  Higher-dimensional topological meta-materials have more flexible than
one-dimensional topological materials, which are more convenient to apply and
solve practical problems. However, in diffusion systems, higher-dimensional
topological states have not been well studied. In this work, we experimentally
realized the 2D topological structure based on a kagome lattice of thermal
metamaterial. Due to the anti-Hermitian properties of the diffusion
Hamiltonian, it has purely imaginary eigenvalues corresponding to the decay
rate. By theoretical analysis and directly observing the decay rate of
temperature through experiments, we present the various corner states in 2D
topological diffusive system. Our work constitutes the first realization of
multiple corner states with high decay rates in a pure diffusion system, which
provides a new idea for the design of topological protected thermal
metamaterial in the future.
