Hall effect and topological phase transition of nonlinear elastic wave metamaterials with local resonators

This work reports the amplitude-induced topological phase transition and Hall effect in nonlinear elastic waves metamaterials with local resonators. The multi scale method is employed to analyze nonlinear effects on the Bragg scattering and locally resonant band gaps. The amplitude-induced band inversion and topological edge states are numerically investigated. A spin Hall insulator is generated by a honeycomb lattice to show how the nonlinearity affects the frequencies of doubly degenerate states. By adjusting the nonlinear elastic wave amplitude, topological phase transition is achieved due to the intercellular and intracellular coupling. The transition from topological boundary states to bulk states is observed by increasing nonlinear elastic wave amplitude. Bidirectional and unidirectional transmissions of topological interface states with amplitude-induced properties can also be realized, which demonstrates robustness against both corners and defects. Furthermore, experiment is performed to support theoretical predictions of topological phase transition and Hall effect of nonlinear elastic wave.