Elastic dislocation states of full-polarization micromechanical metamaterials

Benefiting from the profound advancements in topological metamaterials of condensed matter physics, micromechanical metamaterials have demonstrated extensive applicability in transporting high-frequency elastic waves. However, the full-polarization elastic waves impose profound challenges on the practical applications of micromechanical metamaterials. Since most current studies remain confined to single polarization, we have engineered micromechanical metamaterials capable of eliciting a full polarization response to topological edge and corner modes. Firstly, we design a phononic crystal with $C_4$ symmetry, which exhibits line degeneracies along the boundaries of the Brillouin zone. Line degeneracies are lifted through geometric perturbation, and a higher-order bandgap identified by modal analysis is generated. By successfully separating the high-order bandgaps for in-plane and out-of-plane modes, we achieve edge and corner states in pure in-plane, out-of-plane, and full-polarization configurations. Besides, we first incorporate topological Wannier cycles into full-polarization micromechanical metamaterials. Compared to the edge states in higher-order phases, the robust dislocation states span nearly the entire bandgap, greatly enhancing the utilization of topological protection. Inspired by the mode conversion of elastic waves, we explored the coupling phenomenon between dislocation and edge states, which enhances the energy harvesting and frequency identification capabilities of higher-order dislocation structures. The novel concept of combining helical dislocations with artificial gauge flux significantly expands the manipulation of full-polarization elastic waves, offering a powerful tool for identifying higher-order topological phases.