Understanding the mechanism of high-transition-temperature (high-Tc) superconductivity is a central problem in condensed matter physics. It is often speculated that high-Tc superconductivity arises in a doped Mott insulator1 as described by the Hubbard model2,3,4. An exact solution of the Hubbard model, however, is extremely challenging owing to the strong electron–electron correlation in Mott insulators. Therefore, it is highly desirable to study a tunable Hubbard system, in which systematic investigations of the unconventional superconductivity and its evolution with the Hubbard parameters can deepen our understanding of the Hubbard model. Here we report signatures of tunable superconductivity in an ABC-trilayer graphene (TLG) and hexagonal boron nitride (hBN) moiré superlattice. Unlike in ‘magic angle’ twisted bilayer graphene, theoretical calculations show that under a vertical displacement field, the ABC-TLG/hBN heterostructure features an isolated flat valence miniband associated with a Hubbard model on a triangular superlattice5,6 where the bandwidth can be tuned continuously with the vertical displacement field. Upon applying such a displacement field we find experimentally that the ABC-TLG/hBN superlattice displays Mott insulating states below 20 kelvin at one-quarter and one-half fillings of the states, corresponding to one and two holes per unit cell, respectively. Upon further cooling, signatures of superconductivity (‘domes’) emerge below 1 kelvin for the electron- and hole-doped sides of the one-quarter-filling Mott state. The electronic behaviour in the ABC-TLG/hBN superlattice is expected to depend sensitively on the interplay between the electron–electron interaction and the miniband bandwidth. By varying the vertical displacement field, we demonstrate transitions from the candidate superconductor to Mott insulator and metallic phases. Our study shows that ABC-TLG/hBN heterostructures offer attractive model systems in which to explore rich correlated behaviour emerging in the tunable triangular Hubbard model.
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The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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We acknowledge discussions with G. Zhang and T. Xiang. G.C. and F.W. were supported as part of the Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences. A.L.S. was supported by a National Science Foundation Graduate Research Fellowship and a Ford Foundation Predoctoral Fellowship. The work of I.T.R., E.J.F. and D.G.-G. on this project was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515. For dilution fridge support, low-temperature infrastructure and cryostat support were funded in part by the Gordon and Betty Moore Foundation through grant GBMF3429. Part of the sample fabrication was conducted at the Nano-fabrication Laboratory at Fudan University. Y.Z. acknowledges financial support from the National Key Research Program of China (grants 2016YFA0300703 and 2018YFA0305600), the NSF of China (grants U1732274, 11527805, 11425415 and 11421404) and the Strategic Priority Research Program of the Chinese Academy of Sciences (grant XDB30000000). Z.S. acknowledges support from the National Key Research and Development Program of China (grant 2016YFA0302001) and the NSF of China (grants 11574204 and 11774224). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative, conducted by MEXT, Japan and CREST (JPMJCR15F3), JST. J.J. was supported by the Samsung Science and Technology Foundation under project SSTF-BA1802-06 and by the Korean National Research Foundation grant NRF-2016R1A2B4010105.
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 figures and tables
a, b, Calculated band structure of ABC-TLG/hBN with negative (a) and positive (b) displacement fields. The solid and dashed lines correspond to band structure at the K and K′ valleys, respectively. The energy difference between top- and bottom-layer graphene 2Δ = 20 meV corresponds to the displacement field D = 0.4 V nm−1.
a–c, Density of states of the first electron and hole minibands in the single-particle band structure of the ABC-TLG/hBN moiré superlattice with effective potential energy differences between the bottom and top graphene layer of 2Δ = 0 meV, 10 meV and 20 meV. d–f, The integrated density of states corresponding to a–c, respectively.
a, dVxx/dI as a function of d.c. current. b, Resistance as a function of temperature at B⊥ = 2 T.
Rxx at 1/4 filling as a function of temperatures from 14 K to 250 K, D = −0.54 V nm−1, which indicates that the 1/4-filling Mott state has insulating behaviour at high temperatures.
Vxx and dVxx/dI as a function of the d.c. bias current at a hole-doped 1/2-filling state. The narrow plateau in the I–V curve and the dip of dVxx/dI near zero bias current may be due to very weak superconductivity in this state. Data are taken at T = 0.04 K.
Resistivity of the second ABC-TLG/hBN device as a function of Vt and Vb at T = 1.5 K.
a. Resistivity ρxx–T curve at n = 0.56 × 1012 cm−2, D = 0.55 V nm−1. The high-temperature data above 10 K were measured during a separate cooldown. b, I–V curves at different temperatures, showing a plateau below the critical current of about 6 nA below T = 0.57 K. This plateau region tilts and becomes close to linear at higher temperature, characteristic of a superconducting transition. c, The dV/dI colour plot as a function of d.c. bias current and perpendicular magnetic field at T = 0.05 K. The superconductivity is suppressed by the magnetic field and almost disappears at B ≈ 0.6 T. d, Carrier-density-dependent phase diagram at D = 0.55 V nm−1. The dashed line corresponds to the 1/4 filling.
A description of the calculated band structure of ABC-TLG/hBN with negative and positive displacement fields.