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Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene

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Abstract

Twisted bilayer graphene has a rich phase diagram, including superconductivity. Recently, an unexpected discovery has been the observation of superconductivity in non-twisted graphene bilayers and trilayers. In this Perspective, we give an overview of the search for uncommon phases in non-twisted graphene systems. We first contextualize these recent results within earlier work in the field, before examining the new experimental findings. Finally, we analyse the numerous theoretical models that study the underlying physical processes in these systems.

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Fig. 1: Superconductivity in bilayer graphene.
Fig. 2: Superconductivity in bilayer graphene with WSe2.
Fig. 3: Superconductivity in rhombohedral trilayer graphene.
Fig. 4: Uemura plot.
Fig. 5: Calculated band structures.
Fig. 6: Superconducting order parameters.

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References

  1. Onnes, H. K. The superconductivity of mercury. Comm. Phys. Lab. Univ. Leiden 122, 124 (1911).

    Google Scholar 

  2. Ginzburg, V. L. & Landau, L. D. On the theory of superconductivity. Sov. Phys. JETP 20, 1064 (1950).

    Google Scholar 

  3. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957).

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Stewart, G. R. Heavy-fermion systems. Rev. Mod. Phys. 56, 755–787 (1984).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774–778 (2022).

    Article  ADS  Google Scholar 

  10. Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F. Superconductivity in rhombohedral trilayer graphene. Nature 598, 434–438 (2021).

    Article  ADS  Google Scholar 

  11. Zhang, Y. et al. Enhanced superconductivity in spin–orbit proximitized bilayer graphene. Nature 613, 268–273 (2023).

    Article  ADS  Google Scholar 

  12. Guinea, F. Superconductivity and other phases in graphene multilayers, without twists. J. Club Condens. Matter Phys. https://doi.org/10.36471/JCCM_November_2021_01 (2021).

    Article  Google Scholar 

  13. McClure, J. W. Electron energy band structure and electronic properties of rhombohedral graphite. Carbon 7, 425 (1969).

    Article  Google Scholar 

  14. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

    Article  ADS  Google Scholar 

  15. Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005).

    Article  ADS  Google Scholar 

  16. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).

    Article  ADS  Google Scholar 

  17. Gonzalez, J., Guinea, F. & Vozmediano, M. Non-fermi liquid behavior of electrons in the half-filled honeycomb lattice (a renormalization group approach). Nucl. Phys. B 424, 595 (1994).

    Article  ADS  Google Scholar 

  18. Elias, D. C. et al. Dirac cones reshaped by interaction effects in suspended graphene. Nat. Phys. 7, 701 (2011).

    Article  Google Scholar 

  19. Zhang, Y. et al. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 96, 136806 (2006).

    Article  ADS  Google Scholar 

  20. Goerbig, M. O. Electronic properties of graphene in a strong magnetic field. Rev. Mod. Phys. 83, 1193–1243 (2011).

    Article  ADS  Google Scholar 

  21. McCann, E. & Fal’ko, V. I. Landau-level degeneracy and quantum hall effect in a graphite bilayer. Phys. Rev. Lett. https://doi.org/10.1103/physrevlett.96.086805 (2006).

    Article  Google Scholar 

  22. Koshino, M. & McCann, E. The electronic properties of bilayer graphene. Rep. Prog. Phys. 73, 057503 (2013).

    Google Scholar 

  23. Nilsson, J., Castro Neto, A. H., Peres, N. M. R. & Guinea, F. Electron–electron interactions and the phase diagram of a graphene bilayer. Phys. Rev. B 73, 214418 (2006).

    Article  ADS  Google Scholar 

  24. Min, H., Borghi, G., Polini, M. & MacDonald, A. H. Pseudospin magnetism in graphene. Phys. Rev. B 77, 041407 (2008).

    Article  ADS  Google Scholar 

  25. Vafek, O. Interacting fermions on the honeycomb bilayer: from weak to strong coupling. Phys. Rev. B 82, 205106 (2010).

    Article  ADS  Google Scholar 

  26. Nandkishore, R. & Levitov, L. Dynamical screening and excitonic instability in bilayer graphene. Phys. Rev. Lett. 104, 156803 (2010).

    Article  ADS  Google Scholar 

  27. Lemonik, Y., Aleiner, I. & Fal’ko, V. I. Competing nematic, antiferromagnetic, and spin-flux orders in the ground state of bilayer graphene. Phys. Rev. B 85, 245451 (2012).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  29. McChesney, J. L. et al. Extended van Hove singularity and superconducting instability in doped graphene. Phys. Rev. Lett. 104, 136803 (2010).

    Article  ADS  Google Scholar 

  30. Koshino, M. Interlayer screening effect in graphene multilayers with aba and abc stacking. Phys. Rev. B 81, 125304 (2010).

    Article  ADS  Google Scholar 

  31. Armitage, N. P., Mele, E. J. & Vishwanath, A. Weyl and Dirac semimetals in three-dimensional solids. Rev. Mod. Phys. 90, 015001 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  32. Pamuk, B., Baima, J., Mauri, F. & Calandra, M. Magnetic gap opening in rhombohedral-stacked multilayer graphene from first principles. Phys. Rev. B 95, 075422 (2017).

    Article  ADS  Google Scholar 

  33. Zhang, F., Sahu, B., Min, H. & MacDonald, A. H. Band structure of abc-stacked graphene trilayers. Phys. Rev. B 82, 035409 (2010).

    Article  ADS  Google Scholar 

  34. Slizovskiy, S., McCann, E., Koshino, M. & Fal’ko, V. I. Films of rhombohedral graphite as two-dimensional topological semimetals. Commun. Phys. 2, 164 (2019).

    Article  Google Scholar 

  35. Guinea, F., Castro Neto, A. H. & Peres, N. M. R. Electronic states and Landau levels in graphene stacks. Phys. Rev. B 73, 245426 (2006).

    Article  ADS  Google Scholar 

  36. Arovas, D. P. & Guinea, F. Stacking faults, bound states, and quantum Hall plateaus in crystalline graphite. Phys. Rev. B 78, 245416 (2008).

    Article  ADS  Google Scholar 

  37. Zhang, F., Jung, J., Fiete, G. A., Niu, Q. & MacDonald, A. H. Spontaneous quantum Hall states in chirally stacked few-layer graphene systems. Phys. Rev. Lett. 106, 156801 (2011).

    Article  ADS  Google Scholar 

  38. Muten, J. H., Copeland, A. J. & McCann, E. Exchange interaction, disorder, and stacking faults in rhombohedral graphene multilayers. Phys. Rev. B 104, 035404 (2021).

    Article  ADS  Google Scholar 

  39. Garcia-Ruiz, A., Slizovskiy, S. & Fal’ko, V. I. Flat bands for electrons in rhombohedral graphene multilayers with a twin boundary. Adv. Mater. Interfaces https://doi.org/10.1002/admi.202202221 (2023).

    Article  Google Scholar 

  40. Kopnin, N. B., Heikkilä, T. T. & Volovik, G. E. High-temperature surface superconductivity in topological flat-band systems. Phys. Rev. B 83, 220503 (2011).

    Article  ADS  Google Scholar 

  41. Kopnin, N. B., Ijäs, M., Harju, A. & Heikkilä, T. T. High-temperature surface superconductivity in rhombohedral graphite. Phys. Rev. B 87, 140503 (2013).

    Article  ADS  Google Scholar 

  42. Volovik, G. E. Graphite, graphene, and the flat band superconductivity. JETP Lett. 107, 516 (2018).

    Article  ADS  Google Scholar 

  43. Dresselhaus, M. S. & Dresselhaus, G. Intercalation compounds of graphite. Adv. Phys. 51, 1–186 (2002).

    Article  ADS  Google Scholar 

  44. Smith, R. P. et al. Superconductivity in graphite intercalation compounds. Phys. C Supercond. Appl. 514, 50–58 (2015).

