Topological Phononics and Phonon Diode

Generalizing the concept of topology from electrons to phonons could bring in an intriguing emerging field of "topological phononics". For this purpose we propose a Schr\"odinger-like equation of phonons where topology-related quantities, time reversal symmetry (TRS) and its breaking can be naturally introduced. A Haldane model of phonons for a two-dimensional honeycomb lattice is then developed to describe the interplay of symmetry and quantum (anomalous) Hall-like phonon states. The nontrivial topological phase supports one-way gapless edge states within the bulk gap, which can conduct phonons without dissipation. Moreover, breaking inversion symmetry and TRS simultaneously is suggested to open a route for valley phononics and phonon diode. The findings could help design unprecedented new phononic devices.