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# Independent superconductors and correlated insulators in twisted bilayer graphene

## Abstract

When two sheets of graphene are stacked on top of each other with a small twist of angle θ ≈ 1.1° between them, theory predicts the formation of a flat electronic band1,2. Experiments have shown correlated insulating, superconducting and ferromagnetic states when the flat band is partially filled3,4,5,6,7,8. The proximity of superconductivity to correlated insulators suggested a close relationship between these states, reminiscent of the cuprates where superconductivity arises by doping a Mott insulator. Here, we show that superconductivity can appear far away from the correlated insulating states. Although both superconductivity and correlated insulating behaviour are strongest near the flat-band condition, superconductivity survives to larger detuning of the angle. Our observations are consistent with a ‘competing phases’ picture in which insulators and superconductivity arise from different mechanisms.

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## Data availability

Source data are available for this paper. All other data that support the findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank M. Yankowitz and D.K. Efetov for discussions and D.K. Efetov for sharing unpublished experimental data. This work was primarily supported by the ARO under award no. W911NF-17-1-0323. Y.S. acknowledges support from the Elings Prize Fellowship from the California NanoSystems Institute at the University of California, Santa Barbara. A.F.Y. acknowledges the support of the David and Lucille Packard Foundation under award no. 2016-65145. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, grant no. JPMXP0112101001, JSPS KAKENHI grant no. JP20H00354 and CREST (JPMJCR15F3), JST. A.F.Y. acknowledges the support of the David and Lucille Packard Foundation and the Alfred P. Sloan Foundation.

## Author information

Authors

### Contributions

Y.S. and J.G. fabricated tBLG devices. Y.S. performed the measurements and analysed the data. Y.S. and A.F.Y. wrote the manuscript. T.T. and K.W. grew the hBN crystals.

### Corresponding author

Correspondence to Andrea F. Young.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

## Extended data

### Extended Data Fig. 1 ‘Cut-and-stack’ fabrication technique for tBLG.

a, Optical microscope and schematic images of graphene pre-cutting. A graphene flake is cut into two or more pieces by AFM16. Arrows show pre-cutting line. Scale bar in left images is 10 μm. b, Process flow for tBLG fabrication. All stacking is done at 25C. First, we laminate the 1st half piece of pre-cut graphene by carefully aligning the edge of hBN with the cutting line and picking it up with the hBN flake. After that, we rotate the 2nd half-piece of graphene by about 1.2 − 1. 3 and laminate/pick it up. Dashed arrows show the direction of motion of boundary between adhered and non-adhered PC film.

### Extended Data Fig. 2 Optical microscope images of devices used in this study.

Scale bars equal 5 μm in all images.

### Extended Data Fig. 3 Two terminal conductance across multiple contacts in all five measured tBLG devices.

Measurements were performed at 0.8 K for Devices 1-4 and 4 K for Device 5. White arrows show four-terminal contacts used for ρxx and ρxy. $${\theta }_{\max }$$ and $${\theta }_{\min }$$ are the largest and smallest twist angles calculated from superlattice peaks and ν = ± 2 peaks. The left side contacts (A, B, C and D) of Device 4 shows 1.15 while the right side (E and F) is 1.20. ‘all’ means other all contacts.

### Extended Data Fig. 4 Line cuts of ρxx versus filling factor ν between 6 K and 50 mK.

The curves are at 6, 4, 2, 1.5, 0.9, 0.6, 0.3 and 0.05 K for Devices 1, 2, 3 and 5, and 6, 3, 1.5, 0.6, 0.4, 0.3 and 0.05 K for Device 4.

### Extended Data Fig. 5 Detail of 2D map around a superconducting dome in each device.

Dashed lines show ν = − 2. The superconducting phase in Device 3 is divided by a weak resistive state around ν = − 2 − δ, which does not match the density of the ν = − 2, estimated from the strong resistive states at ν = − 4, 0, 2 and 4.

### Extended Data Fig. 6 ρxx(T) at optimal doping for superconductivity (blue curves) and ν = − 2 (red curves).

The black triangles show indicate 50% deviation from normal state resistivity.

### Extended Data Fig. 7 DC current response in Device 4.

dVxx/dI (a) and Vxx (b) as a function of IDC at ν = − 1.52, − 3.05, − 3.51 at 10 mK.

### Extended Data Fig. 8 Fraunhofer-like interference in Devices 3 and 4.

Field derivatives of differential resistance d2Vxx/dIdB are plotted as a function of IDC and B for Device 3 (a) and 4 (b) and the magnification of b between -10 and 10 nA (c) show periodic oscillations with periodicity of approximately 8 − 10 mT, reminiscent of a Fraunhofer pattern. The field derivative is calculated based on the raw data moving-averaged with neighboring 5 and 10 data points for a and b, respectively, over both B and IDC.

### Extended Data Fig. 9 Fraunhofer-like interference in Devices 1, 2 and 3.

Differential resistance as a function of DC current and magnetic field in Devices 1, 2 and 3 at 10 mK.

### Extended Data Fig. 10 Hall density (nH) as a function of filling factor ν.

The Hall effect measurements are performed at 0.8 K and 0.5 T. The vertical dashed lines show ν = 0, − 2 and 2 filling and horizontal dashed line show the zero density. Device geometry precluded Hall measurements for Device 2.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–5.

## Source data

### Source Data Fig. 1

Numerical data used to generate graphs in Fig. 1.

### Source Data Fig. 2

Numerical data used to generate graphs in Fig. 2.

### Source Data Fig. 3

Numerical data used to generate graphs in Fig. 3.

## Rights and permissions

Reprints and Permissions

Saito, Y., Ge, J., Watanabe, K. et al. Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys. 16, 926–930 (2020). https://doi.org/10.1038/s41567-020-0928-3

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