Robust one-way edge state in convection-diffusion systems

Topological insulators are insulated in the bulk but can support edge states on the surface. Since the discovery of edge states in quantum mechanics systems, the related physics has also been extended to classical wave systems. Here, we manage to reveal that edge states are not necessarily limited to wave systems but can also exist in convection-diffusion systems that are essentially different from wave systems. For this purpose, we study heat transfer in a graphene-like (or honeycomb) lattice to demonstrate thermal edge states with robustness against defects and disorders. Convection is compared to electron cyclotron, which breaks space-reversal symmetry and determines the direction of thermal edge propagation. Diffusion leads to interference-like behavior between opposite convection, preventing temperature propagation in the bulk. We also display thermal unidirectional interface states between two lattices with opposite convection. These results extend the physics of edge states beyond wave systems.