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Emergence of correlations in alternating twist quadrilayer graphene

Abstract

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.

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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.

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Acknowledgements

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

Authors

Contributions

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.

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The authors declare no competing interests.

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

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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.

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Burg, G.W., Khalaf, E., Wang, Y. et al. Emergence of correlations in alternating twist quadrilayer graphene. Nat. Mater. 21, 884–889 (2022). https://doi.org/10.1038/s41563-022-01286-2

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