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Quantum critical behaviour in magic-angle twisted bilayer graphene

Nature Physics volume 18, pages 633–638 (2022)Cite this article

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Abstract

The flat bands1 of magic-angle twisted bilayer graphene (MATBG) host strongly correlated electronic phases such as correlated insulators2,3,4,5,6, superconductors7,8,9,10,11 and a strange metal state12. The strange metal state, believed to be key for understanding the electronic properties of MATBG, is obscured by various phase transitions and so it could not be unequivocally differentiated from a metal undergoing frequent electron–phonon collisions13. Here we report transport measurements in superconducting MATBG in which the correlated insulator states are suppressed by screening. The uninterrupted metallic ground state shows resistivity that is linear in temperature over three orders of magnitude and spans a broad range of doping, including that where a correlation-driven Fermi surface reconstruction occurs. This strange metal behaviour is distinguished by Planckian scattering rates and a linear magnetoresistivity. By contrast, near charge neutrality or a fully filled flat band, as well as for devices twisted away from the magic angle, we observe the archetypal Fermi-liquid behaviour. Our measurements demonstrate the existence of a quantum-critical phase whose fluctuations dominate the metallic ground state throughout a continuum of doping. Further, we observe a transition to the strange metal upon suppression of the superconducting order, suggesting a relationship between quantum fluctuations and superconductivity in MATBG.

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Fig. 1: Temperature dependence of the resistivity of hole-doped MATBG.
Fig. 2: Phase diagram of hole-doped screened MATBG.
Fig. 3: Magnetic field dependence of the resistivity of hole-doped MATBG.

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Data availability

Source data are provided with this paper. All other datasets that support the plots within this publication are available from the corresponding authors upon reasonable request.

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. 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 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Stepanov, P. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020).

    Article  ADS  Google Scholar 

  10. Saito, Y., Ge, J., Watanabe, K., Taniguchi, T. & Young, A. F. Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys 16, 926–930 (2020).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  14. Abrikosov, A. A. & Khalatnikov, I. M. The theory of a Fermi liquid (the properties of liquid 3He at low temperatures). Rep. Prog. Phys. 22, 329–367 (1959).

    Article  ADS  Google Scholar 

  15. Proust, C. & Taillefer, L. The remarkable underlying ground states of cuprate superconductors. Annu. Rev. Condens. Matter Phys. 10, 409–429 (2019).

    Article  ADS  Google Scholar 

  16. Greene, R. L., Mandal, P. R., Poniatowski, N. R. & Sarkar, T. The strange metal state of the electron-doped cuprates. Annu. Rev. Condens. Matter Phys. 11, 213–229 (2020).

    Article  Google Scholar 

  17. Grigera, S. A. et al. Magnetic field-tuned quantum criticality in the metallic ruthenate Sr3Ru2O7. Science 294, 329–332 (2001).

    Article  ADS  Google Scholar 

  18. Shibauchi, T., Carrington, A. & Matsuda, Y. A quantum critical point lying beneath the superconducting dome in iron pnictides. Annu. Rev. Condens. Matter Phys. 5, 113–135 (2014).

    Article  ADS  Google Scholar 

  19. Löhneysen, H. V. et al. Non-Fermi-liquid behaÿvior in a heavy-fermion alloy at a magnetic instability. Phys. Rev. Lett. 72, 3262–3265 (1994).

    Article  ADS  Google Scholar 

  20. Ghiotto, A. et al. Quantum criticality in twisted transition metal dichalcogenides. Nature 597, 345–349 (2021).

    Article  ADS  Google Scholar 

  21. Bruin, J. A. N., Sakai, H., Perry, R. S. & Mackenzie, A. P. Similarity of scattering rates in metals showing T-linear resistivity. Science 339, 804–807 (2013).

    Article  ADS  Google Scholar 

  22. Trovarelli, O. et al. YbRh2Si2: Pronounced non-Fermi-liquid effects above a low-lying magnetic phase transition. Phys. Rev. Lett. 85, 626–629 (2000).

    Article  ADS  Google Scholar 

  23. Licciardello, S. et al. Electrical resistivity across a nematic quantum critical point. Nature 567, 213–217 (2019).

    Article  ADS  Google Scholar 

  24. Gonzàlez, J. & Stauber, T. Marginal Fermi liquid in twisted bilayer graphene. Phys. Rev. Lett. 124, 186801 (2020).

    Article  ADS  Google Scholar 

  25. Efetov, D. K. & Kim, P. Controlling electron-phonon interactions in graphene at ultrahigh carrier densities. Phys. Rev. Lett. 105, 256805 (2010).

