Abstract
The discovery of superconducting and insulating states in magic-angle twisted bilayer graphene (MATBG)1,2 has ignited considerable interest in understanding the nature of electronic interactions in this chemically pristine material. The transport properties of MATBG as a function of doping are similar to those of high-transition-temperature copper oxides and other unconventional superconductors1,2,3, which suggests that MATBG may be a highly interacting system. However, to our knowledge, there is no direct experimental evidence of strong many-body correlations in MATBG. Here we present high-resolution spectroscopic measurements, obtained using a scanning tunnelling microscope, that provide such evidence as a function of carrier density. MATBG displays unusual spectroscopic characteristics that can be attributed to electron–electron interactions over a wide range of doping levels, including those at which superconductivity emerges in this system. We show that our measurements cannot be explained with a mean-field approach for modelling electron–electron interactions in MATBG. The breakdown of a mean-field approach when applied to other correlated superconductors, such as copper oxides, has long inspired the study of the highly correlated Hubbard model3. We show that a phenomenological extended-Hubbard-model cluster calculation, which is motivated by the nearly localized nature of the relevant electronic states of MATBG, produces spectroscopic features that are similar to those that we observed experimentally. Our findings demonstrate the critical role of many-body correlations in understanding the properties of MATBG.
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
$29.99 / 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 Springer Link
- 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
The data that support the findings of this study are available from the corresponding author on reasonable request.
Change history
22 August 2019
This article was amended to correct the Peer review information, which was originally incorrect.
References
Cao, Y. et al. Correlated insulator behavior at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Lee, P. A., Nagaosa, N. & Wen, X. G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17 (2006).
Trambly de Laissardière, G., Mayou, D. & Magaud, L. Localization of Dirac electrons in rotated graphene bilayers. Nano Lett. 10, 804–808 (2010).
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).
Brihuega, I. et al. Unraveling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene by scanning tunneling microscopy and theoretical analysis. Phys. Rev. Lett. 109, 196802 (2012).
Wong, D. et al. Local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene. Phys. Rev. B 92, 155409 (2015).
Kerelsky, A. et al. Magic angle spectroscopy. Preprint at https://arxiv.org/abs/1812.08776 (2018).
Choi, Y. et al. Imaging electronic correlations in twisted bilayer graphene near the magic angle. Preprint at https://arxiv.org/abs/1901.02997 (2019).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Lu, X. et al. Superconductors, orbital magnets, and correlated states in magic angle bilayer graphene. Preprint at https://arxiv.org/abs/1903.06513 (2019).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Preprint at http://arxiv.org/abs/1901.03520 (2019).
Cao, Y. et al. Strange metal in magic-angle graphene with near Planckian dissipation. Preprint at https://arxiv.org/abs/1901.03710 (2019).
Polshyn, H. et al. Phonon scattering dominated electron transport in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1902.00763 (2019).
Koshino, M. et al. Maximally localized Wannier orbitals and the extended Hubbard model for twisted bilayer graphene. Phys. Rev. X 8, 031087 (2018).
Kang, J. & Vafek, O. Symmetry, maximally localized Wannier states, and a low-energy model for twisted bilayer graphene narrow bands. Phys. Rev. X 8, 031088 (2018).
Po, H. C., Zou, L., Vishwanath, A. & Senthil, T. Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene. Phys. Rev. X 8, 031089 (2018).
Lian, B., Wang, Z. & Bernevig, B. A. Twisted bilayer graphene: a phonon driven superconductor. Phys. Rev. Lett. 122, 257002 (2019).
Xie, M. & MacDonald, A. H. On the nature of the correlated insulator states in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1812.04213 (2019).
Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016).
Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).
Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).
Yoo, H. et al. Atomic reconstruction at van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).
Bi, Z., Yuan, N. F. Q. & Fu, L. Designing flat band by strain. Preprint at https://arxiv.org/abs/1902.10146 (2019).
Efros, A. L. Coulomb gap in disordered insulators. J. Phys. C 9, 2021 (1976).
Ashoori, R. C., Lebens, J. A., Bigelow, N. P. & Silsbee, R. H. Equilibrium tunneling from the two-dimensional electron gas in GaAs: evidence for a magnetic-field-induced energy gap. Phys. Rev. Lett. 64, 681–684 (1990).
Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Coulomb barrier to tunneling between parallel two-dimensional electron systems. Phys. Rev. Lett. 69, 3804–3807 (1992).
Feldman, B. E. et al. Observation of a nematic quantum Hall liquid on the surface of bismuth. Science 354, 316 (2016).
Randeria, M. T. et al. Interacting multi-channel topological boundary modes in a quantum Hall valley system. Nature 566, 363–367 (2019).
Ochi, M., Koshino, M. & Kuroki, K. Possible correlated insulating states in magic-angle twisted bilayer graphene under strongly competing interactions. Phys. Rev. B 98, 081102(R) (2018).
Acknowledgements
We acknowledge discussions with N. P. Ong, S. Wu, D. Wong, P. Sambo, L. Glazman, P. Phillips and A. MacDonald. We also acknowledge collaborations with E. Tutuc, K. Kim and Y. Wang during the initial stages of this project. This work has been primarily supported by the Gordon and Betty Moore Foundation as part of the EPiQS initiative (GBMF4530) and DOE-BES grant DE-FG02-07ER46419. Other support for the experimental work was provided by NSF-MRSEC programmes through the Princeton Center for Complex Materials DMR-142054, NSF-DMR-1608848, ExxonMobil through the Andlinger Center for Energy and the Environment at Princeton, and the Princeton Catalysis Initiative. B.J. acknowledges funding from the Alexander von Humboldt foundation through a Feodor Lynen postdoctoral fellowship. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, A3 Foresight by JSPS and the CREST (JPMJCR15F3), JST. B.L. acknowledges support from the Princeton Center for Theoretical Science at Princeton University. B.A.B. acknowledges support from the Department of Energy DE-SC0016239, Simons Investigator Award, the Packard Foundation, the Schmidt Fund for Innovative Research, NSF EAGER grant DMR-1643312, and NSF-MRSEC DMR-1420541.
Author information
Authors and Affiliations
Contributions
Y.X., B.J., C.-L.C., X.L. and A.Y. designed, performed and analysed the STM experiments. X.L., Y.X. and B.J. fabricated the sample. X.L. carried out the finite element electrostatic simulation. B.L. and B.A.B. performed the theoretical calculations. K.W. and T.T. provided hBN crystals. All authors contributed to the writing of the manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Peer review information Nature thanks Miguel M. Ugeda and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
Extended data figures and tables
Extended Data Fig. 1 Non-interacting spectroscopic properties on another region.
a, STM topography showing the moiré superlattice with θ = 1.14°. b, Scanning tunnelling spectra measured on an AA site for slight electron doping (Vg = −10 V, Vset = −200 mV, Iset = 500 pA, Vmod = 0.5 mV). The blue and green arrows mark the step-like features. c, Band structure calculated using the continuum model including the effects of strain and relaxation. MMΛm is a non-high-symmetry direction along which the Dirac points (protected by C2zT symmetry) are located. The black dotted line indicates the Fermi level. The blue (green) dashed line corresponds to the VHS of the first conduction (valence) remote band. d, Corresponding \(\sqrt{{\rm{L}}{\rm{D}}{\rm{O}}{\rm{S}}}\) (offset by −28 meV) on an AA site. The blue and green arrows mark the VHS of the first conduction and valence remote bands.
Extended Data Fig. 2 Lifetime broadening.
a, b, Peak width of the VHS as a function of the VHS energy when both flat bands are filled (a) or emptied (b). The green (a) and yellow (b) curves are the fit using p(E) = p0 + λE2 with p0 = 5.25 meV, λ = 0.021 meV−2 for a and with p0 = 5.1 meV, λ = 0.00072 meV−2 for b. The black dotted line marks E = 17 meV.
Extended Data Fig. 3 Tip band bending effect
a, Schematic (not to scale) of the electrostatic simulation for the device geometry in our experiment. b, Density under and away from the tip as a function of gate voltage, calculated using the geometry in a with height z = 4 Å, radius r = 0.6 nm, a work function difference of 0.25 V and the band structure from Fig. 1e. c, Density and DOS at the Fermi level as a function of gate voltage under the tip with the same parameters as in b. d, e, Zero-bias conductance as a function of gate voltage with different set point conditions (Vset = +200 mV, Iset = 120 pA for d and Vset = −200 mV, Iset = 500 pA for e) showing different apparent gate efficiencies.
