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.