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Supermoiré domains in helical trilayer graphene

Wen-Jun Wang1, Ping-Heng Tan1, 2, and Xin Zhang1, 2,

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 Corresponding author: Ping-Heng Tan, phtan@semi.ac.cn; Xin Zhang, zhangxin@semi.ac.cn

DOI: 10.1088/1674-4926/26030014CSTR: 32376.14.1674-4926.26030014

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[1]
Esaki L, Tsu R. Superlattice and negative differential conductivity in semiconductors. IBM J Res Dev, 1970, 14(1): 61 doi: 10.1016/0026-2714(70)90208-8
[2]
Bistritzer R, MacDonald A H. Moiré bands in twisted double-layer graphene. Proc Natl Acad Sci USA, 2011, 108(30): 12233 doi: 10.1073/pnas.1108174108
[3]
Cao Y, Fatemi V, Fang S A, et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature, 2018, 556(7699): 43 doi: 10.1038/nature26160
[4]
Alden J S, Tsen A W, Huang P Y, et al. Strain solitons and topological defects in bilayer graphene. Proc Natl Acad Sci USA, 2013, 110(28): 11256 doi: 10.1073/pnas.1309394110
[5]
Khalaf E, Kruchkov A J, Tarnopolsky G, et al. Magic angle hierarchy in twisted graphene multilayers. Phys Rev B, 2019, 100(8): 085109 doi: 10.1103/PhysRevB.100.085109
[6]
Nakatsuji N, Kawakami T, Koshino M. Multiscale lattice relaxation in general twisted trilayer graphenes. Phys Rev X, 2023, 13(4): 041007 doi: 10.1103/physrevx.13.041007
[7]
Devakul T, Ledwith P J, Xia L Q, et al. Magic-angle helical trilayer graphene. Sci Adv, 2023, 9(36): eadi6063 doi: 10.1126/sciadv.adi6063
[8]
Hoke J C, Li Y F, Hu Y W, et al. Imaging supermoiré relaxation in helical trilayer graphene. Nat Mater, 2026: 1
[9]
Ilani S, Donev L A K, Kindermann M, et al. Measurement of the quantum capacitance of interacting electrons in carbon nanotubes. Nat Phys, 2006, 2(10): 687 doi: 10.1038/nphys412
[10]
Dean C R, Wang L, Maher P, et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature, 2013, 497(7451): 598 doi: 10.1038/nature12186
[11]
Cao Y, Fatemi V, Demir A, et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature, 2018, 556(7699): 80 doi: 10.1038/nature26154
[12]
Zeng Q Y, Su G X, Song A S, et al. High-quality-factor viscoelastic nanomechanical resonators from moiré superlattices. Nat Commun, 2025, 16: 3793 doi: 10.1038/s41467-025-58981-2
Fig. 1.  (Color online) (a) Schematic of the scanning single-electron transistor (SET) measurement used to probe HTG. The SET tip measures the local inverse compressibility $ \mathrm{d}\mu /\mathrm{d}n $ of an hBN-encapsulated HTG device with a graphite bottom gate (the top hBN is not shown). The inset shows the relaxed supermoiré lattice with triangular $ h $ and $ \overline{h} $ domains meeting at AAA stacking points. (b) Optical micrograph of the device. The black linecut shows the trajectory for inverse compressibility $ \mathrm{d}\mu /\mathrm{d}n $ for Fig.1(e) in the main text of Ref.[8]. The white box marks the scan region and the red box indicates the area shown in the maps below. (c, d) Maps of the local twist angle $ \theta $ and inverse compressibility $ \mathrm{d}\mu /\mathrm{d}n $ before thermal cycling, revealing a triangular supermoiré domain pattern. (e) Reconstructed domain network colored by the ratio of experimental to theoretical domain area $ {A}_{\exp }/{A}_{\text{th}} $. (f, g) Corresponding $ \theta $ and $ \mathrm{d}\mu /\mathrm{d}n $ maps after thermal cycling, showing enlarged domains while the local moiré wavelength remains unchanged. (h) Reconstructed domain network after cycling. (i, j) Calculated dependence of the supermoiré wavelength $ {\lambda }_{\text{SM}} $ on twist-angle mismatch $ \delta \theta $ and heterostrain $ \varepsilon $. (k) Histogram of domain areas before and after cycling, indicating strain-induced domain growth[8].

