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# Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene

An Author Correction to this article was published on 02 July 2020

## Abstract

The recent discovery of correlated insulator states and superconductivity in magic-angle twisted bilayer graphene1,2 has enabled the experimental investigation of electronic correlations in tunable flat-band systems realized in twisted van der Waals heterostructures3,4,5,6. This novel twist angle degree of freedom and control should be generalizable to other two-dimensional systems, which may exhibit similar correlated physics behaviour, and could enable techniques to tune and control the strength of electron–electron interactions. Here we report a highly tunable correlated system based on small-angle twisted bilayer–bilayer graphene (TBBG), consisting of two rotated sheets of Bernal-stacked bilayer graphene. We find that TBBG exhibits a rich phase diagram, with tunable correlated insulator states that are highly sensitive to both the twist angle and the application of an electric displacement field, the latter reflecting the inherent polarizability of Bernal-stacked bilayer graphene7,8. The correlated insulator states can be switched on and off by the displacement field at all integer electron fillings of the moiré unit cell. The response of these correlated states to magnetic fields suggests evidence of spin-polarized ground states, in stark contrast to magic-angle twisted bilayer graphene. Furthermore, in the regime of lower twist angles, TBBG shows multiple sets of flat bands near charge neutrality, resulting in numerous correlated states corresponding to half-filling of each of these flat bands, all of which are tunable by the displacement field as well. Our results could enable the exploration of twist-angle- and electric-field-controlled correlated phases of matter in multi-flat-band twisted superlattices.

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## Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

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## Acknowledgements

We acknowledge discussions with S. Todadri, L. Fu, P. Kim, X. Liu, S. Fang and E. Kaxiras. This work was supported by the National Science Foundation under award DMR-1809802 (data analysis by Y.C.), the Center for Integrated Quantum Materials under NSF grant DMR-1231319 (fabrication by D.R.-L.), the US DOE, BES Office, Division of Materials Sciences and Engineering under award DE-SC0001819 (g-factor analysis by J.M.P.), and the Gordon and Betty Moore Foundation's EPiQS Initiative through grant GBMF4541 to P.J.-H. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, A3 Foresight by JSPS and the CREST (JPMJCR15F3), JST. This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities supported by the National Science Foundation (DMR-0819762) and of Harvard’s Center for Nanoscale Systems, supported by the NSF (ECS-0335765). D.R.-L. acknowledges partial support from Fundació Bancaria “la Caixa” (LCF/BQ/AN15/10380011) and from the US Army Research Office grant number W911NF-17-S-0001 (measurements). O.R.-B. acknowledges support from Fundació Privada Cellex.

## Author information

Authors

### Contributions

Y.C., D.R.-L., O.R.-B. and J.M.P contributed to sample fabrication and transport measurements. Y.C., D.R.-L., O.R.-B., J.M.P and P.J.-H. performed data analysis. K.W. and T.T. provided h-BN samples. Y.C., D.R.-L., O.R.-B., J.M.P. and P.J.-H. wrote the manuscript with input from all co-authors.

### Corresponding authors

Correspondence to Yuan Cao or Pablo Jarillo-Herrero.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Ming-Hao Liu, Hu-Jong Lee and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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

## Extended data figures and tables

### Extended Data Fig. 1 Vtg–Vbg resistance maps of measured TBBG devices.

af, Resistance versus Vtg and Vbg for the six TBBG devices measured, which correspond to the six rows shown in Extended Data Table 1, respectively. g, h, Cross-like feature near −ns/2 in TBBG samples with twist angles θ = 1.23° (g) and θ = 1.09° (h), which might signal the onset of a correlated state.

### Extended Data Fig. 2 Landau fan diagrams and Hall mobilities of the TBBG devices.

a, Resistance of the 1.09° sample versus carrier density and perpendicular magnetic field. b, Hall mobility μHall (left axis) and Hall coefficient RH (right axis) in the 1.09° sample at different carrier densities. cf, Same measurements as in a, b but for the 0.84° (c, d) and 1.23° (e, f) samples, respectively. All measurements are taken at T < 100 mK. The data for the 1.09° device are taken at D/ε0 = 0.2 V nm−1 while the data for the other two devices are taken at D = 0.

### Extended Data Fig. 3 Linear resistance versus temperature behaviour in TBBG.

a, b, Resistance versus temperature curves at different charge densities in the 1.23° sample for the electron-doping side (a) and the hole-doping side (b). The inset in a shows the slope dRxx/dT of the linear RT behaviour as a function of n for T >10 K. c, Selected RT curves near ns/2 from a. d, Similar linear RT behaviour in the 1.09° device. The inset shows the slope dRxx/dT. e, Density-dependent sublinear/linear RT behaviour in the 0.84° device. The inset shows the slope dRxx/dT versus n in log–log scale. The slope is proportional to n to the power of −1.77.

### Extended Data Fig. 4 Additional magnetic field response of TBBG devices.

ad, Response of the ns/4 (a, b) and 3ns/4 (c, d) states in perpendicular magnetic field (a, c) and in-plane magnetic field (b, d) for the θ =1.23° device.

### Extended Data Fig. 5 I–V curves in the 1.23° TBBG device at different carrier densities.

D/ε0 = −0.38 V nm−1. ac, The densities correspond approximately to the ns/4 (a) and ns/2 (c) insulating states while the density for b lies between them. The left axis is the longitudinal voltage Vxx and the right axis is the differential resistance dVxx/dIb.

### Extended Data Fig. 6 Comparison of the gap sizes and the g-factor using small and large excitations.

a, b, The Arrhenius fits of the resistance at the ns/2 state of the 1.23° TBBG device in an in-plane magnetic field. c, d, The same fits for the ns/4 state. a and c are measured using a current excitation of 0.1 nA, while b and d are measured using a voltage excitation of around 100 μV, which induces a current of around 5–10 nA in the sample. The insets in each panel show the corresponding g-factor fittings. In general, by using an excessive excitation, both the energy gaps and the g-factor will be underestimated.

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Cao, Y., Rodan-Legrain, D., Rubies-Bigorda, O. et al. Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene. Nature 583, 215–220 (2020). https://doi.org/10.1038/s41586-020-2260-6

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