    Article  ADS  Google Scholar 

  45. Takada, Y. Theory of superconductivity in graphite intercalation compounds. In Reference Module in Materials Science and Materials Engineering (Elsevier, 2016); https://doi.org/10.1016/b978-0-12-803581-8.00774-8.

  46. Rosseinsky, M. J. et al. Superconductivity at 28 K in RbxC60. Phys. Rev. Lett. 66, 2830–2832 (1991).

    Article  ADS  Google Scholar 

  47. Kelty, S. P., Chen, C.-C. & Lieber, C. M. Superconductivity at 30 K in caesium-doped C60. Nature 352, 223–225 (1991).

    Article  ADS  Google Scholar 

  48. Chakravarty, S. & Kivelson, S. Superconductivity of doped fullerenes. Europhys. Lett. 16, 751–756 (1991).

    Article  ADS  Google Scholar 

  49. Hebard, A. F. et al. Superconductivity at 18 K in potassium-doped C60. Nature 350, 600–601 (1991).

    Article  ADS  Google Scholar 

  50. Hebard, A. F. Superconductivity in doped fullerenes. Phys. Today 45, 26 (November 1992).

    Article  Google Scholar 

  51. Capone, M., Fabrizio, M., Castellani, C. & Tosatti, E. Strongly correlated superconductivity. Science 296, 2364–2366 (2002).

    Article  ADS  Google Scholar 

  52. Nomura, Y., Sakai, S., Capone, M. & Arita, R. Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles. Sci. Adv. https://doi.org/10.1126/sciadv.1500568 (2015).

    Article  Google Scholar 

  53. Calandra, M. & Mauri, F. Theoretical explanation of superconductivity in C6Ca. Phys. Rev. Lett. 95, 237002 (2005).

    Article  ADS  Google Scholar 

  54. Wang, G., Datars, W. R. & Ummat, P. K. Fermi surface of the stage-1 potassium graphite intercalation compound. Phys. Rev. B 44, 8294–8300 (1991).

    Article  ADS  Google Scholar 

  55. Cantaluppi, A. et al. Pressure tuning of light-induced superconductivity in K3C60. Nat. Phys. 14, 837–841 (2018).

    Article  Google Scholar 

  56. Haddon, R., Brus, L. & Raghavachari, K. Electronic structure and bonding in icosahedral C60. Chem. Phys. Lett. 125, 459–464 (1986).

    Article  ADS  Google Scholar 

  57. Erwin, S. C. & Pickett, W. E. Theoretical fermi-surface properties and superconducting parameters for K3C60. Science 254, 842–845 (1991).

    Article  ADS  Google Scholar 

  58. Weitz, R. T., Allen, M. T., Feldman, B. E., Martin, J. & Yacoby, A. Coulomb-driven broken-symmetry states in doubly gated suspended bilayer graphene. Science 330, 812 (2010).

    Article  ADS  Google Scholar 

  59. Freitag, F., Trbovic, J., Weiss, M. & Schönenberger, C. Spontaneously gapped ground state in suspended bilayer graphene. Phys. Rev. Lett. 108, 076602 (2012).

    Article  ADS  Google Scholar 

  60. Bao, W. et al. Minimum conductivity and evidence for phase transitions in ultra-clean bilayer graphene. Proc. Natl Acad. Sci. USA 109, 10802 (2012).

    Article  ADS  Google Scholar 

  61. Varlet, A. et al. Anomalous sequence of quantum Hall liquids revealing a tunable Lifshitz transition in bilayer graphene. Phys. Rev. Lett. 113, 116602 (2014).

    Article  ADS  Google Scholar 

  62. Lee, K. et al. Chemical potential and quantum Hall ferromagnetism in bilayer graphene. Science 345, 58–61 (2014).

    Article  ADS  Google Scholar 

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

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

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  67. San-Jose, P., Gorbachev, R. V., Geim, A. K., Novoselov, K. S. & Guinea, F. Stacking boundaries and transport in bilayer graphene. Nano Lett. 14, 2052 (2014).

