Multiple topological phases in phononic crystals

We report a new topological phononic crystal in a ring-waveguide acoustic system. In the previous reports on topological phononic crystals, there are two types of topological phases: quantum Hall phase and quantum spin Hall phase. A key point in achieving quantum Hall insulator is to break the time-reversal (TR) symmetry, and for quantum spin Hall insulator, the construction of pseudo-spin is necessary. We build such pseudo-spin states under particular crystalline symmetry (C-6v) and then break the degeneracy of the pseudo-spin states by introducing airflow to the ring. We study the topology evolution by changing both the geometric parameters of the unit cell and the strength of the applied airflow. We find that the system exhibits three phases: quantum spin Hall phase, conventional insulator phase and a new quantum anomalous Hall phase.