. et al. Massive Dirac Fermions and Hofstadter Butterfly in a van der Waals Heterostructure. Science 340, 1427–1430 (2013).

    ADS  Google Scholar 

  12. Wang, L. et al. Evidence for a fractional fractal quantum Hall effect in graphene superlattices. Science 350, 1231–1234 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  13. Spanton, E. M. et al. Observation of fractional Chern insulators in a van der Waals heterostructure. Science 360, 62–66 (2018).

    ADS  Google Scholar 

  14. Cheng, B. et al. Fractional and Symmetry-Broken Chern Insulators in Tunable Moiré Superlattices. Nano Lett. 19, 4321–4326 (2019).

    ADS  Google Scholar 

  15. 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).

    ADS  Google Scholar 

  16. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    ADS  Google Scholar 

  17. Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys 15, 237–241 (2019).

    Google Scholar 

  18. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe 2/WS 2 moiré superlattices. Nature 579, 359–363 (2020).

    ADS  Google Scholar 

  19. Wang, L. et al. Magic continuum in twisted bilayer WSe2. Preprint at https://arxiv.org/abs/1910.12147 (2019).

  20. Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).

    ADS  Google Scholar 

  21. Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007).

    ADS  Google Scholar 

  22. 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).

    ADS  Google Scholar 

  23. Bistritzer, R. & MacDonald, A. H. Moiré butterflies in twisted bilayer graphene. Phys. Rev. B 84 (2011).

  24. Barkeshli, M. & Qi, X.-L. Topological Nematic States and Non-Abelian Lattice Dislocations. Phys. Rev. X 2, 031013 (2012).

    Google Scholar 

  25. Knapp, C., Spanton, E. M., Young, A. F., Nayak, C. & Zaletel, M. P. Fractional Chern insulator edges and layer-resolved lattice contacts. Phys. Rev. B 99, 081114 (2019).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  27. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    ADS  Google Scholar 

  28. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    ADS  Google Scholar 

  29. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    ADS  Google Scholar 

  30. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    ADS  Google Scholar 

  31. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

    ADS  Google Scholar 

  32. Song, J. C. W., Samutpraphoot, P. & Levitov, L. S. Topological Bloch bands in graphene superlattices. Proc. Natl Acad. Sci. USA 112, 10879–10883 (2015).

    ADS  MathSciNet  MATH  Google Scholar 

  33. Po, H. C., Zou, L., Vishwanath, A. & Senthil, T. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene. Phys. Rev. X 8, 031089 (2018).

    Google Scholar 

  34. Zou, L., Po, H. C., Vishwanath, A. & Senthil, T. Band structure of twisted bilayer graphene: Emergent symmetries, commensurate approximants, and Wannier obstructions. Physical Review B 98, 085435 (2018).

    ADS  Google Scholar 

  35. Liu, J., Liu, J. & Dai, X. Pseudo Landau level representation of twisted bilayer graphene: band topology and implications on the correlated insulating phase. Phys. Rev. B 99, 155415 (2019).

    ADS  Google Scholar 

  36. Xie, M. & MacDonald, A. H. On the nature of the correlated insulator states in twisted bilayer graphene. Phys. Rev. Lett. 124, 097601 (2020).

    ADS  Google Scholar 

  37. Kang, J. & Vafek, O. Strong coupling phases of partially filled twisted bilayer graphene narrow bands. Phys. Rev. Lett. 122, 246401 (2019).

    ADS  Google Scholar 

  38. Liu, S., Khalaf, E., Lee, J. Y. & Vishwanath, A. Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality. Preprint at https://arxiv.org/abs/1905.07409 (2019).

  39. Liu, J. & Dai, X. Correlated insulating states and the quantum anomalous Hall phenomena at all integer fillings in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1911.03760 (2020).

  40. Wu, F. & Sarma, S. D. Collective excitations of quantum anomalous hall ferromagnets in twisted bilayer graphene. Phys. Rev. Lett. 124, 046403 (2020).

    ADS  Google Scholar 

  41. Zhang, Y., Jiang, K., Wang, Z. & Zhang, F. Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: a Hartree-Fock study. Preprint at https://arxiv.org/abs/2001.02476 (2020).

  42. Bultinck, N. et al. Ground state and hidden symmetry of magic angle graphene at even integer filling. Preprint at https://arxiv.org/abs/1911.02045 (2019).

  43. Dodaro, J. F., Kivelson, S. A., Schattner, Y., Sun, X. Q. & Wang, C. Phases of a phenomenological model of twisted bilayer graphene. Phys. Rev. B 98, 075154 (2018).