    Article  ADS  Google Scholar 

  68. Lee, Y. et al. Competition between spontaneous symmetry breaking and single-particle gaps in trilayer graphene. Nat. Commun. 5, 5656 (2014).

    Article  ADS  Google Scholar 

  69. Zibrov, A. A. et al. Emergent Dirac gullies and gully-symmetry-breaking quantum Hall states in ABA trilayer graphene. Phys. Rev. Lett. 121, 167601 (2018).

    Article  ADS  Google Scholar 

  70. Nam, Y., Ki, D.-K., Koshino, M., McCann, E. & Morpurgo, A. F. Interaction-induced insulating state in thick multilayer graphene. 2D Mater. 3, 045014 (2016).

    Article  Google Scholar 

  71. Nam, Y., Ki, D.-K., Soler-Delgado, D. & Morpurgo, A. F. A family of finite-temperature electronic phase transitions in graphene multilayers. Science 362, 324–328 (2018).

    Article  ADS  Google Scholar 

  72. Kerelsky, A. et al. Moiréless correlations in ABCA graphene. Proc. Natl Acad. Sci. USA 118, e2017366118 (2021).

    Article  Google Scholar 

  73. Esquinazi, P. Invited review: graphite and its hidden superconductivity. Pap. Phys. 5, 050007 (2013).

    Article  Google Scholar 

  74. Esquinazi, P., Heikkilä, T. T., Lysogorskiy, Y. V., Tayurskii, D. A. & Volovik, G. E. On the superconductivity of graphite interfaces. JETP Lett. 100, 336 (2014).

    Article  ADS  Google Scholar 

  75. Esquinazi, P. D. et al. Evidence for room temperature superconductivity at graphite interfaces. Quantum Stud. Math. Found. 5, 41 (2018).

    Article  Google Scholar 

  76. Esquinazi, P. D. Ordered defects: a roadmap towards room temperature superconductivity and magnetic order. Preprint at https://arxiv.org/abs/1902.07489 (2019).

  77. Scheike, T. et al. Can doping graphite trigger room temperature superconductivity? Evidence for granular high-temperature superconductivity in water-treated graphite powder. Adv. Mater. 24, 5826–5831 (2012).

    Article  Google Scholar 

  78. Layek, S. et al. Possible high temperature superconducting transitions in disordered graphite obtained from room temperature deintercalated KC8. Carbon 201, 667–678 (2023).

    Article  Google Scholar 

  79. Ariskina, R., Stiller, M., Precker, C. E., Böhlmann, W. & Esquinazi, P. D. On the localization of persistent currents due to trapped magnetic flux at the stacking faults of graphite at room temperature. Materials 15, 3422 (2022).

    Article  ADS  Google Scholar 

  80. Rousset-Zenou, R. et al. Hidden granular superconductivity above 500 K in off-the-shelf graphite materials. Preprint at https://arxiv.org/abs/2207.09149 (2022).

  81. Yan, K., Peng, H., Zhou, Y., Li, H. & Liu, Z. Formation of bilayer bernal graphene: layer-by-layer epitaxy via chemical vapor deposition. Nano Lett. 11, 1106–1110 (2011).

    Article  ADS  Google Scholar 

  82. Lee, S., Lee, K. & Zhong, Z. Wafer scale homogeneous bilayer graphene films by chemical vapor deposition. Nano Lett. 10, 4702–4707 (2010).

    Article  ADS  Google Scholar 

  83. Zondiner, U. et al. Cascade of phase transitions and dirac revivals in magic-angle graphene. Nature 582, 203–208 (2020).

    Article  ADS  Google Scholar 

  84. Wong, D. et al. Cascade of electronic transitions in magic-angle twisted bilayer graphene. Nature 582, 198–202 (2020).

    Article  ADS  Google Scholar 

  85. Choi, Y. et al. Correlation-driven topological phases in magic-angle twisted bilayer graphene. Nature 589, 536–541 (2021).

