Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Emergence of correlations in alternating twist quadrilayer graphene


Alternating twist multilayer graphene (ATMG) has recently emerged as a family of moiré systems that share several fundamental properties with twisted bilayer graphene, and are expected to host similarly strong electron–electron interactions near the magic angle. Here, we study alternating twist quadrilayer graphene (ATQG) samples with twist angles of 1.96° and 1.52°, which are slightly removed from the magic angle of 1.68°. At the larger angle, we find signatures of correlated insulators only when the ATQG is hole doped, and no signatures of superconductivity, and for the smaller angle we find evidence of superconductivity, while signs of the correlated insulators weaken. Our results provide insight into the twist angle dependence of correlated phases in ATMG and shed light on the nature of correlations in the intermediate coupling regime at the edge of the magic angle range where dispersion and interaction are of the same order.

Your institute does not have access to this article

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Transport and temperature dependence in ATQG.
Fig. 2: θ = 1.96° ATQG in a magnetic field.
Fig. 3: Evidence of superconductivity in θ = 1.52° ATQG.
Fig. 4: Magnetic field response of nascent superconductivity.

Data availability

Source data are provided with this paper. All other supporting data are available from the corresponding author upon reasonable request.

Code availability

The supporting code for this paper is available from the corresponding author upon reasonable request.


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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  7. Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Flavour Hund’s coupling, Chern gaps and charge diffusivity in moiré graphene. Nature 592, 43–48 (2021).

    CAS  Article  Google Scholar 

  8. 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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  10. Polshyn, H. et al. Electrical switching of magnetic order in an orbital Chern insulator. Nature 588, 66–70 (2020).

    CAS  Article  Google Scholar 

  11. Chen, S. et al. Electrically tunable correlated and topological states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 374–380 (2021).

    CAS  Article  Google Scholar 

  12. Xu, S. et al. Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene. Nat. Phys. 17, 619–626 (2021).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  14. Shen, C. et al. Correlated states in twisted double bilayer graphene. Nat. Phys. 16, 520–525 (2020).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  17. He, M. et al. Symmetry breaking in twisted double bilayer graphene. Nat. Phys. 17, 26–30 (2021).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  20. Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

    CAS  Article  Google Scholar 

  21. Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).

    CAS  Article  Google Scholar 

  22. Zhang, Z. et al. Flat bands in twisted bilayer transition metal dichalcogenides. Nat. Phys. 16, 1093–1096 (2020).

    CAS  Article  Google Scholar 

  23. Khalaf, E., Kruchkov, A. J., Tarnopolsky, G. & Vishwanath, A. Magic angle hierarchy in twisted graphene multilayers. Phys. Rev. B 100, 085109 (2019).

    CAS  Article  Google Scholar 

  24. Ledwith, P. J. et al. TB or not TB? Contrasting properties of twisted bilayer graphene and the alternating twist n-layer structures (n=3, 4, 5, …). Preprint at arXiv (2021).

  25. 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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  27. Turkel, S. et al. Orderly disorder in magic-angle twisted trilayer graphene. Science 376, 193–199 (2021).

    Article  CAS  Google Scholar 

  28. Kim, H. et al. Spectroscopic signatures of strong correlations and unconventional superconductivity in twisted trilayer graphene. Preprint at arXiv (2021).

  29. Liu, X., Zhang, N. J., Watanabe, K., Taniguchi, T. & Li, J. I. A. Isospin order in superconducting magic-angle twisted trilayer graphene. Nat. Phys. 18, 522–527 (2022).

    CAS  Article  Google Scholar 

  30. 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).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  34. Lee, J. Y. et al. Theory of correlated insulating behaviour and spin-triplet superconductivity in twisted double bilayer graphene. Nat. Commun. 10, 5333 (2019).

    Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  36. Zhang, X. et al. Correlated insulating states and transport signature of superconductivity in twisted trilayer graphene superlattices. Phys. Rev. Lett. 127, 166802 (2021).

    CAS  Article  Google Scholar 

  37. Berdyugin, A. I. et al. Out-of-equilibrium criticalities in graphene superlattices. Science 375, 430–433 (2022).

    CAS  Article  Google Scholar 

  38. 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).

    CAS  Article  Google Scholar 

  39. Qin, W. & MacDonald, A. H. In-plane critical magnetic fields in magic-angle twisted trilayer graphene. Phys. Rev. Lett. 127, 097001 (2021).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  42. Finney, J. et al. Unusual magnetotransport in twisted bilayer graphene. Proc. Natl Acad. Sci. USA 119, e2118482119 (2022).

    CAS  Article  Google Scholar 

  43. Lake, E. & Senthil, T. Re-entrant superconductivity through a quantum Lifshitz transition in twisted trilayer graphene. Phys. Rev. B 104, 174505 (2021).

    CAS  Article  Google Scholar 

  44. Khalaf, E., Ledwith, P. & Vishwanath, A. Symmetry constraints on superconductivity in twisted bilayer graphene: fractional vortices, 4e condensates or non-unitary pairing. Preprint at arXiv (2020).

  45. Zhang, Y. et al. Ascendance of superconductivity in magic-angle graphene multilayers. Preprint at arXiv (2021).

  46. Park, J. M. et al. Magic-angle multilayer graphene: a robust family of moiré superconductors. Preprint at arXiv (2021).