    ADS  Google Scholar 

  44. Xu, C. & Balents, L. Topological superconductivity in twisted multilayer graphene. Phys. Rev. Lett. 121, 087001 (2018).

    ADS  Google Scholar 

  45. Guinea, F. & Walet, N. R. Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers. Proc. Natl Acad. Sci. USA 115, 13174–13179 (2018).

    ADS  Google Scholar 

  46. Liu, C.-C., Zhang, L.-D., Chen, W.-Q. & Yang, F. Chiral Spin Density Wave and d+ i d Superconductivity in the Magic-Angle-Twisted Bilayer Graphene. Phys. Rev. Lett. 121, 217001 (2018).

    ADS  Google Scholar 

  47. Guo, H., Zhu, X., Feng, S. & Scalettar, R. T. Pairing symmetry of interacting fermions on a twisted bilayer graphene superlattice. Phys. Rev. B 97, 235453 (2018).

    ADS  Google Scholar 

  48. Lian, B., Wang, Z. & Bernevig, B. A. Twisted bilayer graphene: a phonon-driven superconductor. Phys. Rev. Lett. 122, 257002 (2019).

    ADS  Google Scholar 

  49. Wu, F., MacDonald, A. H. & Martin, I. Theory of phonon-mediated superconductivity in twisted bilayer graphene. Phys. Rev. Lett. 121, 257001 (2018).

    ADS  Google Scholar 

  50. Peltonen, T. J., Ojajärvi, R. & Heikkilä, T. T. Mean-field theory for superconductivity in twisted bilayer graphene. Phys. Rev. B 98, 220504 (2018).

    ADS  Google Scholar 

  51. Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011).

    ADS  Google Scholar 

  52. Stepanov, P. et al. The interplay of insulating and superconducting orders in magic-angle graphene bilayers. Preprint at https://arxiv.org/abs/1911.09198 (2019).

  53. Arora, H. S. et al. Superconductivity without insulating states in twisted bilayer graphene stabilized by monolayer Wse2. Preprint at https://arxiv.org/abs/2002.03003 (2020).

  54. Liu, X. et al. Spin-polarized Correlated Insulator and Superconductor in Twisted Double Bilayer Graphene. Preprint at https://arxiv.org/abs/1903.08130 (2019).

  55. Codecido, E. et al. Correlated insulating and superconducting states in twisted bilayer graphene below the magic angle. Sci. Adv. 5, eaaw9770 (2019).

  56. Moriyama, S. et al. Observation of superconductivity in bilayer graphene/hexagonal boron nitride superlattices. Preprint at https://arxiv.org/abs/1901.09356 (2019).

  57. Chen, G. et al. Signatures of tunable superconductivity in a trilayer graphene moiré superlattice. Nature 572, 215–219 (2019).

    Google Scholar 

  58. He, M. et al. Tunable correlation-driven symmetry breaking in twisted double bilayer graphene. Preprint at https://arxiv.org/abs/2002.08904 (2020).

  59. Choi, Y. et al. Electronic correlations in twisted bilayer graphene near the magic angle. Nat. Phys 15, 1174–1180 (2019).

    Google Scholar 

  60. Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).

    ADS  Google Scholar 

  61. Xie, Y. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019).

    ADS  Google Scholar 

  62. Uri, A. et al. Mapping the twist angle and unconventional Landau levels in magic angle graphene. Nature 581, 47–52 (2020).

    ADS  Google Scholar 

  63. Zondiner, U. et al. Cascade of phase transitions and dirac revivals in magic angle graphene. Preprint at https://arxiv.org/abs/1912.06150 (2019).

  64. Wong, D. et al. Cascade of transitions between the correlated electronic states of magic-angle twisted bilayer graphene. Preprint at https://arxiv.org/abs/1912.06145 (2019).

  65. McGilly, L. J. et al. Seeing moiré superlattices. Preprint at https://arxiv.org/abs/1912.06629 (2019).

  66. Utama, M. I. B. et al. Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Preprint at https://arxiv.org/abs/1912.00587 (2019).

  67. Saito, Y., Ge, J., Watanabe, K., Taniguchi, T. & Young, A. F. Decoupling superconductivity and correlated insulators in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1911.13302 (2019).

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

    ADS  Google Scholar 

  69. Kang, J. & Vafek, O. Symmetry, maximally localized Wannier States, and a low-energy model for twisted bilayer graphene narrow bands. Phys. Rev. X 8, 031088 (2018).

    Google Scholar 

  70. Koshino, M. et al. Maximally localized Wannier orbitals and the extended Hubbard Model for twisted bilayer graphene. Phys. Rev. X 8, 031087 (2018).