    Article  ADS  Google Scholar 

  86. Zhou, H. et al. Half- and quarter-metals in rhombohedral trilayer graphene. Nature 598, 429–433 (2021).

    Article  ADS  Google Scholar 

  87. de la Barrera, S. C. et al. Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field. Nat. Phys. https://doi.org/10.1038/s41567-022-01616-w (2022).

    Article  Google Scholar 

  88. Seiler, A. M. et al. Quantum cascade of correlated phases in trigonally warped bilayer graphene. Nature 608, 298–302 (2022).

    Article  ADS  Google Scholar 

  89. Arora, H. S. et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature 583, 379–384 (2020).

    Article  ADS  Google Scholar 

  90. Konschuh, S., Gmitra, M., Kochan, D. & Fabian, J. Theory of spin–orbit coupling in bilayer graphene. Phys. Rev. B 85, 115423 (2012).

    Article  ADS  Google Scholar 

  91. Gmitra, M. & Fabian, J. Proximity effects in bilayer graphene on monolayer WSe2: field-effect spin valley locking, spin–orbit valve, and spin transistor. Phys. Rev. Lett. 119, 146401 (2017).

    Article  ADS  Google Scholar 

  92. Khoo, J. Y., Morpurgo, A. F. & Levitov, L. On-demand spin–orbit interaction from which-layer tunability in bilayer graphene. Nano Lett. 17, 7003–7008 (2017).

    Article  ADS  Google Scholar 

  93. Guerrero-Avilés, R., Pelc, M., Geisenhof, F. R., Weitz, R. T. & Ayuela, A. Rhombohedral trilayer graphene is more stable than its Bernal counterpart. Nanoscale 14, 16295–16302 (2022).

    Article  Google Scholar 

  94. Cea, T., Pantaleón, P. A., Walet, N. R. & Guinea, F. Electrostatic interactions in twisted bilayer graphene. Nano Mater. Sci. 4, 27–35 (2022).

    Article  Google Scholar 

  95. Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).

    Article  ADS  Google Scholar 

  96. Hao, Z. et al. Electric field-tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science 371, 1133–1138 (2021).

    Article  ADS  Google Scholar 

  97. Cao, Y., Park, J. M., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Pauli-limit violation and re-entrant superconductivity in moiré graphene. Nature 595, 526–531 (2021).

    Article  ADS  Google Scholar 

  98. Zhang, Y. et al. Promotion of superconductivity in magic-angle graphene multilayers. Science 377, 1538–1543 (2022).

    Article  ADS  Google Scholar 

  99. Park, J. M. et al. Robust superconductivity in magic-angle multilayer graphene family. Nat. Mater. 21, 877–883 (2022).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  102. Lau, C. N., Bockrath, M. W., Mak, K. F. & Zhang, F. Reproducibility in the fabrication and physics of moiré materials. Nature 602, 41–50 (2022).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  104. Nuckolls, K. P. et al. Strongly correlated Chern insulators in magic-angle twisted bilayer graphene. Nature 588, 610–615 (2020).

    Article  ADS  Google Scholar 

  105. Saito, Y. et al. Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene. Nat. Phys. 17, 478–481 (2021).

    Article  Google Scholar 

  106. Wu, S., Zhang, Z., Watanabe, K., Taniguchi, T. & Andrei, E. Y. Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene. Nat. Mater. 20, 488–494 (2021).

    Article  ADS  Google Scholar 

  107. Pierce, A. T. et al. Unconventional sequence of correlated Chern insulators in magic-angle twisted bilayer graphene. Nat. Phys. 17, 1210–1215 (2021).

    Article  Google Scholar 

  108. Stepanov, P. et al. Competing zero-field Chern insulators in superconducting twisted bilayer graphene. Phys. Rev. Lett. 127, 197701 (2021).

    Article  ADS  Google Scholar 

  109. Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).

    Article  ADS  Google Scholar 

  110. Cao, Y. et al. Nematicity and competing orders in superconducting magic-angle graphene. Science 372, 264–271 (2021).

    Article  ADS  Google Scholar 

  111. Rozen, A. et al. Entropic evidence for a Pomeranchuk effect in magic-angle graphene. Nature 592, 214–219 (2021).

    Article  ADS  Google Scholar 

  112. Saito, Y. et al. Isospin Pomeranchuk effect in twisted bilayer graphene. Nature 592, 220–224 (2021).

    Article  ADS  Google Scholar 

  113. Cea, T., Pantaleón, P. A., Phong, Vo. T. & Guinea, F. Superconductivity from repulsive interactions in rhombohedral trilayer graphene: a Kohn–Luttinger-like mechanism. Phys. Rev. B 105, 075432 (2022).

    Article  ADS  Google Scholar 

  114. Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene. Nat. Phys. 2, 177–180 (2006).

    Article  Google Scholar 

  115. Zhang, F. & MacDonald, A. H. Distinguishing spontaneous quantum Hall states in bilayer graphene. Phys. Rev. Lett. 108, 186804 (2012).

    Article  ADS  Google Scholar 

  116. Cvetkovic, V., Throckmorton, R. E. & Vafek, O. Electronic multicriticality in bilayer graphene. Phys. Rev. B 86, 075467 (2012).

    Article  ADS  Google Scholar 

  117. Martin, J., Feldman, B. E., Weitz, R. T., Allen, M. T. & Yacoby, A. Local compressibility measurements of correlated states in suspended bilayer graphene. Phys. Rev. Lett. https://doi.org/10.1103/physrevlett.105.256806 (2010).

    Article  Google Scholar 

  118. Bao, W. et al. Stacking-dependent band gap and quantum transport in trilayer graphene. Nat. Phys. 7, 948 (2011).

    Article  Google Scholar 

  119. Shi, Y. et al. Electronic phase separation in multilayer rhombohedral graphite. Nature 584, 210–214 (2020).

    Article  ADS  Google Scholar 

  120. Zhang, Y. et al. Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009).

    Article  ADS  Google Scholar 

  121. Lake, E., Patri, A. S. & Senthil, T. Pairing symmetry of twisted bilayer graphene: a phenomenological synthesis. Phys. Rev. B 106, 104506 (2022).

    Article  ADS  Google Scholar 

  122. Chou, Y.-Z., Wu, F., Sau, J. D. & Das Sarma, S. Acoustic-phonon-mediated superconductivity in Bernal bilayer graphene. Phys. Rev. B 105, L100503 (2022).

    Article  ADS  Google Scholar 

  123. Chou, Y.-Z., Wu, F., Sau, J. D. & Das Sarma, S. Acoustic-phonon-mediated superconductivity in moiréless graphene multilayers. Phys. Rev. B 106, 024507 (2022).

    Article  ADS  Google Scholar 

  124. Chou, Y.-Z., Wu, F. & Das Sarma, S. Enhanced superconductivity through virtual tunneling in Bernal bilayer graphene coupled to WSe2. Phys. Rev. B 106, L180502 (2022).

    Article  ADS  Google Scholar 

  125. Chou, Y.-Z., Wu, F., Sau, J. D. & Das Sarma, S. Acoustic-phonon-mediated superconductivity in rhombohedral trilayer graphene. Phys. Rev. Lett. 127, 187001 (2021).

    Article  ADS  Google Scholar 

  126. Szabó, A. L. & Roy, B. Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene. Phys. Rev. B 105, L201107 (2022).

    Article  ADS  Google Scholar 

  127. Dong, Z., Chubukov, A. V. & Levitov, L. Spin-triplet superconductivity at the onset of isospin order in biased bilayer graphene. Preprint at https://arXiv.org/abs/2205.13353 (2022).

  128. Szabó, A. L. & Roy, B. Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene. Phys. Rev. B 105, L081407 (2022).

    Article  ADS  Google Scholar 

  129. Dong, Z. & Levitov, L. Superconductivity in the vicinity of an isospin-polarized state in a cubic Dirac band. Preprint at https://arXiv.org/abs/2109.01133 (2021).

