Convection-modulated topological edge mode and extended-localized criticality in thermal metamaterials

Convection offers a dynamic and flexible approach to achieving a variety of novel physical phenomena beyond pure conduction. Here, we demonstrate that thermal metamaterials with convection modulation enable the realization of non-Hermitian topological edge modes and bulk mode criticality. We illustrate that a periodic modulation can induce localized edge modes within the band gap. The temperature field of the topological state is localized at the edge rings, decaying exponentially at a fixed rate. Additionally, we introduce an extended-localized criticality through the quasiperiodic convection modulation in thermotics. The convections have an advantage of fantastic tunability in the application. Our work proposes a scheme for implementing topological modes and bulk mode criticality through modulating convection in diffusion systems, paving the way for the design of reconfigurable thermal devices.