Realization of the Thermal Haldane Lattice.

The quantum Hall effect and topological insulators have sparked significant interest in the investigation of topological photonics, mechanics, and acoustics with the objective of realizing robust topological one-way states. However, diffusion, such as heat transport, neither responds to magnetic fields nor possesses intrinsic spin, and is therefore devoid of propagation characteristics typical of wave dynamic fields. Accordingly, the identification of Chern or topological insulators within a diffusive context has long been considered challenging, if not impossible. Here, we propose a thermal analog of the Haldane model that supports one-way transport of heat. We endow the temperature field with a degree of freedom corresponding to the wave function's phase, and demonstrate that complex couplings can be effectively synthesized by tailoring intralayer and interlayer hopping. Furthermore, we have fabricated the thermal Haldane lattice by incorporating actively controlled, programmable thermal sources, and experimentally observed the evidence of thermal chiral edge states. This Letter may offer insights into the flexible and robust manipulation of heat and mass transfer.