Lossy phononic metamaterials for valley manipulation

Abstract: Non-Hermitian physics characterized by complex band spectra has established a new paradigm in condensed matter systems and metamaterials. Recently, non-Hermitian gain and nonreciprocity are deliberately introduced to valley manipulation, leading to various phenomena beyond the Hermitian scenarios, such as the amplified topological whispering gallery modes as an acoustic laser. In contrast, pure loss is inevitable in practice and generally regarded as a detrimental factor. Here, we reveal that the coupling loss can manipulate valley degrees of freedom in a phononic metamaterial. Three distinct valley-related effects, including valley-resolved nonreciprocity that functions as a valley filter, valley-dependent skin effects where bulk states from different valleys localize at opposite boundaries, and valley-projected edge states with boundary-dependent lifetimes that leads to an anomalous beam splitting, are demonstrated through theoretical analysis and airborne sound experiments. Owing to the easy preparation of loss, our findings shed light on both non-Hermitian and valley physics and may facilitate innovative applications of valley-related devices.