  130. Chatterjee, S., Wang, T., Berg, E. & Zaletel, M. P. Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene. Nat. Commun. https://doi.org/10.1038/s41467-022-33561-w (2022).

    Article  Google Scholar 

  131. You, Y.-Z. & Vishwanath, A. Kohn–Luttinger superconductivity and intervalley coherence in rhombohedral trilayer graphene. Phys. Rev. B 105, 134524 (2022).

    Article  ADS  Google Scholar 

  132. Jimeno-Pozo, A., Sainz-Cruz, H., Cea, T., Pantaleón, P. A. & Guinea, F. Superconductivity from electronic interactions and spin–orbit enhancement in bilayer and trilayer graphene. Preprint at https://arxiv.org/abs/2210.02915 (2022).

  133. Cea, T., Pantaleón, P. A., Phong, Vo. T. & Guinea, F. Superconductivity from repulsive interactions in rhombohedral trilayer graphene: a Kohn–Luttinger-like mechanism. Phys. Rev. B 105, 075432 (2022).

    Article  ADS  Google Scholar 

  134. Qin, W. et al. Functional renormalization group study of superconductivity in rhombohedral trilayer graphene. Preprint at https://arxiv.org/abs/2203.09083 (2022).

  135. Lu, D.-C., Wang, T., Chatterjee, S. & You, Y.-Z. Correlated metals and unconventional superconductivity in rhombohedral trilayer graphene: a renormalization group analysis. Phys. Rev. B 106, 155115 (2022).

    Article  ADS  Google Scholar 

  136. Ghazaryan, A., Holder, T., Serbyn, M. & Berg, E. Unconventional superconductivity in systems with annular fermi surfaces: application to rhombohedral trilayer graphene. Phys. Rev. Lett. 127, 247001 (2021).

    Article  ADS  Google Scholar 

  137. Wagner, G., Kwan, Y. H., Bultinck, N., Simon, S. H. & Parameswaran, S. A. Superconductivity from repulsive interactions in Bernal-stacked bilayer graphene. Preprint at https://arxiv.org/abs/2302.00682 (2023).

  138. Cea, T. Superconductivity induced by the intervalley Coulomb scattering in a few layers of graphene. Phys. Rev. B 107, L041111 (2023).

    Article  ADS  Google Scholar 

  139. Dai, H., Ma, R., Zhang, X. & Ma, T. Quantum Monte Carlo study of superconductivity in rhombohedral trilayer graphene under an electric field. Preprint at https://arxiv.org/abs/2204.06222 (2022).

  140. Dai, H., Hou, J., Zhang, X., Liang, Y. & Ma, T. Mott insulating state and d + id superconductivity in an ABC graphene trilayer. Phys. Rev. B 104, 035104 (2021).

    Article  ADS  Google Scholar 

  141. Kohn, W. & Luttinger, J. M. New mechanism for superconductivity. Phys. Rev. Lett. 15, 524–526 (1965).

    Article  ADS  MathSciNet  Google Scholar 

  142. Calderón, M. J., Camjayi, A. & Bascones, E. Mott correlations in ABC graphene trilayer aligned with hBN. Phys. Rev. B 106, L081123 (2022).

    Article  ADS  Google Scholar 

  143. Huang, C. et al. Spin and orbital metallic magnetism in rhombohedral trilayer graphene. Preprint at https://arxiv.org/abs/2203.12723 (2022).

  144. Juričić, V., Muñoz, E. & Soto-Garrido, R. Optical conductivity as a probe of the interaction-driven metal in rhombohedral trilayer graphene. Nanomaterials 12, 2927 (2022).

    Article  Google Scholar 

  145. Ghazaryan, A., Holder, T., Berg, E. & Serbyn, M. Multilayer graphenes as a platform for interaction-driven physics and topological superconductivity. Phys. Rev. B 107, 104502 (2023).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  147. Kazmierczak, N. P. et al. Strain fields in twisted bilayer graphene. Nat. Mater. 20, 956 (2021).

