Protected acoustic edge states in honeycomb lattice
Valley Hall phononic insulators exploit broken inversion symmetry in a honeycomb lattice. Two sublattices (A/B) with different masses m_A ≠ m_B open a topological bandgap at the Dirac points K and K'. The valley Chern numbers C_K = ±1/2 predict topologically protected edge modes at the domain wall between regions of opposite mass contrast. These edge states carry vibration energy without backscattering from defects.