Evaluation of topological protection in kagome lattice-based thermal diffusion systems

We evaluated topological protection for edge and higher-order corner states in topological diffusion systems based on the breathing kagome lattice. In the kagome lattice, the corner states appear at the corner boundary where all three Wannier centers in nontrivial unit cells are located. The three Wannier centers in a unit cell can be placed on the obtuse- and acute-corner boundaries utilizing the armchair boundary, generating topological acute- and obtuse-corner states. For another representative zigzag boundary, only the acute-corner unit cell has three Wannier centers located at the boundary; hence, only the acute-corner state appears. Our band analysis and numerical studies show that the topologically protected decay behavior for armchair boundaries is as robust as that for zigzag boundaries, unlike wave phenomena with space and time periodicities. Our findings can guide the flexible design of topological diffusion applications such as heat localization and recovery systems.