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# Robust superconductivity in magic-angle multilayer graphene family

## Abstract

The discovery of correlated states and superconductivity in magic-angle twisted bilayer graphene (MATBG) established a new platform to explore interaction-driven and topological phenomena. However, despite multitudes of correlated phases observed in moiré systems, robust superconductivity appears the least common, found only in MATBG and more recently in magic-angle twisted trilayer graphene. Here we report the experimental realization of superconducting magic-angle twisted four-layer and five-layer graphene, hence establishing alternating twist magic-angle multilayer graphene as a robust family of moiré superconductors. This finding suggests that the flat bands shared by the members play a central role in the superconductivity. Our measurements in parallel magnetic fields, in particular the investigation of Pauli limit violation and spontaneous rotational symmetry breaking, reveal a clear distinction between the N = 2 and N > 2-layer structures, consistent with the difference between their orbital responses to magnetic fields. Our results expand the emergent family of moiré superconductors, providing new insight with potential implications for design of new superconducting materials platforms.

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## Data availability

The data that support the current study are available from Harvard Dataverse50.

## Code availability

The codes that support the current study are available from Harvard Dataverse50.

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## Acknowledgements

We thank A. Vishwanath, E. Khalaf and P. Ledwith for fruitful discussions. This work was primarily supported by the US Department of Energy (DOE), Office of Basic Energy Sciences (BES), Division of Materials Sciences and Engineering under award DE-SC0001819 (J.M.P. and S.S.). Help with transport measurements and data analysis were supported by the National Science Foundation (DMR-1809802), and the STC Center for Integrated Quantum Materials (NSF grant no. DMR-1231319) (Y.C.). Help with device fabrication was supported by the Air Force Office of Scientific Research (AFOSR) 2DMAGIC MURI FA9550-19-1-0390 (L.X.). P.J.-H. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF9463. P.J.-H. acknowledges partial support by the Fundación Ramon Areces and the CIFAR Quantum Materials programme. The development of new nanofabrication and characterization techniques enabling this work was supported by the US DOE Office of Science, BES, under award DE-SC0019300. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan (grant no. JPMXP0112101001), JSPS KAKENHI (grant no. JP20H00354), CREST(grant no. JPMJCR15F3) and JST. This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities supported by the National Science Foundation (grant no. DMR-0819762) and of Harvard’s Center for Nanoscale Systems, supported by the NSF (grant no. ECS-0335765).

## Author information

Authors

### Contributions

J.M.P. and Y.C. fabricated the samples and performed transport measurements, with help from L.-Q.X. and S.S. K.W. and T.T. provided hBN samples. J.M.P. and Y.C. performed numerical simulations. J.M.P., Y.C. and P.J-H. performed data analysis, discussed the results and wrote the manuscript with input from all co-authors.

### Corresponding authors

Correspondence to Jeong Min Park or Pablo Jarillo-Herrero.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

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

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

## Extended data

### Extended Data Fig. 1 Calculated band structure of MATNG in the presence of electric displacement field $$\frac{D}{{\varepsilon }_{0}}=0.5$$ V/nm.

The calculation uses the screened electrostatic potential calculated as illustrated in Extended Data Fig. 6c. For all N>2 MATNG structures, the electric displacement field hybridizes the flat bands with other dispersive bands.

### Extended Data Fig. 2 ν-D phase diagrams of MAT4G and MAT5G devices.

Devices 4A-C shown in (a-c) are MAT4G devices, while Devices 5A-E shown in (d-i) are MAT5G devices. Device 5B-1 and 5B-2 are two different contacts from the same device that shares the same top gate and back gate. All measurements were performed at T ~ 200 mK. In all MAT5G devices, we find the superconductivity region to be either approaching or exceeding ν = 4, which is indicated by blue dashed lines in (d-i).

### Extended Data Fig. 3 Landau fan diagrams of MAT4G and MAT5G devices.

All measurements were performed at T ~ 200 mK.

