Selectable diffusion direction with topologically protected edge modes

Topological insulators provide great potential to control diffusion phenomena as well as waves. In addition to the thermal localization and robust decay as reported, the topological edge states with higher degree of freedom offers a route to control directional diffusion. Here, we show that the direction of thermal diffusion can be selected by the contributions of the topologically protected edge modes in a honeycomb-shaped structure. Considering the thermal diffusion between the nearest neighboring sites of the honeycomb-shaped unit cells, the cells allow unidirectional heat balance from a macroscopic perspective when we set the structure to the temperature corresponding to the edge mode type. Moreover, this diffusion system is found to be immune to defects owing to the robustness of topological states. Our work points to exciting avenues for controlling diffusion phenomena.