Extended Data Fig. 4 Additional example of the breakdown of the non-interacting description.
a, dI/dV spectra measured on an AA site as a function of sample bias (energy) and gate voltage on the region with θ = 1.14° (Vset = −200 mV, Iset = 500 pA, Vmod = 0.5 mV). b, Normalized dI/dV spectra at different gate voltages extracted from a. The curves are shifted vertically by 0.5 nS each for clarity. The black dotted line indicates the Fermi level.
Extended Data Fig. 5 Density-dependent spectroscopy on a non-magic-angle device.
a, dI/dV measured on an AA site as a function of sample bias and gate voltage on the region with θ = 1.72° (Vset = −100 mV, Iset = 180 pA, Vmod = 2 mV). b–e, Normalized dI/dV spectra at different gate voltages extracted from a. The curves are shifted vertically by 0.4 each for clarity. The black dotted line indicates the Fermi level. We note that the electron and hole dopings are symmetric, which can be achieved by different tip conditioning (see Methods for discussion).
Extended Data Fig. 6 Mean-field calculations.
a, b, Normalized dI/dV spectra obtained from a non-interacting model (a) and a Hartree–Fock calculation (b) for different filling factors. The curves are each shifted vertically by 0.3 each for clarity. c, Individual flavour filling as a function of total filling factor, indicating the presence of spontaneous spin or valley polarization near half-filling of the flat bands from the Hartree–Fock calculation.
Extended Data Fig. 7 Extended Hubbard model with six sites.
a, Schematic of a six-site cluster two-orbital Hubbard model with on-site energy \(\pm \epsilon \), hopping t, on-site Coulomb interaction U, near-neighbour interactions V0 (same orbital) and V1 (different orbitals). b, Local spectral weight computed from the exact diagonalization of a six-site cluster Hubbard model for different filling factors with \(\epsilon =9\), t = 0.75, U = 30, V0 = 5, V1 = 3.8 (see Methods). The curves beyond \(\pm {n}_{0}\) are obtained by assuming a constant DOS at the Fermi level from the remote bands. The curves are shifted vertically by 0.25 each for clarity. c, Band broadening as a function of the ratio of the on-site Coulomb interaction U to the non-interacting band width 6t, while maintaining V0 = U/6, V1 = U/7.9.
Extended Data Fig. 8 Extended Hubbard model on a honeycomb lattice.
a, Schematics of a 6-unit-cell lattice with one orbital per site, hopping t, nearest site interaction V0 (different sublattices) and next-nearest site interaction V1 (same lattices). b, Local spectral weight computed from the exact diagonalization of a 6-unit-cell lattice Hubbard model for different filling factors with \(\epsilon =8.5\), t = 0.75, V0 = 18.2, V1 = 4.4 (see Methods). The curves beyond \(\pm {n}_{0}\) are obtained by assuming a constant DOS at the Fermi level from the remote bands. The curves are shifted vertically by 0.25 each for clarity. c, Band broadening as a function of the ratio of the nearest site interaction V0 to the non-interacting band width 3t, while maintaining V0 = 4.2V1.
Rights and permissions
About this article
Cite this article
Xie, Y., Lian, B., Jäck, B. et al. Spectroscopic signatures of many-body correlations in magic-angle twisted bilayer graphene. Nature 572, 101–105 (2019). https://doi.org/10.1038/s41586-019-1422-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/s41586-019-1422-x
This article is cited by
-
Dynamically tunable moiré exciton Rydberg states in a monolayer semiconductor on twisted bilayer graphene
Nature Materials (2024)
-
Imaging moiré excited states with photocurrent tunnelling microscopy
Nature Materials (2024)
-
Flat bands, strange metals and the Kondo effect
Nature Reviews Materials (2024)
-
Heterostrain-induced flat bands in untwisted bilayer graphene
Acta Mechanica Sinica (2024)
-
Spin-orbit coupling induced Van Hove singularity in proximity to a Lifshitz transition in Sr4Ru3O10
npj Quantum Materials (2024)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.
