Higher-order topological states in thermal diffusion

Abstract

Unlike conventional topological materials that carry topological states at their boundaries, higher-order topological materials are able to support topological states at boundaries of boundaries, such as corners and hinges. While band topology has been recently extended into thermal diffusion for thermal metamaterials, its realization is limited to a one-dimensional (1D) thermal lattice, lacking access to the higher-order topology. In this work, we report on the experimental realization of a higher-order thermal topological insulator in a generalized two-dimensional (2D) diffusion lattice. The topological corner states for thermal diffusion are observed in the bandgap of diffusion rate of the bulk, as a consequence of the anti-Hermitian nature of the diffusion Hamiltonian. The topological protection of these thermal corner states is demonstrated with the stability of their diffusion profile in the presence of amorphous deformation. Our work constitutes the first realization of higher-order topology in a purely diffusive systems, and opens the door for future thermal management with topological protection beyond 1D geometries.