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Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices

Author

Listed:
  • C. R. Dean

    (The City College of New York)

  • L. Wang

    (Columbia University)

  • P. Maher

    (Columbia University)

  • C. Forsythe

    (Columbia University)

  • F. Ghahari

    (Columbia University)

  • Y. Gao

    (Columbia University)

  • J. Katoch

    (University of Central Florida)

  • M. Ishigami

    (University of Central Florida)

  • P. Moon

    (Tohoku University, Sendai 980-8578, Japan)

  • M. Koshino

    (Tohoku University, Sendai 980-8578, Japan)

  • T. Taniguchi

    (National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan)

  • K. Watanabe

    (National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan)

  • K. L. Shepard

    (Columbia University)

  • J. Hone

    (Columbia University)

  • P. Kim

    (Columbia University)

Abstract

Moiré superlattices arising in bilayer graphene coupled to hexagonal boron nitride provide a periodic potential modulation on a length scale ideally suited to studying the fractal features of the Hofstadter energy spectrum in large magnetic fields.

Suggested Citation

  • C. R. Dean & L. Wang & P. Maher & C. Forsythe & F. Ghahari & Y. Gao & J. Katoch & M. Ishigami & P. Moon & M. Koshino & T. Taniguchi & K. Watanabe & K. L. Shepard & J. Hone & P. Kim, 2013. "Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices," Nature, Nature, vol. 497(7451), pages 598-602, May.
    • Handle: RePEc:nat:nature:v:497:y:2013:i:7451:d:10.1038_nature12186
    DOI: 10.1038/nature12186
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    Cited by:

    1. Qing Rao & Wun-Hao Kang & Hongxia Xue & Ziqing Ye & Xuemeng Feng & Kenji Watanabe & Takashi Taniguchi & Ning Wang & Ming-Hao Liu & Dong-Keun Ki, 2023. "Ballistic transport spectroscopy of spin-orbit-coupled bands in monolayer graphene on WSe2," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    2. Lutao Li & Junjie Yao & Juntong Zhu & Yuan Chen & Chen Wang & Zhicheng Zhou & Guoxiang Zhao & Sihan Zhang & Ruonan Wang & Jiating Li & Xiangyi Wang & Zheng Lu & Lingbo Xiao & Qiang Zhang & Guifu Zou, 2023. "Colloid driven low supersaturation crystallization for atomically thin Bismuth halide perovskite," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    3. Wenqiang Zhou & Jing Ding & Jiannan Hua & Le Zhang & Kenji Watanabe & Takashi Taniguchi & Wei Zhu & Shuigang Xu, 2024. "Layer-polarized ferromagnetism in rhombohedral multilayer graphene," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    4. Zeya Li & Junwei Huang & Ling Zhou & Zian Xu & Feng Qin & Peng Chen & Xiaojun Sun & Gan Liu & Chengqi Sui & Caiyu Qiu & Yangfan Lu & Huiyang Gou & Xiaoxiang Xi & Toshiya Ideue & Peizhe Tang & Yoshihir, 2023. "An anisotropic van der Waals dielectric for symmetry engineering in functionalized heterointerfaces," Nature Communications, Nature, vol. 14(1), pages 1-9, December.
    5. Pratap Chandra Adak & Subhajit Sinha & Debasmita Giri & Dibya Kanti Mukherjee & Chandan & L. D. Varma Sangani & Surat Layek & Ayshi Mukherjee & Kenji Watanabe & Takashi Taniguchi & H. A. Fertig & Arij, 2022. "Perpendicular electric field drives Chern transitions and layer polarization changes in Hofstadter bands," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    6. Jing Ding & Hanxiao Xiang & Wenqiang Zhou & Naitian Liu & Qianmei Chen & Xinjie Fang & Kangyu Wang & Linfeng Wu & Kenji Watanabe & Takashi Taniguchi & Na Xin & Shuigang Xu, 2024. "Engineering band structures of two-dimensional materials with remote moiré ferroelectricity," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    7. Guowen Yuan & Weilin Liu & Xianlei Huang & Zihao Wan & Chao Wang & Bing Yao & Wenjie Sun & Hang Zheng & Kehan Yang & Zhenjia Zhou & Yuefeng Nie & Jie Xu & Libo Gao, 2023. "Stacking transfer of wafer-scale graphene-based van der Waals superlattices," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    8. Valerio Di Giulio & P. A. D. Gonçalves & F. Javier García de Abajo, 2022. "An image interaction approach to quantum-phase engineering of two-dimensional materials," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    9. Junxiong Hu & Junyou Tan & Mohammed M. Al Ezzi & Udvas Chattopadhyay & Jian Gou & Yuntian Zheng & Zihao Wang & Jiayu Chen & Reshmi Thottathil & Jiangbo Luo & Kenji Watanabe & Takashi Taniguchi & Andre, 2023. "Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures," Nature Communications, Nature, vol. 14(1), pages 1-8, December.
    10. Mohit Kumar Jat & Priya Tiwari & Robin Bajaj & Ishita Shitut & Shinjan Mandal & Kenji Watanabe & Takashi Taniguchi & H. R. Krishnamurthy & Manish Jain & Aveek Bid, 2024. "Higher order gaps in the renormalized band structure of doubly aligned hBN/bilayer graphene moiré superlattice," Nature Communications, Nature, vol. 15(1), pages 1-7, December.
    11. Xingdan Sun & Shihao Zhang & Zhiyong Liu & Honglei Zhu & Jinqiang Huang & Kai Yuan & Zhenhua Wang & Kenji Watanabe & Takashi Taniguchi & Xiaoxi Li & Mengjian Zhu & Jinhai Mao & Teng Yang & Jun Kang & , 2021. "Correlated states in doubly-aligned hBN/graphene/hBN heterostructures," Nature Communications, Nature, vol. 12(1), pages 1-8, December.
    12. Hongguang Wang & Jiawei Zhang & Chen Shen & Chao Yang & Kathrin Küster & Julia Deuschle & Ulrich Starke & Hongbin Zhang & Masahiko Isobe & Dennis Huang & Peter A. van Aken & Hidenori Takagi, 2024. "Direct visualization of stacking-selective self-intercalation in epitaxial Nb1+xSe2 films," Nature Communications, Nature, vol. 15(1), pages 1-11, December.
    13. Yungi Jeong & Hangyeol Park & Taeho Kim & Kenji Watanabe & Takashi Taniguchi & Jeil Jung & Joonho Jang, 2024. "Interplay of valley, layer and band topology towards interacting quantum phases in moiré bilayer graphene," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    14. Robin Huber & Max-Niklas Steffen & Martin Drienovsky & Andreas Sandner & Kenji Watanabe & Takashi Taniguchi & Daniela Pfannkuche & Dieter Weiss & Jonathan Eroms, 2022. "Band conductivity oscillations in a gate-tunable graphene superlattice," Nature Communications, Nature, vol. 13(1), pages 1-7, December.
    15. Daniel Shaffer & Jian Wang & Luiz H. Santos, 2022. "Unconventional self-similar Hofstadter superconductivity from repulsive interactions," Nature Communications, Nature, vol. 13(1), pages 1-12, December.
    16. Jubin Nathawat & Ishiaka Mansaray & Kohei Sakanashi & Naoto Wada & Michael D. Randle & Shenchu Yin & Keke He & Nargess Arabchigavkani & Ripudaman Dixit & Bilal Barut & Miao Zhao & Harihara Ramamoorthy, 2023. "Signatures of hot carriers and hot phonons in the re-entrant metallic and semiconducting states of Moiré-gapped graphene," Nature Communications, Nature, vol. 14(1), pages 1-11, December.

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