### Extended Data Fig. 4 Superconducting properties in other MAT4G and MAT5G devices.

(a-c) Temperature-dependent Vxx − I curves in device 4A, 4C and 5D. (d-f) ν − T phase diagrams in device 4A, 4C and 5D. (g-i) TBKT and Ginzburg-Landau coherent length ξGL in device 4C, 5D and 5E. The error bars in (g-i) correspond to ξGL extracted using p=30% (point), 35% (lower bound), and 25% (upper bound).

### Extended Data Fig. 5 ν-D map of BKT transition temperature in device 4B, 5A, 5B-1, and 5C.

(a-d) TBKT as a function of ν and D in device 4B (a), 5A (b), 5B-1 (c), and 5C (d).

### Extended Data Fig. 6 Modeling layer-inhomogeneous screening in MATNG.

(a) Schematic of N graphene layers being gated by a top gate (TG) and bottom gate (BG). The electric displacement field between the graphene layers is reduced compared to the field outside the stack due to screening. (b) By assuming a finite density of states $${{{\mathcal{D}}}}$$ on each graphene layer, we model the N-layer system as a capacitor network, where $${{{{\rm{c}}}}}_{{{{\rm{q}}}}}={{{{\rm{e}}}}}^{2}{{{\mathcal{D}}}}$$ is the quantum capacitance and cg = ε0/d is the geometric capacitance. (c) Calculated electrostatic potential vi on each layer for MATBG, MATTG, MAT4G, MAT5G and MAT6G (N = 2, …, 6), assuming bandwidth W=20 meV, and external displacement field $$\frac{{{{\rm{D}}}}}{{\varepsilon }_{0}}=0.5V/nm$$. The twist angle is the same as in Fig. 4, except for 6L which is 1.99°. Here the midplane (the plane of the $$\frac{{{{\rm{N}}}}+1}{2}$$-th layer when N is odd and the midplane between $$\frac{{{{\rm{N}}}}}{2}$$-th layer and ($$\frac{{{{\rm{N}}}}}{2}+1$$)-th layer when N is even) is set to be zero both in layer position and in electrostatic potential. For comparison, the electrostatic potential without screening eDdx/ε0 is shown as the dashed line, where $$-\frac{({{{\rm{N}}}}-1)}{2} < {{{\rm{x}}}} < \frac{({{{\rm{N}}}}-1)}{2}$$ is the layer position (horizontal axis) and d=0.34 nm is the interlayer distance).

### Extended Data Fig. 7 Typical optical microscope images for MAT4G and MAT5G devices.

The illustration shows the split-gate geometry for the Josephson junction. Data from all contacts including the ones not shown in the figures exhibit robust superconductivity.

### Extended Data Fig. 8 In-plane magnetic field response in other MAT4G and MAT5G devices.

(a-d) Absence of rotational symmetry breaking in other MAT4G and MAT5G devices. The filling factors for (a-d) are ν = − 3.41, − 1.95, − 3.50, − 2.33, respectively, and the electric displacement fields are $$\frac{{{{\rm{D}}}}}{{\varepsilon }_{0}}=0.29V/nm,0.29V/nm,0V/nm,0V/nm$$, respectively. (d-e) Pauli limit violation in Device 4C measured at ν = 2.29 and $$\frac{{{{\rm{D}}}}}{{\varepsilon }_{0}}=0V/nm$$ (d) and Device 5E measured at ν = 2.59 and $$\frac{{{{\rm{D}}}}}{{\varepsilon }_{0}}=0V/nm$$ (e).

### Extended Data Fig. 9 D-independent Pauli limit violation in MAT4G.

(a-b) shows the D-Band D-T map of Rxx in device 4B. We find the critical in-plane field and critical temperature follow similar trend with D, indicating that the PVR, which is proportional to the ratio between them, is largely independent of D. (c-d) Same trend is observed in device 4C.

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Park, J.M., Cao, Y., Xia, LQ. et al. Robust superconductivity in magic-angle multilayer graphene family. Nat. Mater. 21, 877–883 (2022). https://doi.org/10.1038/s41563-022-01287-1

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• DOI: https://doi.org/10.1038/s41563-022-01287-1

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Nature Materials (2022)