Topological insulator based locally resonant phononic crystals: Wave propagation and acoustic band gaps

In the present work the acoustic band structure of a two-dimensional phononic crystal (PC) containing an organic ferroelectric (PVDF- polyvinylidene fluoride) and topological insulator (Bi2Te3) were investigated by the plane-wave-expansion (PWE) method. Two-dimensional PC with square lattices composed of Bi2Te3 cylindrical rods embedded in the PVDF matrix are studied to find the existence of stop bands for the waves of certain energy. Phononic band diagram = (k) for a 2D PC along the ?-X-M-? path in the square Brillouin zone show four stop bands in the frequency range 0.01-8.0kHz.