Diffusive skin effect and topological heat funneling

Non-Hermitian wave system has attracted intense attentions in the past decade since it reveals interesting physics and generates various counterintuitive effects. However, in the diffusive system that is inherently non-Hermitian with natural dissipation, the robust control of heat flow is hitherto still a challenge. Here we introduce the skin effect into diffusive systems. Different from the skin effect in wave systems, where asymmetric couplings were enabled by dynamic modulations or judicious gain/loss engineering, asymmetric couplings of the temperature fields in diffusive systems can be realized by directly contacted metamaterial channels. Topological heat funneling is further presented, where the temperature field automatically concentrates towards a designated position and shows a strong immunity against the defects. Our work indicates that the diffusive system can provide a distinctive platform for exploring non-Hermitian physics as well as thermal topology. Non-Hermitian systems can house a range of unusual physical phenomena such as the skin-effect which has been typically observed in optical lattices and electrical circuits. Here, the authors show the non-Hermitian skin effect in thermal transport, demonstrating that the topologically protected heat flow can be realized by using thermal metamaterials.