Valley Hall phases in Kagome lattices

Abstract

We report the finding of the analogous valley Hall effect in phononic systems arising from mirror symmetry breaking, in addition to spatial inversion symmetry breaking. We study topological phases of plates and spring-mass models in Kagome and modified Kagome arrangements. By breaking the inversion symmetry it is well known that a defined valley Chern number arises. We also show that effectively, breaking the mirror symmetry leads to the same topological invariant. Based on the bulk-edge correspondence principle, protected edge states appear at interfaces between two lattices of different valley Chern numbers. By means a plane wave expansion method and the multiple scattering theory for periodic and finite systems respectively, we computed the Berry curvature, the band inversion, mode shapes and edge modes in plate systems. We also find that appropriate multi-point excitations in finite system gives rise to propagating waves along a one-way path only.

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• Linking scalar elastodynamics and non-Hermitian quantum mechanics
• Broadband Frequency and Spatial On-Demand Tailoring of Topological Wave Propagation Harnessing Piezoelectric Metamaterials
• Structure-Composition Correspondence in Crystalline Metamaterials for Acoustic Valley-Hall Effect and Unidirectional Sound Guiding
• High-Quality Resonances in Quasi-Periodic Clusters of Scatterers for Flexural Waves
• Topological Pseudospin Hall Effect and Multi-frequency Corner Modes in Kagome-based Lattices