Abstract
Moiré materials have enabled the realization of flat electron bands and quantum phases that are driven by the strong correlations associated with flat bands1,2,3,4. Superconductivity has been observed, but only in graphene moiré materials5,6,7,8,9. The absence of robust superconductivity in moiré materials beyond graphene, such as semiconductor moiré materials4, has remained a mystery and challenged our current understanding of superconductivity in flat bands. Here we report the observation of robust superconductivity in both 3.5° and 3.65° twisted bilayer tungsten diselenide (WSe2), which hosts a hexagonal moiré lattice10,11. Superconductivity emerges near half-band filling and zero external displacement fields. The optimal superconducting transition temperature is about 200 mK in both cases and constitutes about 1–2% of the effective Fermi temperature; the latter is comparable to the value in high-temperature cuprate superconductors12 and suggests strong pairing. The superconductor borders on two distinct metals below and above half-band filling; it undergoes a continuous transition to a correlated insulator by tuning the external displacement field. The observed superconductivity on the verge of Coulomb-induced charge localization suggests roots in strong electron correlations12,13.
This is a preview of subscription content, access via your institution
Access options
Access Nature and 54 other Nature Portfolio journals
Get Nature+, our best-value online-access subscription
£14.99 / 30 days
cancel any time
Subscribe to this journal
Receive 51 print issues and online access
£199.00 per year
only £3.90 per issue
Buy this article
- Purchase on SpringerLink
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Data availability
Source data are provided with this paper. All other data are available from the corresponding authors upon reasonable request.
References
Andrei, E. Y. & MacDonald, A. H. Graphene bilayers with a twist. Nat. Mater. 19, 1265–1275 (2020).
Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).
Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155–163 (2021).
Mak, K. F. & Shan, J. Semiconductor moiré materials. Nat. Nanotechnol. 17, 686–695 (2022).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).
Hao, Z. et al. Electric field-tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science 371, 1133–1138 (2021).
Wu, F., Lovorn, T., Tutuc, E., Martin, I. & MacDonald, A. Topological insulators in twisted transition metal dichalcogenide homobilayers. Phys. Rev. Lett. 122, 086402 (2019).
Devakul, T., Crépel, V., Zhang, Y. & Fu, L. Magic in twisted transition metal dichalcogenide bilayers. Nat. Commun. 12, 6730 (2021).
Uemura, Y. Condensation, excitation, pairing, and superfluid density in high-Tc superconductors: the magnetic resonance mode as a roton analogue and a possible spin-mediated pairing. J. Phys. Condens. Matter 16, S4515 (2004).
Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012).
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).
Zhao, W. et al. Gate-tunable heavy fermions in a moiré Kondo lattice. Nature 616, 61–65 (2023).
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. 13, 031037 (2023).
Foutty, B. A. et al. Mapping twist-tuned multiband topology in bilayer WSe2. Science 384, 343–347 (2024).
Kang, K. et al. Evidence of the fractional quantum spin Hall effect in moiré MoTe2. Nature 628, 522–526 (2024).
Oh, M. et al. Evidence for unconventional superconductivity in twisted bilayer graphene. Nature 600, 240–245 (2021).
Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F. Superconductivity in rhombohedral trilayer graphene. Nature 598, 434–438 (2021).
Kim, H. et al. Evidence for unconventional superconductivity in twisted trilayer graphene. Nature 606, 494–500 (2022).
Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774–778 (2022).
Zhang, Y. et al. Enhanced superconductivity in spin–orbit proximitized bilayer graphene. Nature 613, 268–273 (2023).
Hsu, Y.-T., Vaezi, A., Fischer, M. H. & Kim, E.-A. Topological superconductivity in monolayer transition metal dichalcogenides. Nat. Commun. 8, 14985 (2017).
Slagle, K. & Fu, L. Charge transfer excitations, pair density waves, and superconductivity in moiré materials. Phys. Rev. B 102, 235423 (2020).
Schrade, C. & Fu, L. Nematic, chiral and topological superconductivity in transition metal dichalcogenides. Phys. Rev. B 110, 035143 (2024).
Hsu, Y.-T., Wu, F. & Das Sarma, S. Spin–valley locked instabilities in moiré transition metal dichalcogenides with conventional and higher-order Van Hove singularities. Phys. Rev. B 104, 195134 (2021).
Bélanger, M., Fournier, J. & Sénéchal, D. Superconductivity in the twisted bilayer transition metal dichalcogenide WSe2: a quantum cluster study. Phys. Rev. B 106, 235135 (2022).