    Google Scholar 

  71. Carr, S., Fang, S., Po, H. C., Vishwanath, A. & Kaxiras, E. Derivation of Wannier orbitals and minimal-basis tight-binding Hamiltonians for twisted bilayer graphene: first-principles approach. Phys. Rev. Res 1, 033072 (2019).

    Google Scholar 

  72. Goodwin, Z. A. H., Corsetti, F., Mostofi, A. A. & Lischner, J. Twist-angle sensitivity of electron correlations in moiré graphene bilayers. Phys. Rev. B 100, 121106 (2019).

    ADS  Google Scholar 

  73. Pizarro, J. M., Rösner, M., Thomale, R., Valentí, R. & Wehling, T. O. Internal screening and dielectric engineering in magic-angle twisted bilayer graphene. Phys. Rev. B 100, 161102 (2019).

    ADS  Google Scholar 

  74. Liu, X. et al. Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening. Preprint at https://arxiv.org/abs/2003.11072 (2020).

  75. Tsuei, C. C. & Kirtley, J. R. Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000).

    ADS  Google Scholar 

  76. Polshyn, H. et al. Large linear-in-temperature resistivity in twisted bilayer graphene. Nat. Phys 15, 1011–1016 (2019).

    Google Scholar 

  77. Cao, Y. et al. Strange metal in magic-angle graphene with near Planckian dissipation. Phys. Rev. Lett. 124, 076801 (2020).

    ADS  Google Scholar 

  78. Cao, Y. et al. Electric field tunable correlated states and magnetic phase transitions in twisted bilayer-bilayer graphene. Nature https://doi.org/10.1038/s41586-020-2260-6 (2020).

  79. Burg, G. W. et al. Correlated insulating states in twisted double bilayer graphene. Phys. Rev. Lett. 123, 197702 (2019).

    ADS  Google Scholar 

  80. Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys https://doi.org/10.1038/s41567-020-0825-9 (2020).

    Article  Google Scholar 

  81. Zhang, Z. et al. Flat bands in small angle twisted bilayer WSe2. Preprint at https://arxiv.org/abs/1910.13068 (2019).

  82. Zaletel, M. P., Mong, R. S. K., Pollmann, F. & Rezayi, E. H. Infinite density matrix renormalization group for multicomponent quantum Hall systems. Phys. Rev. B 91, 045115 (2015).

    ADS  Google Scholar 

  83. Carr, S., Fang, S., Jarillo-Herrero, P. & Kaxiras, E. Pressure dependence of the magic twist angle in graphene superlattices. Phys. Rev. B 98, 085144 (2018).

    ADS  Google Scholar 

  84. Chittari, B. L., Leconte, N., Javvaji, S. & Jung, J. Pressure induced compression of flatbands in twisted bilayer graphene. Electron. Struct 1, 015001 (2018).

    Google Scholar 

  85. Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).

    ADS  Google Scholar 

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Acknowledgements

We thank K. Hejazi and C. Liu for assistance with preparation of Fig. 1c. L.B. acknowledges support by the NSF CMMT program under award no. DMR-1818533; the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-FG02-08ER46524 and the UCSB NSF Quantum Foundry through Q-AMASE-i program award no. DMR-1906325. A.F.Y. acknowledges the support of the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0020043 and the UCSB NSF Quantum Foundry through Q-AMASE-i program award no. DMR-1906325. C.R.D. acknowledges the support of the Pro-QM EFRC funded by the US Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0019443. D.K.E. acknowledges support from the Ministry of Economy and Competitiveness of Spain through the ‘Severo Ochoa’ program for Centres of Excellence in R&D (SE5-0522), Fundació Privada Cellex, Fundació Privada Mir-Puig, the Generalitat de Catalunya through the CERCA program, the H2020 Programme under grant agreement no. 820378, Project: 2D·SIPC and the La Caixa Foundation.

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Authors and Affiliations

  1. Kavli Institute of Theoretical Physics, University of California, Santa Barbara, CA, USA

    Leon Balents

  2. Canadian Institute for Advanced Research, Toronto, Ontario, Canada

    Leon Balents

  3. Department of Physics, Columbia University, New York, NY, USA

    Cory R. Dean

  4. ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona, Spain

    Dmitri K. Efetov

  5. Department of Physics, University of California, Santa Barbara, CA, USA

    Andrea F. Young

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Balents, L., Dean, C.R., Efetov, D.K. et al. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020). https://doi.org/10.1038/s41567-020-0906-9

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