Untying the insulating and superconducting orders in magic-angle graphene

Abstract

The coexistence of superconducting and correlated insulating states in magic-angle twisted bilayer graphene1,2,3,4,5,6,7,8,9,10,11 prompts fascinating questions about their relationship. Independent control of the microscopic mechanisms that govern these phases could help uncover their individual roles and shed light on their intricate interplay. Here we report on direct tuning of electronic interactions in this system by changing the separation distance between the graphene and a metallic screening layer12,13. We observe quenching of correlated insulators in devices with screening layer separations that are smaller than the typical Wannier orbital size of 15 nanometres and with twist angles that deviate slightly from the magic angle of 1.10 ± 0.05 degrees. Upon extinction of the insulating orders, the vacated phase space is taken over by superconducting domes that feature critical temperatures comparable to those in devices with strong insulators. In addition, we find that insulators at half-filling can reappear in small out-of-plane magnetic fields of 0.4 tesla, giving rise to quantized Hall states with a Chern number of 2. Our study suggests re-examination of the often-assumed ‘parent-and-child’ relation between the insulating and superconducting phases in moiré graphene, and suggests a way of directly probing the microscopic mechanisms of superconductivity in strongly correlated systems.

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Fig. 1: Screening-controlled MATBG phase diagrams for near-magic twist angles.
Fig. 2: The dependence of the superconductivity and correlated insulating phases on temperature and density.
Fig. 3: Formation of Chern insulators in small out of plane magnetic field.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We are grateful for discussions with P. Jarillo-Herrero, A. MacDonald, A. Young, L. Balents, A. Bernevig, B. Lian and C. Dean. D.K.E. acknowledges support from the Ministry of Economy and Competitiveness of Spain through the “Severo Ochoa” programme for Centres of Excellence in R&D (SE5-0522), Fundació Privada Cellex, Fundació Privada Mir-Puig, the Generalitat de Catalunya through the CERCA program, the H2020 Programme under grant agreement number 820378, Project 2D·SIPC and the La Caixa Foundation. L.L. acknowledges support from the Science and Technology Center for Integrated Quantum Materials, NSF grant number DMR-1231319; and Army Research Office Grant W911NF-18-1-0116. F.H.L.K. acknowledges support from the ERC consolidator grant TOPONANOP (grant agreement number 726001). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, and CREST (JPMJCR15F3), JST. P.S. acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement number 754510.

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Authors

Contributions

D.K.E, X.L. and P.S. conceived and designed the experiments. P.S., X.L. and I.D. performed the experiments. P.S. and D.K.E. analysed the data. A.F. and L.L. performed the theoretical modelling. T.T. and K.W. contributed materials. D.K.E. and F.H.L.K. supported the experiments. D.K.E, L.L. and P.S. wrote the paper.

Corresponding author

Correspondence to Dmitri K. Efetov.

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The authors declare no competing interests.

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Peer review information Nature thanks Ronny Thomale, Emanuel Tutuc 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 Fig. 1 Screening layer fabrication method.

a, The sacrificial PC layer is used to pick up the top hBN, which is further used to pick up the first half of a monolayer graphene flake. b, The second half of the graphene flake is rotated by 1.10° to 1.15° and subsequently picked up by the hBN/graphene stack on the PC. c, The heterostructure is further placed on the bottom hBN, which serves as a dielectric spacer. d, e, At the final step the heterostructure is placed on top of the target wafer and the PC layer is removed with chloroform.

Extended Data Fig. 2 AFM and optical micrographs for samples D1, D2 and D3.

a, D1; b, D2; c, D3. The main panels are optical images of the final stacks, from which all three devices were fabricated. The insets demonstrate AFM scans of the final devices etched into multi-terminal Hall bar geometries. The dashed black squares show AFM image areas. The bottom hBN thickness measurements are shown on the lower panels. Height profiles are taken along the white dashed arrow lines. Scale bars, 5 μm.

Extended Data Fig. 3 Two-terminal conductance measurements across all available contacts in device D1.

