Model for topological phononics and phonon diode

The quantum anomalous Hall effect, an exotic topological state first theoretically predicted by Haldane and recently experimentally observed, has attracted enormous interest for low-power-consumption electronics. In this work, we derived a Schr\"odinger-like equation of phonons, where topology-related quantities, time-reversal symmetry, and its breaking can be naturally introduced similar to the process for electrons. Furthermore, we proposed a phononic analog of the Haldane model, which makes the novel quantum (anomalous) Hall-like phonon states characterized by one-way gapless edge modes immune to scattering. The topologically nontrivial phonon states are useful not only for conducting phonons without dissipation but also for designing highly efficient phononic devices, like an ideal phonon diode, which could find important applications in future phononics.