[1]
Esaki L, Tsu R. Superlattice and negative differential conductivity in semiconductors. IBM J Res Dev, 1970, 14(1): 61 doi: 10.1016/0026-2714(70)90208-8
[2]
Bistritzer R, MacDonald A H. Moiré bands in twisted double-layer graphene. Proc Natl Acad Sci USA, 2011, 108(30): 12233 doi: 10.1073/pnas.1108174108
[3]
Cao Y, Fatemi V, Fang S A, et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature, 2018, 556(7699): 43 doi: 10.1038/nature26160
[4]
Alden J S, Tsen A W, Huang P Y, et al. Strain solitons and topological defects in bilayer graphene. Proc Natl Acad Sci USA, 2013, 110(28): 11256 doi: 10.1073/pnas.1309394110
[5]
Khalaf E, Kruchkov A J, Tarnopolsky G, et al. Magic angle hierarchy in twisted graphene multilayers. Phys Rev B, 2019, 100(8): 085109 doi: 10.1103/PhysRevB.100.085109
[6]
Nakatsuji N, Kawakami T, Koshino M. Multiscale lattice relaxation in general twisted trilayer graphenes. Phys Rev X, 2023, 13(4): 041007 doi: 10.1103/physrevx.13.041007
[7]
Devakul T, Ledwith P J, Xia L Q, et al. Magic-angle helical trilayer graphene. Sci Adv, 2023, 9(36): eadi6063 doi: 10.1126/sciadv.adi6063
[8]
Hoke J C, Li Y F, Hu Y W, et al. Imaging supermoiré relaxation in helical trilayer graphene. Nat Mater, 2026: 1
[9]
Ilani S, Donev L A K, Kindermann M, et al. Measurement of the quantum capacitance of interacting electrons in carbon nanotubes. Nat Phys, 2006, 2(10): 687 doi: 10.1038/nphys412
[10]
Dean C R, Wang L, Maher P, et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature, 2013, 497(7451): 598 doi: 10.1038/nature12186
[11]
Cao Y, Fatemi V, Demir A, et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature, 2018, 556(7699): 80 doi: 10.1038/nature26154
[12]
Zeng Q Y, Su G X, Song A S, et al. High-quality-factor viscoelastic nanomechanical resonators from moiré superlattices. Nat Commun, 2025, 16: 3793 doi: 10.1038/s41467-025-58981-2
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    Received: 10 March 2026 Revised: Online: Accepted Manuscript: 20 March 2026

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      Wen-Jun Wang, Ping-Heng Tan, Xin Zhang. Supermoiré domains in helical trilayer graphene[J]. Journal of Semiconductors, 2026, In Press. doi: 10.1088/1674-4926/26030014 ****W J Wang, P H Tan, and X Zhang, Supermoiré domains in helical trilayer graphene[J]. J. Semicond., 2026, accepted doi: 10.1088/1674-4926/26030014
      Citation:
      Wen-Jun Wang, Ping-Heng Tan, Xin Zhang. Supermoiré domains in helical trilayer graphene[J]. Journal of Semiconductors, 2026, In Press. doi: 10.1088/1674-4926/26030014 ****
      W J Wang, P H Tan, and X Zhang, Supermoiré domains in helical trilayer graphene[J]. J. Semicond., 2026, accepted doi: 10.1088/1674-4926/26030014

      Supermoiré domains in helical trilayer graphene

      DOI: 10.1088/1674-4926/26030014
      CSTR: 32376.14.1674-4926.26030014
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      • Wen-Jun Wang is a Master student at the University of the Chinese Academy of Sciences. She obtained her Bachelor degree in Tsinghua University. She is working on Moiré NEMS
      • Ping-Heng Tan is a professor at the Institute of Semiconductors, Chinese Academy of Sciences. He obtained his B.S. degree in Physics from Peking University in 1996 and his Ph.D. from the Institute of Semiconductors, Chinese Academy of Sciences in 2001. From 2001 to 2003, he worked as a postdoctoral research associate at the Walter Schottky Institute of the Technical University of Munich. He was a K. C. Wong Royal Society Fellow at the University of Cambridge from 2006 to 2007. His current research focuses on two-dimensional layered materials, carbon nanomaterials, topological insulators, and other novel low-dimensional semiconductor optoelectronic materials. In 2012, he received the National Science Fund for Distinguished Young Scholars
      • Xin Zhang is a professor at the Institute of Semiconductors, Chinese Academy of Sciences. He received his Ph.D. from the Institute of Semiconductors, Chinese Academy of Sciences in 2015. Then he consecutively worked as a postdoctoral research associate at Centre national de la recherche scientifique (CNRS), Nanyang Technological University and Concordia University. His research interests focus on novel MEMS/NEMS and their valuable applications in quantum measurements and sensing. His publications have received a total of more than 7000 citations with a h index of 23 as of March 2026
      • Corresponding author: phtan@semi.ac.cnzhangxin@semi.ac.cn
      • Received Date: 2026-03-10
        Available Online: 2026-03-20

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