Schoch Effect in Topological Phononic Crystals

Abstract

This article investigates the Schoch negative displacement phenomenon at the interface between two-dimensional topological acoustic materials and traditional materials. The results show that a negative Schoch displacement occurs at the frequency of the Dirac point in the phononic crystal. At this point, the reciprocal of the effective bulk modulus of the phononic crystal tends to zero, making it an acoustic metamaterial with a refractive index close to zero. At the same time, the maximum value of the effective impedance of the phononic crystal and the real part of the reflection coefficient undergo a 2π phase transition at the corresponding frequency. When the phononic crystal is spliced into a topological supercell structure, a larger negative Schoch displacement is observed. This study demonstrates that topological phononic crystals can achieve negative Schoch displacement. The negative Schoch displacement realized in this article provides a new theoretical reference for designing acoustic devices based on interface waves.