Multiple topological phases in phononic crystals

Abstract

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 (C6v) 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.The quantum anomalous Hall phase is first observed in phononics and cannot be simply classified by the Chern number or Z2 index since it results from TR-broken quantum spin Hall phase. We develop a tight-binding model to capture the essential physics of the topological phase transition. The analytical calculation based on the tight-binding model shows that the spin Chern number is a topological invariant to classify the bandgap. The quantum anomalous Hall insulator has a spin Chern number C±=(1,0) indicating the edge state is pseudo-spin orientation dependent and robust against TR-broken impurities.We also perform finite-element numerical simulations to verify the topological differences of the bandgaps. At the interface between a conventional insulator and a quantum anomalous Hall insulator, pseudo-spin dependent one-way propagation interface states are clearly observed, which are strikingly deferent from chiral edge states resulting from quantum Hall insulator and pairs of helical edge states resulting from quantum spin Hall insulator. Moreover, our pseudo-spin dependent edge state is robust against TR-broken impurities, which also sheds lights on spintronic devices.