biostudies-literatureCheng ZChinese University of Hong Kong (CUHK)National Natural Science Foundation of China (National Science Foundation of China)9669https://www.ebi.ac.uk/biostudies/studies/S-EPMC12583446biostudies-literatureUnknown16(1)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-Nature communicationsObservation of returning Thouless pumping.PMC125834464937205, 4937206, 4053729 and 441176562401491Yue SZhao YXXie WLong YTeo HTYu ZZhang BXue HCheng ZfalseObservation of returning Thouless pumping.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-2025-01-01T00:00:00Z2025 Nov2026-06-05T11:30:21.868Z2026-05-16T03:12:58.208ZS-EPMC125834464118424810.1038/s41467-025-64671-w