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.

拓扑绝缘体在整体上是绝缘的，但可以支持表面上的边缘状态。自从在量子力学系统中发现边缘态以来，相关物理学也被扩展到经典波系统。在这里，我们设法揭示边缘状态不一定限于波动系统，也可以存在于与波动系统本质不同的对流扩散系统中。为此，我们研究了类石墨烯（或蜂窝）晶格中的热传递，以证明热边缘状态对缺陷和紊乱具有鲁棒性。对流与电子回旋加速器相比，它打破了空间反转对称性并决定了热边缘传播的方向。扩散会导致相反对流之间产生类似干扰的行为，从而阻止温度在整体中传播。我们还显示了具有相反对流的两个晶格之间的热单向界面态。这些结果将边缘状态的物理学扩展到波系统之外。