  Topological insulators provide great potentials to control diffusion
phenomena as well as waves. Here, we show that the direction of thermal
diffusion can be selected by the contributions of the topologically protected
edge modes via the quantum spin Hall effect in a honeycomb-shaped structure. We
demonstrate that when we set our structure to the temperature corresponding to
the type of edge mode, the direction of thermal diffusion can be tuned.
Moreover, this diffusion system is found to be immune to defects owing to the
robustness of topological states. Our work points to exciting new avenues for
controlling diffusion phenomena.
