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Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene

Nature Physics volume 17, pages 478–481 (2021)Cite this article

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Abstract

When the twist angle between two layers of graphene is approximately 1.1°, interlayer tunnelling and rotational misalignment conspire to create a pair of flat bands1 that are known to host various insulating, superconducting and magnetic states when they are partially filled2,3,4,5,6,7. Most work has focused on the zero-magnetic-field phase diagram, but here we show that twisted bilayer graphene in a finite magnetic field hosts a cascade of ferromagnetic Chern insulators with Chern number ∣C∣ = 1, 2 and 3. The emergence of the Chern insulators is driven by the interplay of the moiré superlattice with the magnetic field, which endows the flat bands with a substructure of topologically non-trivial subbands characteristic of the Hofstadter butterfly8,9. The new phases can be accounted for in a Stoner picture10; in contrast to conventional quantum Hall ferromagnets, electrons polarize into between one and four copies of a single Hofstadter subband1,11,12. Distinct from other moiré heterostructures13,14,15, Coulomb interactions dominate in twisted bilayer graphene, as manifested by the appearance of Chern insulating states with spontaneously broken superlattice symmetry at half filling of a C = −2 subband16,17. Our experiments show that twisted bilayer graphene is an ideal system in which to explore the strong-interaction limit within partially filled Hofstadter bands.

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Fig. 1: Hofstadter subband ferromagnetism.
Fig. 2: Magnetic-field-driven symmetry-breaking transition to a C = −3 Chern insulator.
Fig. 3: SBCIs.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We acknowledge discussions with E. Berg, I. Protopopov, T. Senthil and M. Zaletel. The experimental work was primarily supported by the ARO under W911NF-17-1-0323. Y.S. acknowledges the support of the Elings Prize Fellowship from the California NanoSystems Institute at University of California, Santa Barbara. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, and CREST (JPMJCR15F3), JST. A.F.Y. acknowledges the support of the David and Lucille Packard Foundation under award 2016-65145. L.R. was supported by the Swiss National Science Foundation via an Ambizione grant. D.A.A. acknowledges the support of the Swiss National Science Foundation.

Author information

Authors and Affiliations

  1. Department of Physics, University of California at Santa Barbara, Santa Barbara, CA, USA

    Yu Saito, Jingyuan Ge & Andrea F. Young

  2. California NanoSystems Institute, University of California at Santa Barbara, Santa Barbara, CA, USA

    Yu Saito

  3. Department of Theoretical Physics, University of Geneva, Geneva, Switzerland

    Louk Rademaker & Dmitry A. Abanin

  4. National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe & Takashi Taniguchi

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  1. Yu Saito
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Contributions

Y.S. and J.G. fabricated tBLG devices. Y.S. performed the measurements and analysed the data. L.R. and D.A.A. performed the theoretical calculations. Y.S. and A.F.Y. wrote the paper with input from L.R. and D.A.A. T.T. and K.W. grew the hBN crystals.

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Correspondence to Andrea F. Young.

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The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Emil Bergholtz, Feng Wang and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Device characterization.

a, Optical microscope images of a device used in this study. Scale bar equals 5μm. b, Two terminal conductance G2 across multiple contacts at 4 K showing high degree of uniformity. ‘All’ denotes all other contacts.

Extended Data Fig. 2 Landau fan diagram up to 13.5 T.

a, ρxx as a function of ν and B at a nominal temperature of 10 mK. b, Schematic of observed Chern insulator structure, showing gapped states that follow linear trajectories parameterized by ν = tnΦ + s. nΦ and ν are the magnetic flux quanta and number of electrons per moiré unit cell, respectively. Three trajectory classes are distinguished by color: Integer quantum Hall (IQH) (gray; s= 0,t ∈ Z), Chern insulators (CI) (blue; s, t ∈ Z, s ≠ 0) and symmetrybroken Chern insulators (SBCI) (magenta; fractionals,t ∈ Z).

Extended Data Fig. 3 Landau fan diagram of Hall conductivity.

a, b,σyx as a function of ν and B at 4 K (a) and 10 mK (b).

Extended Data Fig. 4 Superconductivity near ν = − 2.

a, ρxx as a function of ν and T around ν=-2. b, Line cut of ρxx as a function of T at ν = − 2.46. c, dVxx/dI as a function of magnetic field at a nominal temperature of 10 mK and ν = − 2. Both current and magnetic fields suppress the low resistance state with Fraunhofer like oscillation.

Extended Data Fig. 5 Landau fan diagram at low magnetic fields at 0.4 K.

a, ρxx as a function of ν and B. b, Schematic observed Chern insulator structure based on a. c, Line cuts of ρxx at 0.6 T in a. d, Line cuts of ρxx at 2.0 T in a.

Extended Data Fig. 6 C = +3 Chern insulator from ν = + 2.

a, b, ρxx(a) and σyx(b) as a function of ν and B in negative fillings at 10 mK. c, d, ρxx (c) and σyx (d) as a function of ν in negative fillings between 0.3 and 4.7 K e, Line cuts of ρxx (black) and σyx(red) as a function of B along with yellow lines in a and b. Dashed line corresponds to 3e2/h. f, The thermal activation gap of C= +3 Chern insulator as a function of B. The values are calculated from the fits to an Arrhenius law, \({\rho }_{{\rm{xx}}} \sim \exp (-\Delta /2{\rm{T}})\). Error bars in the gaps represent the uncertainty arising from determining the linear (thermally activated) regime for the fit.

Extended Data Fig. 7 Temperate dependence of a C=-3 Chern insulator from ν = − 1.

a, b, ρxx(a) and σyx(b) as a function of ν in negative fillings between 0.3 and 4.7 K. c, The thermal activation gap of C=-3 Chern insulator as a function of B. The values are calculated from the fits to an Arrhenius law, \({\rho }_{{\rm{xx}}} \sim \exp (-\Delta /2{\rm{T}})\). Error bars in the gaps represent the uncertainty arising from determining the linear (thermally activated) regime for the fit.

Extended Data Fig. 8 Symmetry broken Chern insulators from (t,s) = (+3,+1/2) and (+2,+3/2).

a, ρxx as a function of ν and B in a range of 6-12 T.b, σyx as a function of ν and B in a range of 6-12 T. c, Schematic observed Chern insulators corresponding to the observations in a parameterized by ν = tnΦ + s. Red lines correspond to SBCI state with (t,s) = (+3,+1/2) and (+2,+3/2).d, Line cuts of ρxx and σyx around 10 T at positive fillings.

Extended Data Fig. 9 Thermal activation gaps Δ of SBCIs.

a, Δ of SBCI with (t,s) = (-3,-1/2)and (-2,-3/2) as a function of B. b, Δ of SBCI with (t,s) = (+3,+1/2) and (+2,+3/2) as a function of B.

Supplementary information

Supplementary Information

Supplementary Sections 1–3 and Figs. 1–3.

Source data

Source Data Fig. 1

Numerical data used to generate graphs in Fig. 1.

Source Data Fig. 2

Numerical data used to generate graphs in Fig. 2.

Source Data Fig. 3

Numerical data used to generate graphs in Fig. 3.

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Saito, Y., Ge, J., Rademaker, L. et al. Hofstadter subband ferromagnetism and symmetry-broken Chern insulators in twisted bilayer graphene. Nat. Phys. 17, 478–481 (2021). https://doi.org/10.1038/s41567-020-01129-4

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