The key shows two-terminal conductance measurements G2 between different contact pairs corresponding to the inset optical image of the device. Numbers on the device optical micrograph correspond to measured global twist angle values between contact pairs (extracted from resistance maxima). Scale bar, 5 μm. Data are taken at 20 mK.

Extended Data Fig. 4 Superconductivity state characterization in device D1.

The right- (left-) hand panels refers to the superconductivity pocket in the valence (conductance) band on the top panel of Fig. 1c. a, b, Temperature activation of superconductivity for both pockets on the absolute resistivity scale. The insets demonstrate a zoomed-in range of temperatures from 0 K to 1.5 K. c, d, Berezinskii–Kosterlitz–Thouless (BKT) measurements of differential resistance dVxx/dI versus d.c. current bias Idc for both superconductivity pockets. The insets show d.c. voltage as a function of d.c. current bias taken at different temperatures for optimally doped superconductivity states. e, f, Differential conductance dVxx/dI (colour scales) as a function of perpendicular magnetic field B and d.c. current bias Idc shows distinct diamond-like features for both pockets. Zoomed-in images (to the right of each panel) show clear Fraunhofer interference patterns, which are a firm proof of superconductivity. g, h, Ginzburg–Landau coherence length measurements for both pockets. Critical field Bc versus critical temperature Tc taken at half the normal state resistance values. Black dots refer to experimentally obtained values; blue lines are linear fits to the data. We estimate coherence lengths ξGL = 38 nm (g) and ξGL = 101 nm (h).

Extended Data Fig. 5 Hall density measurements in device D1.

Hall density nH versus charge carrier density n extracted from the low-field Hall resistance measurements at 160 mT.

Extended Data Fig. 6 Check for alignment to hBN.

a, Optical image of the monolayer graphene flake on SiO2 substrate used for fabrication of the MATBG heterostructure. White dashed arrows indicate preferable lattice directions (zig-zag or armchair). b, Optical image of the top hBN flake. c, Optical micrograph of the bottom hBN flake. d, Optical image of the final stack on SiO2 substrate. The black dashed arrow indicates the edge of the top hBN shown in b. The orange dashed arrow corresponds to the edge of the bottom hBN shown in panel c. Black (orange) numbers correspond to the angle between the white dashed arrow (graphene edge) and the top (bottom) hBN. We estimate the twist angle between the bottom hBN and MATBG to be about 7(±1.5)° or 23(±1.5)° and between the top hBN and MATBG to be about 25(±1.5)° or 5(±1.5)°. Furthermore, we do not find signatures of alignment to hBN in the magnetic field Shubnikov–de Haas oscillation data for any of the three devices (for example, Extended Data Fig. 7). Scale bars, 20 μm.

Extended Data Fig. 7 Full range magnetic field phase diagram in device D1 at 30 mK.

a, Longitudinal sheet resistance Rxx (colour scale) versus change carrier density n and perpendicular magnetic field B. b, Schematic image of Landau levels shown in a. Solid lines correspond to fourfold degenerate levels with quantized plateaus νLL = 4, 8, 12, … Dashed lines show broken spin and/or valley degeneracy levels. Dark red features to the left show Chern-like insulator states originating from (ν = −2)-filled or (ν = −3)-filled superlattice unit cell corresponding to quantization of 2e2/h (or of e2/h). Blue and green shaded stripes on the left correspond to the superlattice unit cell with commensurate fillings ν = −2 and −3, respectively.

Extended Data Fig. 8 Effect of low magnetic field on correlated states in device D1.

a, Longitudinal sheet resistance Rxx (colour scale) versus charge carrier density n and perpendicular magnetic field B. Iac = 10 nA. b, Rxx as a function of charge carrier density n for valence band superconductivity pockets in a. Iac = 10 nA. c, Resistance versus charge carrier density for valence band superconductivity pockets in a. Iac = 1 nA.

Supplementary information

Supplementary Information

This file contains a discussion of the model used to describe screening in graphene/hBN/graphite heterostructure, including Supplementary Figures 1–4 and additional references.

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Stepanov, P., Das, I., Lu, X. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020). https://doi.org/10.1038/s41586-020-2459-6

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