Scherer, M. M., Kennes, D. M. & Classen, L. Chiral superconductivity with enhanced quantized Hall responses in moiré transition metal dichalcogenides. npj Quantum Mater. 7, 100 (2022).
Crépel, V., Guerci, D., Cano, J., Pixley, J. & Millis, A. Topological superconductivity in doped magnetic moiré semiconductors. Phys. Rev. Lett. 131, 056001 (2023).
Klebl, L., Fischer, A., Classen, L., Scherer, M. M. & Kennes, D. M. Competition of density waves and superconductivity in twisted tungsten diselenide. Phys. Rev. Res. 5, L012034 (2023).
Wu, Y.-M., Wu, Z. & Yao, H. Pair-density-wave and chiral superconductivity in twisted bilayer transition metal dichalcogenides. Phys. Rev. Lett. 130, 126001 (2023).
Zegrodnik, M. & Biborski, A. Mixed singlet-triplet superconducting state within the moiré t−J−U model applied to twisted bilayer WSe2. Phys. Rev. B 108, 064506 (2023).
Zhou, B. & Zhang, Y.-H. Chiral and nodal superconductors in the t−J model with valley contrasting flux on a triangular moiré lattice. Phys. Rev. B 108, 155111 (2023).
Xie, Y.-M. & Law, K. Orbital Fulde–Ferrell pairing state in moiré Ising superconductors. Phys. Rev. Lett. 131, 016001 (2023).
Akbar, W., Biborski, A., Rademaker, L. & Zegrodnik, M. Topological superconductivity with mixed singlet-triplet pairing in moiré transition metal dichalcogenide bilayers. Phys. Rev. B 110, 064516 (2024).
Tinkham, M. Introduction to Superconductivity (Courier Corporation, 2004).
Saito, Y., Nojima, T. & Iwasa, Y. Highly crystalline 2D superconductors. Nat. Rev. Mater. 2, 16094 (2017).
Smidman, M. et al. Unconventional fully gapped superconductivity in the heavy-fermion metal CeCu2Si2. Rev. Mod. Phys. 95, 031002 (2023).
Törmä, P., Peotta, S. & Bernevig, B. A. Superconductivity, superfluidity and quantum geometry in twisted multilayer systems. Nat. Rev. Phys. 4, 528–542 (2022).
Pan, H., Wu, F. & Das Sarma, S. Band topology, Hubbard model, Heisenberg model, and Dzyaloshinskii–Moriya interaction in twisted bilayer WSe2. Phy. Rev. Res. 2, 033087 (2020).
Bi, Z. & Fu, L. Excitonic density wave and spin-valley superfluid in bilayer transition metal dichalcogenide. Nat. Commun. 12, 642 (2021).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Ghiotto, A. et al. Quantum criticality in twisted transition metal dichalcogenides. Nature 597, 345–349 (2021).
Gustafsson, M. V. et al. Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2. Nat. Mater. 17, 411–415 (2018).
Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol. 13, 246–252 (2018).
Fallahazad, B. et al. Shubnikov–de Haas oscillations of high-mobility holes in monolayer and bilayer WSe2: Landau level degeneracy, effective mass, and negative compressibility. Phys. Rev. Lett. 116, 086601 (2016).
Li, T. et al. Continuous Mott transition in semiconductor moiré superlattices. Nature 597, 350–354 (2021).
Tang, Y. et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021).
Mourachkine, A. High-Temperature Superconductivity in Cuprates: The Nonlinear Mechanism and Tunneling Measurements (Kluwer Academic Publishers, 2002).
Acknowledgements
We thank B. A. Bernevig, D. Chowdhury, S. Das Sarma, L. Fu, C. Jian, E.-A. Kim, K. T. Law, A. H. MacDonald and Q. Si for discussions; and J. Zhu and P. Knüppel for technical discussions. This work was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award number DE-SC0019481 (transport measurements), the National Science Foundation DMR-1807810 (sample fabrication) and the Air Force Office of Scientific Research under award number FA9550-20-1-0219 (modelling). It was also funded in part by the Gordon and Betty Moore Foundation (grant number GBMF11563). We used the Cornell NanoScale Facility, an NNCI member supported by NSF Grant NNCI-2025233, for sample fabrication. The growth of the hBN crystals was supported by the Elemental Strategy Initiative of MEXT, Japan, and CREST (JPMJCR15F3), JST.
