Fig. 1: Unit design for topological and ordinary states.

a Schematic of the honeycomb-shaped unit cell. Each of the nearest neighboring sites (black) is connected by the beams with the effective diffusivity D₁ (blue). The neighboring unit cells are connected by the beams with the effective diffusivity D₂ (red). D₁ and D₂ are effective diffusivities obtained by normalizing thermal diffusivities (λc⁻¹ρ⁻¹) with L⁻². λ, c, and ρ are thermal conductivity, thermal capacity, and density, respectively. L = 15 mm and w = 2 mm are the length and width of the beams. d = 20 mm is the diameter of the disc-shaped site. a₁ and a₂ are unit vectors. b–d Spectra of the eigenvalues for the infinite periodic honeycomb lattice with (b) r > 1 (D₁ = 0.765, D₂ = 0.518, (c) r = 1 (D₁ = D₂ = 0.68), and (d) r < 1 (D₁ = 0.6, D₂ = 0.85). r is the ratio of D₁ and D₂. Each of the doubly degenerated modes in (b) and (d) are labeled as i–iv and i'–iv'. e, f Site temperature corresponding to the eigenfunctions in the unit cell at modes (e) i–iv and (f) i'–iv'.