Switchable phonon diodes using nonlinear topological Maxwell lattices

Recent progress in topological mechanics has revealed a family of Maxwell lattices that exhibit topologically protected floppy edge modes. These modes lead to a strongly asymmetric elastic wave response. In this paper, we show how topological Maxwell lattices can be used to realize nonreciprocal transmission of elastic waves. Our design leverages the asymmetry associated with the availability of topological floppy edge modes and the geometric nonlinearity built into the mechanical systems' response to achieve the desired nonreciprocal behavior, which can be further utilized to form a phonon diode via the addition of on-site pinning potentials that blocks the linear transmission and only allows the signal to transmit in one way. Finally, the nonreciprocal wave transmission can be switched on and off via topological phase transitions, paving the way to the design of cellular metamaterials that can serve as tunable topologically protected phonon diodes.