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Broken-symmetry states at half-integer band fillings in twisted bilayer graphene

Abstract

The dominance of Coulomb interactions over the kinetic energy of electrons in flat moiré bands of magic-angle twisted bilayer graphene (TBG) gives rise to a variety of correlated phases, including correlated insulators1,2,3, superconductivity2,4,5, orbital ferromagnetism2,6, Chern insulators7,8,9,10 and nematicity11. Most of these phases occur when the carrier density is at or near an integer number of carriers per moiré unit cell. However, the demonstration of ordered states at fractional moiré band fillings at zero applied magnetic field is more challenging. Here we report the observation of states near half-integer band fillings 0.5 and ±3.5 at near-zero magnetic field in TBG proximitized by tungsten diselenide. Furthermore, at a band filling near −0.5, a symmetry-broken Chern insulator emerges at high magnetic field that is compatible with the band structure calculations within a translational symmetry-broken supercell with twice the area of the original TBG moiré cell. Our results are consistent with a spin or charge density wave ground state in TBG in the zero-magnetic-field limit.

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Fig. 1: Electrical characterization and low-field Hall measurements in device D1, with θ ≈ 1.14°.
Fig. 2: Symmetry-broken states at ν ≈ −0.5 and ±3.5 in device D2, with θ ≈ 1.16°.
Fig. 3: Zero-field thermoelectricity.
Fig. 4: Degeneracy lifting of the folded bands.

Data availability

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

Code availability

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

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Acknowledgements

We gratefully acknowledge the usage of the MNCF and NNFC facilities at CeNSE, IISc. U.C. acknowledges funding from SERB via grants nos. ECR/2017/001566 and SPG/2020/000164. N.L. was supported by the Korean National Research Foundation grant no. NRF-2020R1A2C3009142 and A.S. by grant no. NRF-2020R1A5A1016518. D.L. was supported by the Korean Ministry of Land, Infrastructure and Transport (MOLIT) from the Innovative Talent Education Program for Smart Cities. J.J. was supported by the Samsung Science and Technology Foundation under project no. SSTF-BAA1802-06. We acknowledge computational support from KISTI through grant no. KSC-2021-CRE-0389 and the resources of the Urban Big Data and AI Institute (UBAI) at the University of Seoul and the network support from KREONET. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan (grant no. JPMXP0112101001) and JSPS KAKENHI (grants nos. JP19H05790 and JP20H00354).

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Contributions

S.B. fabricated the devices, performed the measurements and analysed the data. B.G., M.P. and P.S.M. assisted with measurements and analysis. K.W. and T.T. grew the hBN crystals. A.G. and U.C. advised on experiments. N.L., S.A., D.L. and J.J. performed the theoretical calculations. S.B., N.L., J.J. and U.C. wrote the manuscript, with input from other authors.

Corresponding authors

Correspondence to Saisab Bhowmik, Jeil Jung or U. Chandni.

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Extended data

Extended Data Fig. 1 Low-field Hall data in device D1, θ ≈ 1.140.

a. nH − ν plot for B = 0.3 − 1.2 T. b. σxy as a function of ν for the same range of B. The zero crossings at ν = 0.5, 1 and 3.5 and reset at ν = 2 and 3 are robust with B.

Source data

Extended Data Fig. 2 Low-field Hall data in device D2, θ ≈ 1.160.

a. nH − ν plot for B = 0.2 − 2 T. The sign change at ν = 3.5 appears at the lowest B-field of 0.2 T. In addition, the reset at charge carriers is observed at ν = ± 2. b. σxy as a function of ν for the same range of B.

Extended Data Fig. 3 Hall conductivity at B = 9 T in device D2.

σxy shows plateaus as σxy = Ce2/h associated with the minima in σxx. Different color bars (blue for the CNP, green for ν = 1, ± 2, 3 and red for ν = − 0.5) have been used to show the sequence of symmetry-broken nearly quantized states nucleating from several partial fillings of flat bands.

Extended Data Fig. 4 Magneto-thermoelectricity measurements in device D1.

Thermoelectric voltage V measured at B = 0, 1, 1.5, and 2 T and T = 3 K for a heating current of 300 nA. The feature at ν = 3.5 is clearly visible at all B. A tiny shoulder develops in the vicinity of ν = 0.5, that is particularly prominent at B = 2 T.

Source data

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Supplementary Figs. 1–8.

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Bhowmik, S., Ghawri, B., Leconte, N. et al. Broken-symmetry states at half-integer band fillings in twisted bilayer graphene. Nat. Phys. 18, 639–643 (2022). https://doi.org/10.1038/s41567-022-01557-4

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