Fig. 4: Observation of the quadrupole topological phases in heat transport solely induced by non-Hermitian couplings.

a Photo of a fabricated square-lattice (16 sites) with different intercell and intracell coupling channels. The grey-shadowed and black-dashed areas respectively indicate the over-coupling and under-coupling channels. b Spectra of the thermal quadrupole topological phases induced by non-Hermitian couplings. c Measured temperature field intensities at corresponding boundaries. The measured regions are marked by colored borders in Supplementary Fig. 6c. d–f Captured temperature distributions at steady state after the field evolutions at the peaks of the corner, edge, and bulk spectra as indicated by the red, blue, and black dashed lines in (c), and their locations are indicated by the dashed white lines in d–f. β is the ratio between the intercell and intracell thermal coupling strengths.