Strongly localized states at the band-inverting interface with periodic lattice dislocations

We have constructed an interface which separates two different phononic crystals (PCs) with respectively effective negative density and negative bulk modulus through band inversion. Besides the eigenstates in weak localization stemming from the sign flipping of imaginary acoustic impedances at the interface, we observed an unusual type of strongly localized states at the band-inverting contact after a periodic lattice dislocation is purposely introduced. From the layered multiple scattering theory, we have uncovered that the underlying physics for these unique interface states in the hetero-structured PC are due to nontrivial constructive interferences of high-ordered Mie-scattered acoustic waves from the mismatched cylinders. The intriguing features include interface resonances of enormous quality factors (∼3×104) and chiral field patterns along the dislocation line. We envision potential applications of the work in slow sound trapping, notch filtering, and nonlinearity strengthening, etc.