Unconventional domain tessellations in moiré-of-moiré lattices

Daesung Park, Changwon Park, Kunihiro Yananose, Eunjung Ko, Byunghyun Kim, Rebecca Engelke, Xi Zhang, Konstantin Davydov, Matthew Green, Hyun-Mi Kim, Sang Hwa Park, Jae Heon Lee, Seul-Gi Kim, Hyeongkeun Kim, Kenji Watanabe, Takashi Taniguchi, Sang Mo Yang, Ke Wang, Philip Kim, Young-Woo Son () and Hyobin Yoo ()
Additional contact information
Daesung Park: Seoul National University
Changwon Park: Korea Institute for Advanced Study
Kunihiro Yananose: Korea Institute for Advanced Study
Eunjung Ko: Korea Institute for Advanced Study
Byunghyun Kim: Seoul National University
Rebecca Engelke: Harvard University
Xi Zhang: University of Minnesota
Konstantin Davydov: University of Minnesota
Matthew Green: University of Minnesota
Hyun-Mi Kim: Korea Electronics Technology Institute
Sang Hwa Park: Sogang University
Jae Heon Lee: Sogang University
Seul-Gi Kim: Korea Electronics Technology Institute
Hyeongkeun Kim: Korea Electronics Technology Institute
Kenji Watanabe: National Institute for Materials Science
Takashi Taniguchi: National Institute for Materials Science
Sang Mo Yang: Sogang University
Ke Wang: University of Minnesota
Philip Kim: Harvard University
Young-Woo Son: Korea Institute for Advanced Study
Hyobin Yoo: Seoul National University

Nature, 2025, vol. 641, issue 8064, 896-903

Abstract: Abstract Imposing incommensurable periodicity on the periodic atomic lattice can lead to complex structural phases consisting of locally periodic structure bounded by topological defects1–8. Twisted trilayer graphene (TTG) is an ideal material platform to study the interplay between different atomic periodicities, which can be tuned by twist angles between the layers, leading to moiré-of-moiré lattices9–26. Interlayer and intralayer interactions between two interfaces in TTG transform this moiré-of-moiré lattice into an intricate network of domain structures at small twist angles, which can harbour exotic electronic behaviours9–26. Here we report a complete structural phase diagram of TTG with atomic-scale lattice reconstruction. Using transmission electron microscopy (TEM) combined with a new interatomic potential simulation27,28, we show several large-scale moiré lattices, including triangular, kagome and a corner-shared hexagram-shaped domain pattern. Each domain is bounded by a 2D network of domain-wall lattices. In the limit of small twist angles, two competing structural orders—rhombohedral and Bernal stackings—with a slight energy difference cause unconventional lattice reconstruction with spontaneous symmetry breaking (SSB) and nematic instability, highlighting the importance of long-range interlayer interactions across entire van der Waals layers. The diverse tessellation of distinct domains, whose topological network can be tuned by the adjustment of the twist angles, establishes TTG as a platform for exploring the interplay between emerging quantum properties and controllable nontrivial lattices.

Date: 2025
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DOI: 10.1038/s41586-025-08932-0

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