Download references


The work at The University of Texas at Austin was supported by the National Science Foundation (NSF) grants MRSEC DMR-1720595 and EECS-2122476; Army Research Office under MURI grants no. W911NF-17-1-0312 and W911NF-14-1-0016; and the Welch Foundation grant F-2018-20190330. E.K. was funded by the Simons Collaboration on Ultra-Quantum Matter, a Simons Foundation grant (618615). Work was partly done at the Texas Nanofabrication Facility supported by the NSF grant no. NNCI-2025227. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001) and JSPS KAKENHI (grant nos. JP19H05790 and JP20H00354).

Author information

Authors and Affiliations



G.W.B. and E.T. conceived and designed the experiment. G.W.B. fabricated and measured the samples, and Y.W. assisted with measurements. G.W.B., E.K. and E.T. analysed the data. E.K. provided band structure calculations. K.W. and T.T. provided the boron nitride crystals. All authors contributed to discussions and writing of the manuscript.

Corresponding author

Correspondence to Emanuel Tutuc.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review information

Peer review information

Nature Materials thanks Chun Ning Lau, Aaron Sharpe and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Arrhenius plot of correlated and band insulators in θ = 1.96° ATQG.

Log-scale Rxx vs. 1/T at n/ns = 0, −1/2, and −1, using the same data as in Fig. 1f of the main text. The linear portions of each trace are marked by a dashed line.

Extended Data Fig. 2 θ = 1.52° ATQG at B = 1 T.

a-b, Rxx (a) and Rxy (b) vs. n/ns and E at B = 1 T. Similar to the Fig. 2 data for θ = 1.96° ATQG, Rxx maxima become more apparent at half and full-filling and Rxy data show trend reversals indicative of a phase transition at the correlated insulators.

Extended Data Fig. 3 dV/dI vs I at different n/ns and E.

a, Rxx vs. n/ns and E in the θ = 1.52° sample, the same data shown in Fig. 3a of the main text. The dots indicate points where the dV/dI vs. I measurements were taken. b, dV/dI vs. I at n/ns = 1/2 + δ (upper left), 0 - δ (upper right), −1/2 - δ (lower left), and 1 + δ (lower right). The line colors correspond to the dot colors in a. Two primary observations can be made from the data. First, regions near half-filling show a critical current in the dV/dI vs. I at all E, while data acquired at other fillings show a dV/dI that is insensitive to I. Second, the peaks in dV/dI are generally most pronounced at larger E, in agreement with the theoretical picture that the critical temperature increases at finite E for samples with a twist angle below the magic angle24.

Extended Data Fig. 4 Additional temperature dependence in the θ = 1.52° ATQG.

a-b, Rxx vs. n/ns and E at T = 160 mK (a) and T = 1.5 K (b). At the lower temperature, E-dependent regions of low resistance appear at n = ±(ns/2 + δ) while all other regions remain insensitive to temperature between the two contour plots. c, Rxx vs. n/ns and T at E = 0 V/nm. Low resistance domes form on the higher density side of half-filling on both the electron and hole side. Consistent with a, b, the data suggest a higher critical temperature on the electron side compared to the hole side. d, ΔRxx vs. E and T at n/ns = 1/2 + δ for T between 1.5 K and 6 K, where ΔRxx is the percentage change in Rxx from the T = 1.5 K value. Rxx changes more rapidly at larger E, suggesting an onset of correlations at higher temperatures with increasing E.

Extended Data Fig. 5 Evidence of superconductivity on hole side.

a, V vs. I at n/ns = −0.75 and E = 0.3 V/nm for temperatures between 528 mK and 1.540 K in the θ = 1.52° sample. At the highest temperature, the critical current behavior is extinguished and the characteristic becomes linear. b, dV/dI vs I and B at the same n/ns and E as in a. A small B-field suppresses the nascent superconductivity, similar to the Fig. 4a data of the main text.

Extended Data Fig. 6 Twist angle uniformity in the ATQG samples.

a-b, Optical micrographs of the θ = 1.96° (a) and θ = 1.52° (b) samples. The voltage probe contacts are labeled in each panel, and the scale bars are 5 µm. c-d, representative traces of Rxx vs. VTG in the θ = 1.96° (c) and θ = 1.52° (d) samples using four different voltage probe contact pairs. For the θ = 1.96° sample, the Rxx maxima corresponding to the band insulators at 0 ns and −1ns closely align, confirming a uniform twist angle to within ±0.01° throughout the channel. Similarly, in the θ = 1.52° sample, the positions of the resistance maxima at +1 ns and resistance dips at ns/2 + δ that precede the superconducting state closely match across all contact pairs.

Extended Data Fig. 7 Landau fans in the θ = 1.52° ATQG.

a, Rxx vs. n/ns and B at E = 0 V/nm, showing quantum oscillations as described in the Methods section. b, Landau fans observed in panel a, along with the Landau level filling factor. The filling factor of 6 at n = ns/2 is indicative of a band with Chern number 2, as discussed in the main text for the θ = 1.96° sample.

Extended Data Fig. 8 Landau fans near nascent superconductivity.

Rxx vs. n/ns and B at E = −0.4 V/nm in the θ = 1.52° sample. The prominent Landau levels are labeled. Near half-filling, the low resistance domes diminish at small B values, and a resistance maximum develops at the correlated insulator.

Source data

Source Data Fig. 1

Source data for Fig. 1b–g.

Source Data Fig. 2

Source data for Fig. 2a–f

Source Data Fig. 3

Source data for Fig. 3.

Source Data Fig. 4

Source data for Fig. 4.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Burg, G.W., Khalaf, E., Wang, Y. et al. Emergence of correlations in alternating twist quadrilayer graphene. Nat. Mater. 21, 884–889 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing