Thank you for visiting nature.com. 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.

# Isospin order in superconducting magic-angle twisted trilayer graphene

## Abstract

The discovery of magic-angle twisted trilayer graphene unlocks various properties of the superconducting phase, such as violation of the Pauli limit and re-entrant superconductivity at large in-plane magnetic fields1,2,3. Here we integrate magic-angle twisted trilayer graphene into a double-layer structure to study the superconducting phase. Using proximity screening from the adjacent metallic layer, we examine the stability of superconductivity and demonstrate that Coulomb repulsion competes with the mechanism underlying Cooper pairing. Furthermore, we use a combination of transport and thermodynamic measurements to probe the ground-state order4,5,6, which points towards a spin-polarized and valley-unpolarized configuration at half moiré filling and for the Fermi surface at doping levels close to that point. Our findings provide important constraints for theoretical models aiming to understand the nature of superconductivity. A possible scenario is that electron–phonon coupling stabilizes a superconducting phase with a spin-triplet, valley-singlet order parameter7,8,9,10,11,12,13.

This is a preview of subscription content, access via your institution

## Relevant articles

• ### Alternating twisted multilayer graphene: generic partition rules, double flat bands, and orbital magnetoelectric effect

npj Computational Materials Open Access 13 May 2022

## Access options

\$39.95

Prices may be subject to local taxes which are calculated during checkout

## Data availability

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

## References

1. 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).

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

3. 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).

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

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

6. 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).

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

8. 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).

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

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

11. 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).

12. Lian, B., Wang, Z. & Bernevig, B. A. Twisted bilayer graphene: a phonon-driven superconductor. Phys. Rev. Lett. 122, 257002 (2019).

13. Wu, F., MacDonald, A. H. & Martin, I. Theory of phonon-mediated superconductivity in twisted bilayer graphene. Phys. Rev. Lett. 121, 257001 (2018).

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

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

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

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

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

19. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).

20. Lee, K. et al. Chemical potential and quantum Hall ferromagnetism in bilayer graphene. Science 345, 58–61 (2014).

21. Ponomarenko, L. et al. Tunable metal–insulator transition in double-layer graphene heterostructures. Nat. Phys. 7, 958–961 (2011).

22. Ochi, M., Koshino, M. & Kuroki, K. Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions. Phys. Rev. B 98, 081102 (2018).

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

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

25. Kang, J., Bernevig, B. A. & Vafek, O. Cascades between light and heavy fermions in the normal state of magic-angle twisted bilayer graphene. Phys. Rev. Lett. 127, 266402 (2021).

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

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

28. Kim, H. et al. Spectroscopic signatures of strong correlations and unconventional superconductivity in twisted trilayer graphene. Preprint at https://arxiv.org/abs/2109.12127 (2021).

29. Turkel, S. et al. Twistons in a sea of magic. Preprint at https://arxiv.org/abs/2109.12631 (2021).

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

31. Cornfeld, E., Rudner, M. S. & Berg, E. Spin-polarized superconductivity: order parameter topology, current dissipation, and multiple-period Josephson effect. Phys. Rev. Res. 3, 013051 (2021).

32. Khalaf, E., Chatterjee, S., Bultinck, N., Zaletel, M. P. & Vishwanath, A. Charged skyrmions and topological origin of superconductivity in magic-angle graphene. Sci. Adv. 7, eabf5299 (2021).

## Acknowledgements

We thank A. Young, O. Vafek and Y. Zhang for helpful discussions. This work was primarily supported by Brown University. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement no. DMR-1644779 and the State of Florida. Device fabrication was performed in the Institute for Molecular and Nanoscale Innovation at Brown University. We acknowledge the use of equipment funded by the MRI award DMR-1827453. 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. 19H05790, 20H00354 and 21H05233).

## Author information

Authors

### Contributions

X.L. and N.J.Z. fabricated the device and performed the measurements. X.L., N.J.Z. and J.I.A.L. analysed the data. X.L., N.J.Z. and J.I.A.L. wrote the manuscript. K.W. and T.T. provided the hBN crystals.

### Corresponding author

Correspondence to J. I. A. Li.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Physics thanks Bheema Chittari 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

### Extended Data Fig. 1 The device characterization.

(a) Optical image of the hybrid double-layer device. The red, green and white dashed contours highlight tTLG, Bernal bilayer graphene and the middle 2 nm thick hBN layers, respectively. The hall bar channel is fabricated in the bubble-free region. The scale bar is 5 μm. (b) The four-terminal longitudinal resistance RtTLG obtained from different contact pairs labelled in (a) vs νtTLG at T = 100 mK. The measured RtTLG are almost the same among different contact pairs, showing the high uniformity in this device.

### Extended Data Fig. 2 The effect of in-plane Zeeman coupling at different DtTLG.

The longitudinal resistance RtTLG as a function of νtTLG and DtTLG at (a) B = 0 T and (b) total magnetic field Btotal = 10 T measured at T = 20 mK. (c) The linecuts of RtTLG vs νtTLG at different total magnetic field Btotal and DtTLG extracted from (a) and (b). The total magnetic field is oriented at an angle relative to the device plane of θ = 2.

### Extended Data Fig. 3 The Coulomb screening effect on superconductivity near νtTLG = -2 in the Pauli limit violation regime.