    Article  ADS  Google Scholar 

  148. Cao, Y. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020).

    Article  ADS  Google Scholar 

  149. Liu, X. et al. Tunable spin-polarized correlated states in twisted double bilayer graphene. Nature 583, 221–225 (2020).

    Article  ADS  Google Scholar 

  150. Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686 (2022).

    Article  ADS  Google Scholar 

  151. Holleis, L. et al. Ising superconductivity and nematicity in bernal bilayer graphene with strong spin orbit coupling. Preprint at https://arxiv.org/abs/2303.00742 (2023).

  152. Maiti, S. & Chubukov, A. V. Superconductivity from repulsive interaction. In AIP Conference Proceedings, Vol. 1550, 3 (AIP, 2013); https://doi.org/10.1063/1.4818400.

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Acknowledgements

The authors are thankful to A.V. Chubukov, J.A. Silva-Guillen, E. Bascones and G. Naumis for illuminating discussions. The authors acknowledge support from the Severo Ochoa programme for centres of excellence in R&D (CEX2020-001039-S/AEI/10.13039/501100011033); from the European Commission, within the Graphene Flagship, Core 3, grant number 881603; and from grants NMAT2D (Comunidad de Madrid, Spain), SprQuMat (Ministerio de Ciencia e Innovación, Spain) and (MAD2D-CM)-MRR MATERIALES AVANZADOS-IMDEA-NC. V.T.P. acknowledges support from the Department of Energy under grant number DE-FG02-84ER45118, the NSF Graduate Research Fellowships Program and the P.D. Soros Fellowship for New Americans.

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Authors and Affiliations

  1. IMDEA Nanoscience, Madrid, Spain

    Pierre A. Pantaleón, Alejandro Jimeno-Pozo, Héctor Sainz-Cruz & Francisco Guinea

  2. Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA, USA

    Võ Tiến Phong

  3. Department of Physical and Chemical Sciences, University of L’Aquila, L’Aquila, Italy

    Tommaso Cea

  4. Donostia International Physics Center, San Sebastian, Spain

    Francisco Guinea

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  1. Pierre A. Pantaleón
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  6. Francisco Guinea
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Glossary

Berezinskii–Kosterlitz–Thouless theory

A description of a phase transition typical of 2D systems, characterized by the unbinding of topological objects (vortices) as the temperature is increased.

Dirac semimetal

A non-gapped electronic system that can be described with the Dirac equation, which is commonly used to compute the dispersion of relativistic fermions.

Flavour-symmetry-breaking

In the case of graphene and related materials, the combination of valley and spin degrees of freedom defines the ‘flavour’. Flavour-symmetry-breaking refers to the lifting of degeneracy between flavours.

Fraunhofer pattern

Effect on the critical current of the interference between the superconducting phases induced by a magnetic field.

Ising spin–orbit

Coupling between the spin and orbital degrees of freedom that pins the electron spin to an out-of-plane direction.

Lifshitz transition

Singular change in the shape and/or topology of the Fermi surface.

Pauli limit

Upper bound for the magnitude of the magnetic field that can be applied to a conventional superconductor before it goes out of the superconducting phase.

Stoner model

A model for magnetic materials that describes the magnetic phases as arising from the repulsion of electrons with opposite spin placed on the same atomic orbital.

van Hove singularities

The logarithmic divergence of the density of states (DOS) caused by a saddle-point in the electronic band structure.

Wigner crystal

Localization of electrons at low densities owing to the Coulomb repulsion.

Zeeman effect

Lifting of the degeneracy of the spin degree of freedom as a response to an external magnetic field.

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Pantaleón, P.A., Jimeno-Pozo, A., Sainz-Cruz, H. et al. Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene. Nat Rev Phys 5, 304–315 (2023). https://doi.org/10.1038/s42254-023-00575-2

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