Author information
Authors and Affiliations
Contributions
Y.X. and Z.H. fabricated the devices, performed the transport measurements and analysed the data. K.W. and T.T. grew the bulk hBN crystals. K.F.M. and J.S. designed the scientific objectives and oversaw the project. All authors discussed the results and commented on the paper.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Peer review
Peer review information
Nature thanks Sergio de la Barrera and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Extended data figures and tables
Extended Data Fig. 1 Sample and device characterization.
a, Three-dimensional schematic of a tWSe2 dual-gated device. Both the top gate (TG) and bottom gate (BG) are made of hBN and few-layer graphite (Gr). The tWSe2 sample is contacted by Pt electrodes. The Pd contact gates (CG) and split gates (SG) turn on the Pt contacts and turn off the parallel channels, respectively. b, Optical micrograph of the 3.65° device. Specific features of interest are BG (enclosed by the black dashed line), TG (black solid line), uniform moiré region (red dashed line) and contact electrode 1–6. The scale bar is 4 µm. c,d, Filling factor dependence of two-terminal resistance R2t for different contact pairs at T = 1 K and B = 0 T. The sample is an insulator at ν ≈ 1 for E = 55 mV/nm (c). The variation in filling factor for the resistance peak is about 0.025, which corresponds to a disorder density of 1 × 1011 cm−2. The sample is a metal at ν ≈ 1 for E = 100 mV/nm (d) and the four-terminal resistance is below 350 Ω. The contact resistance is determined from R2t to be 10–40 kΩ.
Extended Data Fig. 2 Calibration of the moiré density.
a,b, Longitudinal resistance R as a function of E and ν at 50 mK under B = 0 T (a) and 12 T (b). Large bias current is used in the measurement and superconductivity is not observed in a. Landau levels are clearly observed in b. Landau levels with index νLL = 2-8 (denoted by dotted lines) in the layer-polarized region are spin- and valley-polarized (i.e. nondegenerate). In addition, the Zeeman-split vHS features under B = 12 T are marked by dashed lines; these features interrupt the quantum oscillations (the vertical stripes in b). The midpoint of the Zeeman-split features is in good agreement with the location of the single vHS feature under B = 0 T (dashed line in a). c, Landau level index νLL as a function of moiré lattice filling ν follows a linear dependence (blue line). The moiré density is determined from the slope to be nM ≈ (4.25 ± 0.03) × 1012 cm−2. d, R as a function of B and ν at 50 mK and E = 100 mV/nm. Two sets of Landau fan emerging from the moiré band edges (i.e. ν = 0 and ν = 2) are marked by the dashed lines. The results give the same moiré density as above. e, The derivative of the sample conductance with respect to \(\nu ({dG}/d\nu )\) as a function of ν and 1/B at 50 mK and E = 100 mV/nm. Hofstadter’s oscillations are observed as periodic crossings of Landau levels in 1/B, as denoted by the horizontal dashed lines. f, 1/B at the dashed lines in e as a function of the periodic index q. A linear fit to the data gives a 1/B period (5.8 ± 0.1) × 10−3 T−1, which corresponds to nM ≈ (4.22 ± 0.06) × 1012 cm−2. The value is in good agreement with that obtained from a-c.
Extended Data Fig. 3 Superconductivity in different measurement configurations.
a,b, Measurement configurations for four-terminal resistances: R46,23 (a) and R15,24 (b). A bias current is applied on the first two electrodes and the voltage drop is measured using the second two electrodes. The electrodes are labelled as in Extended Data Fig. 1b. Results in the main text are obtained using configuration a. c, Longitudinal resistance R as a function of E and ν at 50 mK and zero magnetic field using configuration b. d, Filling dependence of longitudinal resistance R for measurement configuration a and b at E ≈ 8 mV/nm and T = 50 mK. Independent of the measurement configuration, superconductivity is observed in tWSe2 near ν = 1.
Extended Data Fig. 4 Electronic band structure of 3.65°-tWSe2 from the continuum model.
a-c, Topmost moiré valence bands of the K-valley state for E = 0 mV/nm (a), 100 mV/nm (b) and 200 mV/nm (c). d-f, The corresponding electronic DOS as a function of filling ν. The vHS moves from ν < 1 at E = 0 mV/nm to ν > 1 at E = 200 mV/nm. The non-monotonic electric field dependence of DOS at the vHS is dependent on the lifetime broadening we include in the calculations.
