Unconventional superconductivity in magic-angle graphene superlattices

Abstract

The behaviour of strongly correlated materials, and in particular unconventional superconductors, has been studied extensively for decades, but is still not well understood. This lack of theoretical understanding has motivated the development of experimental techniques for studying such behaviour, such as using ultracold atom lattices to simulate quantum materials. Here we report the realization of intrinsic unconventional superconductivity—which cannot be explained by weak electron–phonon interactions—in a two-dimensional superlattice created by stacking two sheets of graphene that are twisted relative to each other by a small angle. For twist angles of about 1.1°—the first ‘magic’ angle—the electronic band structure of this ‘twisted bilayer graphene’ exhibits flat bands near zero Fermi energy, resulting in correlated insulating states at half-filling. Upon electrostatic doping of the material away from these correlated insulating states, we observe tunable zero-resistance states with a critical temperature of up to 1.7 kelvin. The temperature–carrier-density phase diagram of twisted bilayer graphene is similar to that of copper oxides (or cuprates), and includes dome-shaped regions that correspond to superconductivity. Moreover, quantum oscillations in the longitudinal resistance of the material indicate the presence of small Fermi surfaces near the correlated insulating states, in analogy with underdoped cuprates. The relatively high superconducting critical temperature of twisted bilayer graphene, given such a small Fermi surface (which corresponds to a carrier density of about 1011 per square centimetre), puts it among the superconductors with the strongest pairing strength between electrons. Twisted bilayer graphene is a precisely tunable, purely carbon-based, two-dimensional superconductor. It is therefore an ideal material for investigations of strongly correlated phenomena, which could lead to insights into the physics of high-critical-temperature superconductors and quantum spin liquids.

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Figure 1: Two-dimensional superconductivity in a graphene superlattice.
Figure 2: Gate-tunable superconductivity in magic-angle TBG.
Figure 3: Magnetic-field response of the superconducting states in magic-angle TBG.
Figure 4: Temperature–density phase diagrams of magic-angle TBG at different magnetic fields.
Figure 5: Quantum oscillations in magic-angle TBG at high fields.
Figure 6: Superconductivity in the strong-coupling limit.

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Acknowledgements

We acknowledge discussions with R. Ashoori, S. Carr, R. Comin, L. Fu, P. A. Lee, L. Levitov, K. Rajagopal, S. Todadri, A. Vishwanath and M. Zwierlein. This work was primarily supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4541 and the STC Center for Integrated Quantum Materials (NSF grant number DMR-1231319) for device fabrication, transport measurements and data analysis (Y.C., P.J.-H.), and theoretical calculations (S.F.). Data analysis by V.F. was supported by AFOSR grant number FA9550-16-1-0382. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan and JSPS KAKENHI grant numbers JP15K21722 and JP25106006. This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities, supported by the NSF (DMR-0819762), and of Harvard’s Center for Nanoscale Systems, supported by the NSF (ECS-0335765). E.K. acknowledges additional support by ARO MURI award W911NF-14-0247.

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Contributions

Y.C. fabricated samples and performed transport measurements. Y.C., V.F. and P.J.-H. performed data analysis and discussed the results. P.J.-H. supervised the project. S.F. and E.K. provided numerical calculations. K.W. and T.T. provided hexagonal boron nitride samples. Y.C., V.F. and P.J.-H. co-wrote the manuscript with input from all co-authors.

Corresponding authors

Correspondence to Yuan Cao or Pablo Jarillo-Herrero.

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Reviewer Information Nature thanks E. Mele, J. Robinson and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Evidence of phase-coherent transport in superconducting magic-angle TBG.

a, b, Differential resistance dV/dI versus bias current I and perpendicular field B, at two different charge densities n, corresponding to those in Fig. 3a. Periodic oscillations are observed in the critical current (identified approximately as the position of the bright peaks in dV/dI). c, d, Simulations intended to reproduce qualitatively the behaviour observed in a and b.

Extended Data Figure 2 Supplementary quantum oscillation data.

a, b, Quantum oscillations in device M1 (a; θ = 1.16°, data shown for Rxx) and device D1 (b; θ = 1.08°, data shown for the two-probe conductance G2). The first derivative with respect to the gate-defined charge density n has been taken in both cases to enhance the colour contrast. Both devices exhibit a Landau fan that emerges from the half-filling state −ns/2 and have a Landau level sequence of −2, −4, −6, −8, …, consistent with the results shown in Fig. 5. By comparison, the Landau fans that start from charge neutrality have a sequence of −4, −8, −12, …

Extended Data Figure 3 Low-field Hall effect in magic-angle TBG.

a, b, Low-field Hall effect for devices M1 (a) and M2 (b). The Hall density is plotted as a function of the total charge density induced by the gate (n), measured at temperatures from 0.4 K to 31.8 K. Coloured vertical bars correspond to densities of −ns, −ns/2, ns/2 and ns for the two samples. Dashed lines are the expected Hall density if the offset given in the corresponding formula is considered.

Supplementary information

Band structure twisted bilayer graphene – animation

This video shows the evolution of the band structure of twisted bilayer graphene as a function of twist angle, from 3 degrees to 0.8 degrees. (MOV 667 kb)

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Cao, Y., Fatemi, V., Fang, S. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018). https://doi.org/10.1038/nature26160

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