The density range of superconducting region ΔnSC as a function of Bernal density nBLG at DBLG = -38 mV/nm measured at B = 4.5 T and T = 300 mK. Due to the Pauli limit at the optimal doping $${B}_{\parallel }^{Pauli}$$ is about 4.2 T, this result is measured at B > $${B}_{\parallel }^{Pauli}$$, where the Pauli limit is violated. The inset shows RtTLG vs νtTLG measured at DBLG = -38 mV/nm with different nBLG at B = 5.5 T and T = 300 mK. ΔnSC is determined by the boundary of the superconducting region, which is practically defined by the density where RtTLG < 100 Ω. At the optimal doping, DBLG = − 38 mV/nm and nBLG = 0 correspond to DtTLG= 205 mV/nm for tTLG. Similar to the results in Fig. 1e, ΔnSC in the Pauli limit violation regime is also minimum when Bernal bilayer is fully insulating (nBLG = 0).

### Extended Data Fig. 4 Define the tilt angle for the in-plane magnetic field measurements.

(a) Inverse Hall resistance as a function of carrier density ntTLG near the charge neutrality point measured at Btotal = 10 T and T = 20 mK. According to $${R}_{xy}^{-1}=ne/{B}_{\perp }$$, by calculating the slope from the linear fitting shown as the dashed line, we obtain B = 0.35 T, which corresponds to the tilt angle of θ = 2. (b) Hall resistance Rxy versus bottom voltage bias Vbot measured with different fixed tilt angles θ at Btotal = 15 T and T = 300 mK. The right panel shows the inverse Hall resistance vs ntTLG at θ = 0.55 , and the linear fitting is shown as the black dashed line. The tilt angle is calculated as the same method in (a). The blue trace shows Rxy measured at the minimum tilt angle. Given the small Hall resistance, variations in Rxy are most likely dominated by mixing from the longitudinal channel. This minimum tilt angle in our measurement is regarded as the nominal zero tilt angle, where all the fully in-plane magnetic field dependence measurements are performed.

### Extended Data Fig. 5 The in-plane magnetic field dependence of RtTLG at νtTLG = − 2.

RtTLG as a function of νtTLG at different in-plane magnetic field B measured at (a) DtTLG = 400 mV/nm and (b) DtTLG = 0 mV/nm, respectively, and T = 300 mK. (c) The value of the resistance peak at νtTLG = − 2 as a function of in-plane magnetic field B extracted from (a) and (b).

### Extended Data Fig. 6 Hall density.

(a-b) Hall density nH as a function of DtTLG and νtTLG at T = 20 mK measured at (a) B = 0.5 T and (b) Btotal = 10 T oriented at an angle relative to the device plane of θ = 2. Isospin-symmetry-breaking transitions, manifested in Hall density resets, remain largely unchanged in the presence of an in-plane B field.

### Extended Data Fig. 7 Pomeranchuk effect near νtTLG = + 1.

(a) Chemical potential μtTLG and (b) inverse compressibility dμtTLG/dνtTLG measured near νtTLG = + 1 at B = 0 (top panel) and Btotal = 10 T oriented at an angle relative to the device plane of 2 (bottom panel). The jump in μtTLG and the sharp peak in dμtTLG/dνtTLG denote the Fermi surface reconstruction, which shifts to smaller filling with increasing temperature. At the same time, the position of the same isospin transition appears largely insensitive to in-plane Zeeman coupling. This confirms that the spin degree of freedom is frozen, owing to large spin stiffness, and the Pomeranchuk transition is driven by fluctuations in valley isospin moment.

## Supplementary information

### Supplementary Information

Supplementary Data

### Supplementary Data

Source Data Supplementary Fig. 1

### Supplementary Data

Source Data Supplementary Fig. 2

### Supplementary Data

Source Data Supplementary Fig. 3

### Supplementary Data

Source Data Supplementary Fig. 4

### Supplementary Data

Source Data Supplementary Fig. 6

### Supplementary Data

Source Data Supplementary Fig. 7

### Supplementary Data

Source Data Supplementary Fig. 8

## Source data

### Source Data Fig. 1

Statistical source data.

### Source Data Fig. 2

Statistical source data.

### Source Data Fig. 3

Statistical source data.

### Source Data Fig. 4

Statistical source data.

### Source Data Extended Data Fig. 1

Statistical source data.

### Source Data Extended Data Fig. 2

Statistical source data.

### Source Data Extended Data Fig. 3

Statistical source data.

### Source Data Extended Data Fig. 4

Statistical source data.

### Source Data Extended Data Fig. 5

Statistical source data.

### Source Data Extended Data Fig. 6

Statistical source data.

### Source Data Extended Data Fig. 7

Statistical source data.

## Rights and permissions

Reprints and Permissions

Liu, X., Zhang, N.J., Watanabe, K. et al. Isospin order in superconducting magic-angle twisted trilayer graphene. Nat. Phys. 18, 522–527 (2022). https://doi.org/10.1038/s41567-022-01515-0

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41567-022-01515-0

• ### Zero-field superconducting diode effect in small-twist-angle trilayer graphene

• Jiang-Xiazi Lin
• Phum Siriviboon
• J.I.A. Li

Nature Physics (2022)

• ### Emergence of correlations in alternating twist quadrilayer graphene

• G. William Burg
• Eslam Khalaf
• Emanuel Tutuc

Nature Materials (2022)

• ### Alternating twisted multilayer graphene: generic partition rules, double flat bands, and orbital magnetoelectric effect

• Bo Xie
• Ran Peng
• Jianpeng Liu

npj Computational Materials (2022)