Extended Data Fig. 5 Hall resistance.
a,b, Longitudinal resistance R (a) and Hall resistance Rxy (b) as a function of B and ν at T = 50 mK and E = 0 mV/nm. Large bias (above the critical current) is applied, and superconductivity is not observed. The strong Rxy response below filling 0.9 under small magnetic fields is an artifact because of the large magneto resistance and the coarse field step. The vHS manifests a peak in R (a) and a sign change in Rxy (b). The dashed lines are a guide to the eye of the location of the vHS for negative magnetic fields. The vHS is located at ν < 1 for B = 0 and rapidly disperses with B likely due to the combined Zeeman and orbital effects. c,d, Linecut of a,b at ν = 0.8 (c) and ν = 1.1 (d) with fine field scans. The measurement configuration is shown in the inset. We symmetrize and anti-symmetrize the response under positive and negative fields to obtain R and Rxy, respectively. Both forward and backward field scans are displayed. Magnetic hysteresis is not observed. Anomalous Hall effect is also not observed (Rxy = 0). The artifact in b is removed under fine field scans.
Extended Data Fig. 6 Determination of TP and Bc2.
a, Temperature dependence of the zero-bias resistance R at ν ≈ 1 (E ≈ 8 mV/nm and B = 0). The pairing temperature TP (≈ 250 mK, vertical dashed line) is defined as the temperature, at which the measured resistance (blue line) deviates from the projected normal-state resistance (orange line) by 20%. Blue line: polynomial fit to the data (symbols); orange line: linear fit to the normal-state resistance ranging from 300–400 mK. b, Magnetic-field dependence of the longitudinal resistance R at differing temperatures (ν ≈ 1 and E ≈ 8 mV/nm). c, Magnetic-field dependence of R at 50 mK. The critical field Bc2 (≈ 80 mT) is defined as the magnetic field, at which the orange and black dashed lines cross. Here the orange line is a linear fit to the normal-state resistance, and the black line is a fit of the unpinned vortex model, \(R\propto \frac{B}{{B}_{C2}}\), to experiment for B < BC2. d, Bias dependence of the differential resistance \(\frac{{dV}}{{dI}}\) at varying magnetic fields (ν = 1, E ≈ 8 mV/nm and T = 50 mK). The dashed line corresponds to Bc2.
Extended Data Fig. 7 Thermal activation analysis.
a, Arrhenius plot of the longitudinal resistance R at varying E (for ν = 1 and B = 0). The dashed lines show the thermal activation fit and the range of data where the fit is good. b, Extracted gap size T0 from a as a function of E near EC ≈ 11.7 mV/nm. The gap vanishes continuously as E approaches EC from above.
Extended Data Fig. 8 Superconductivity in a 3.5° device.
a,b, Longitudinal resistance R as a function of E and ν at 50 mK; b shows a zoom-in view of the boxed region in a. The dashed lines in a (a guide to the eye) separate the layer-hybridized and layer-polarized regions. The dotted lines in b are a guide to the eye of the zero-resistance region observed at 50 mK. c, Temperature dependence of zero-bias resistance R with two temperature scales, TBKT ≈ 160 mK and TP ≈ 210 mK. d, Differential resistance, \(\frac{{dV}}{{dI}}\), as a function of bias Iat different temperatures under zero applied magnetic field. The critical current vanishes continuously with increasing temperature. e, Differential resistance as a function of I under different magnetic fields at 50 mK. The critical current vanishes continuously with increasing magnetic field. f, Temperature dependence of zero-bias resistance R over a broad temperature range showing the temperature scale T*.
Extended Data Fig. 9 Van Hove singularity in a 4.6-degree device.
a,b, Longitudinal resistance R (a) and weak-field Hall resistance Rxy (b) as a function of E and ν at 1.5 K under B = 0.5 T. No correlated insulating state is observed at ν = 1 in this twist angle. The dotted line traces the vHS, where R shows a peak and Rxy changes sign. The dashed lines separate the layer-hybridized and layer-polarized regions. c, Electronic DOS versus E and ν. The vHS (ν ≈ 0.84 at E = 0) disperses towards higher ν with increasing E. The result is in good agreement with experiment.
Extended Data Fig. 10 Determination of Tcoh.
a, R as a function of T2 at varying filling factors for ν > 1. The dependence at low temperatures is described by R = R0 + AT2 (dashed line). At Tcoh, R deviates from the T2-dependence by 10% (arrows). The solids lines are polynomial fits to the data points. b, Filling factor dependence of Tcoh using 10% and 20% thresholds. The general trend is the same for the two thresholds.
Supplementary information
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Xia, Y., Han, Z., Watanabe, K. et al. Superconductivity in twisted bilayer WSe2. Nature (2024). https://doi.org/10.1038/s41586-024-08116-2
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41586-024-08116-2