Magnetic Bloch states at integer flux quanta induced by super-moiré potential in graphene aligned with twisted boron nitride

Yaqi Ma, Meizhen Huang (mhuangai@connect.ust.hk), Xu Zhang, Weixiong Hu, Zishu Zhou, Kai Feng, Wenhui Li, Yong Chen, Chenxuan Lou, Weikang Zhang, Haoxi Ji, Yibo Wang, Zefei Wu, Xiaodong Cui, Wang Yao, Shichao Yan, Zi Yang Meng (zymeng@hku.hk) and Ning Wang (phwang@ust.hk)
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Yaqi Ma: The Hong Kong University of Science and Technology
Meizhen Huang: The Hong Kong University of Science and Technology
Xu Zhang: The University of Hong Kong
Weixiong Hu: ShanghaiTech University
Zishu Zhou: The Hong Kong University of Science and Technology
Kai Feng: The University of Hong Kong
Wenhui Li: ShanghaiTech University
Yong Chen: The Hong Kong University of Science and Technology
Chenxuan Lou: The Hong Kong University of Science and Technology
Weikang Zhang: The Hong Kong University of Science and Technology
Haoxi Ji: The Hong Kong University of Science and Technology
Yibo Wang: The Hong Kong University of Science and Technology
Zefei Wu: The Hong Kong University of Science and Technology
Xiaodong Cui: The University of Hong Kong
Wang Yao: The University of Hong Kong
Shichao Yan: ShanghaiTech University
Zi Yang Meng: The University of Hong Kong
Ning Wang: The Hong Kong University of Science and Technology

Nature Communications, 2025, vol. 16, issue 1, 1-9

Abstract: Abstract Two-dimensional electron systems in both magnetic fields and periodic potentials are described by the Hofstadter butterfly, a fundamental problem of solid-state physics. While moiré systems provide a powerful method to realize this type of spectrum, previous experiments have been limited to fractional flux quanta regime, due to the difficulty of building ~ 50 nm periodic modulations. Here, we demonstrate a super-moiré strategy to overcome this challenge. By aligning monolayer graphene (G) with 1.0° twisted hexagonal boron nitride (t-hBN), a 63.2 nm bichromatic G/t-hBN super-moiré is constructed, made possible by exploiting the electrostatic nature of t-hBN potential. Under magnetic field $$B$$ B , magnetic Bloch states at $$\phi /{\phi }_{0}=1-9$$ ϕ / ϕ 0 = 1 − 9 are achieved and observed as integer Brown-Zak oscillations, expanding the flux quanta from fractions to integers. Theoretical analysis reproduces these experimental findings. This work opens promising avenues to study unexplored Hofstadter butterfly, explore emergent topological order at integer flux quanta and engineer long-wavelength periodic modulations.

Date: 2025
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DOI: 10.1038/s41467-025-57111-2

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