Unconventional superconductivity in magic-angle graphene superlattices

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

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

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

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

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

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

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)

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

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

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

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

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

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)

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

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

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

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

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

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)

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

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)

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

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

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

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

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

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

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

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

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

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

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

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)

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

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

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)

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)

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)

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

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

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

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

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

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)

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)

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)

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)

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

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)

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

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)

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

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)

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)

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

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

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)

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)

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

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

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

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

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

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

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