    Article  ADS  Google Scholar 

  26. Wu, F., Hwang, E. & Sarma, S. D. Phonon-induced giant linear-in-T resistivity in magic angle twisted bilayer graphene: Ordinary strangeness and exotic superconductivity. Phys. Rev. B 99, 165112 (2019).

    Article  ADS  Google Scholar 

  27. Liu, X. et al. Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening. Science 371, 1261–1265 (2021).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  30. Zaanen, J. Why the temperature is high. Nature 430, 512–513 (2004).

    Article  ADS  Google Scholar 

  31. Legros, A. et al. Universal T-linear resistivity and Planckian dissipation in overdoped cuprates. Nat. Phys. 15, 142–147 (2019).

    Article  Google Scholar 

  32. Daou, R. et al. Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-Tc superconductor. Nat. Phys. 5, 31–34 (2009).

    Article  Google Scholar 

  33. Hayes, I. M. et al. Scaling between magnetic field and temperature in the high-temperature superconductor BaFe2(As1−xPx)2. Nat. Phys. 12, 916–919 (2016).

    Article  Google Scholar 

  34. Giraldo-Gallo, P. et al. Scale-invariant magnetoresistance in a cuprate superconductor. Science 361, 479–481 (2019).

    Article  ADS  Google Scholar 

  35. Liao, Z. M., Zhou, Y. B., Wu, H. C., Han, B. H. & Yu, D. P. Observation of both classical and quantum magnetoresistance in bilayer graphene. Europhys. Lett. 94, 57004 (2011).

    Article  ADS  Google Scholar 

  36. Kisslinger, F. et al. Linear magnetoresistance in mosaic-like bilayer graphene. Nat. Phys. 11, 650–653 (2015).

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful for fruitful discussions with A. MacDonald, P. Jarillo-Herrero and P. Coleman. D.K.E. acknowledges support from the Ministry of Economy and Competitiveness of Spain through the ‘Severo Ochoa’ programme for Centres of Excellence in R&D (SE5-0522), Fundació Privada Cellex, Fundació Privada Mir-Puig, the Generalitat de Catalunya through the CERCA programme and funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 852927). J.D.-M. acknowledges support from the INphINIT ‘la Caixa’ Foundation (ID 100010434) fellowship programme (LCF/BQ/DI19/11730021). G.D.B. acknowledges funding from the ‘Presidencia de la Agencia Estatal de Investigación’ within the ‘Convocatoria de tramitación anticipada, correspondiente al año 2019, de las ayudas para contratos predoctorales (Ref. PRE2019-088487) para la formación de doctores contemplada en el Subprograma Estatal de Formación del Programa Estatal de Promoción del Talento y su Empleabilidad en I+D+i, en el marco del Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020, cofinanciado por el Fondo Social Europeo’. I.D. acknowledges support from the INphINIT ‘La Caixa’ (ID 100010434) fellowship programme (LCF/BQ/DI19/11730030). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant number JPMXP0112101001) and JSPS KAKENHI (grant numbers 19H05790 and JP20H00354). L.L. acknowledges support from the Science and Technology Center for Integrated Quantum Materials, NSF Grant No. DMR-1231319 and Army Research Office Grant W911NF-18-1-0116.

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Authors and Affiliations

  1. ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Barcelona, Spain

    Alexandre Jaoui, Ipsita Das, Giorgio Di Battista, Jaime Díez-Mérida, Xiaobo Lu & Dmitri K. Efetov

  2. National Institute for Material Sciences, Tsukuba, Japan

    Kenji Watanabe & Takashi Taniguchi

  3. Department of Physics, Tokyo Institute of Technology, Tokyo, Japan

    Hiroaki Ishizuka

  4. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Hiroaki Ishizuka & Leonid Levitov

Authors
  1. Alexandre Jaoui
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Contributions

D.K.E. and X.L. conceived and designed the experiments. I.D., G.D.B., J.D.-M. and X.L. fabricated the devices. A.J., I.D., G.D.B., J.D.-M. and X.L. performed the measurements. A.J. analysed the data. A.J., H.I. and L.L. performed the theoretical modelling. T.T. and K.W. contributed materials. D.K.E. supported the experiments. A.J. and D.K.E. wrote the paper.

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Correspondence to Alexandre Jaoui or Dmitri K. Efetov.

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Supplementary Information

Supplementary Notes A–J, Figs. 1–8 and Table 1.

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Source Data Fig. 1

Numerical source data for Fig. 1.

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Source Data Fig. 3

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Jaoui, A., Das, I., Di Battista, G. et al. Quantum critical behaviour in magic-angle twisted bilayer graphene. Nat. Phys. 18, 633–638 (2022). https://doi.org/10.1038/s41567-022-01556-5

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