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Diffusive topological transport in spatiotemporal thermal lattices


Topological phases have been studied in photonic, acoustic and phononic metamaterials, promising a range of applications. Such topological modes usually stem from collective resonant effects in periodic lattices. One may, therefore, expect similar features to be forbidden for thermal diffusion that is purely dissipative and mostly incoherent, prohibiting collective resonances. Here we report the discovery of diffusion-based topological states supported by spatiotemporally modulated advections stacked over a fluidic surface. This arrangement imitates a periodic propagating potential in an effective thermal lattice. We observe edge states in topologically non-trivial and bulk states in topologically trivial lattices. Interface states form at boundaries between these two types of lattice, manifesting inhomogeneous thermal properties on the fluidic surface. Our findings establish a framework for topological diffusion and thermal edge or bulk states, and it may allow a distinct mechanism for the flexible manipulation of diffusive phenomena for robust heat and mass transfer.

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Fig. 1: Topological transport in thermal diffusion.
Fig. 2: Measured results for topologically non-trivial and trivial responses in the gapped phase.
Fig. 3: Measured temperature profiles and effective thermal resistances for Case I.
Fig. 4: Measured temperature profiles and effective thermal resistances for Case II.

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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C.-W.Q. acknowledges financial support from the Ministry of Education, Republic of Singapore (grant no. R-263-000-E19-114). A.A. acknowledges financial support from the Office of Naval Research with grant no. N00014-19-1-2011, the Vannevar Bush Faculty Fellowship, the Air Force Office of Scientific Research with MURI grant no. FA9550-18-1-0379 and the Simons Foundation. Y.Y. and H.C. acknowledge the National Natural Science Foundation of China (NNSFC) under grant nos. 61625502, 61975176, 11961141010 and 62175215; the Top-Notch Young Talents Program of China; and the Fundamental Research Funds for the Central Universities. X.Z. acknowledges financial support from the Chongqing Natural Science Foundation (grant no. cstc2021jcyj-msxmX0627) and the Science and Technology Research Program of Chongqing Municipal Education Commission (grant no. KJQN202000829).

Author information

Authors and Affiliations



G.X. and C.-W.Q. conceived the idea. G.X., X.Z. and C.-W.Q. proposed the methodology. G.X., Y.Y., H.C., A.A. and C.-W.Q. performed the theoretical derivations. G.X. and X.Z. implemented the experimental investigations. G.X., Y.Y., X.Z. and C.-W.Q. made the visualizations. G.X., Y.Y., H.C., A.A. and C.-W.Q. performed the theoretical analysis and wrote the manuscript. C.-W.Q. supervised the work. All the authors contributed to the discussion and to finalizing the manuscript.

Corresponding author

Correspondence to Cheng-Wei Qiu.

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The authors declare no competing interests.

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Nature Physics thanks Muamer Kadic and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 The entire structure and experimental setups.

a indicates the entire structure for implementing advections (effective oscillations) on the fluid surface, a constraint shell is adopted outside the fluid surface to keep the concentric rotations for each unit and the internal gear. During the measurements, this constraint shell is removed to directly capture the temperature-related data of the fluid surface. b and c present the fabricated dynamic components and their combinations consisting of 40 internal gear sets for modulating the fluid surface. The azimuthal direction of the units is marked in (b). The black dashed border in (c) indicates the region for IR images when fluid is coated on these dynamic components, while the interval of two neighboring deriving gears on a transmission shaft is 4a. The black dot marked with ‘1’ indicates the first unit of the entire system at the initial location of z = 0. d provides the real experiment setups, and the left upper inset presents the general engagement of the internal gear set for one unit cell. The colored dots indicate the corresponding motors.

Supplementary information

Supplementary Information

Supplementary Notes 1–4 and Figs. 1–5.

Supplementary Video 1

Temperature profiles of the case with non-trivial lattices.

Supplementary Video 2

Temperature profiles of the case with trivial lattices.

Supplementary Video 3

Temperature profiles of manipulated Case I.

Supplementary Video 4

Temperature profiles of manipulated Case II.

Supplementary Video 5

Illustrations of the mechanism for dynamic control.

Source data

Source Data Fig. 1

Source data for Fig. 1d.

Source Data Fig. 2

Source data for Fig. 2a–h.

Source Data Fig. 3

Source data for Fig. 3b–e.

Source Data Fig. 4

Source data for Fig. 4b–e.

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Xu, G., Yang, Y., Zhou, X. et al. Diffusive topological transport in spatiotemporal thermal lattices. Nat. Phys. 18, 450–456 (2022).

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