Observation of returning Thouless pumping

Zheyu Cheng, Sijie Yue, Yang Long, Wentao Xie, Zixuan Yu, Hau Tian Teo, Y. X. Zhao (), Haoran Xue () and Baile Zhang ()
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Zheyu Cheng: Nanyang Technological University
Sijie Yue: Nanjing University
Yang Long: Tongji University
Wentao Xie: The Chinese University of Hong Kong
Zixuan Yu: Nanyang Technological University
Hau Tian Teo: Nanyang Technological University
Y. X. Zhao: The University of Hong Kong
Haoran Xue: The Chinese University of Hong Kong
Baile Zhang: Nanyang Technological University

Nature Communications, 2025, vol. 16, issue 1, 1-7

Abstract: Abstract Introduced by David Thouless in 1983, Thouless pumping is a driving mechanism for topological systems where the pumped charge is quantized by the Chern number. The recent theoretical demonstration of returning Thouless pumping describes a system where the quantized charge pumped during the first half of the cycle returns to zero in the second half. This mechanism leads to crystalline symmetry-protected delicate topological insulators that, unlike conventional topological bands, are not atomically obstructed and can be described by Wannier functions. More precisely, delicate topologies feature multicellular Wannier functions, extending beyond a single unit cell. Here, by using adding synthetic dimension, we realize a two-dimensional delicate topological insulator consisting of a set of one-dimensional acoustic crystals with finely tuned geometric parameters. Measuring acoustic bands and wavefunctions, we directly observe returning Thouless pumping and symmetric multicellular Wannier functions and establish a bulk-boundary correspondence between Chern numbers of the sub-Brillouin zone and gapless boundary modes. Our experimental demonstration of returning Thouless pumping expands the current understanding of topological phases of matter, enriching it with crystalline symmetries.

Date: 2025
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DOI: 10.1038/s41467-025-64671-w

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