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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.

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Fig. 1: Magic-angle tTLG in a double-layer structure and Coulomb screening.
Fig. 2: Isospin orders.
Fig. 3: Effect of displacement field DtTLG.
Fig. 4: Isospin Pomeranchuk effect and spin stiffness.

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.

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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 and Affiliations

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.

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The authors declare no competing interests.

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Nature Physics thanks Bheema Chittari and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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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.

Source data

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.

Source data

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).

Source data

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.

Source data

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).

Source data

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.

Source data

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.

Source data

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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

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