Abstract
Topological phases of sound enable unconventional confinement of acoustic energy at the corners in higher-order topological insulators. These unique states which go beyond the conventional bulk-boundary correspondence have recently been extended to non-Hermitian wave physics comprising finite crystal structures including loss and gain units. We use a multiple scattering theory to calculate these topologically trapped complex states that agree very well to finite element predictions. Moreover, our semi-numerical tool allows us to compute the spectral dependence of corner states in the presence of defects, illustrating the limits of the topological resilience of these confined non-Hermitian acoustic states.
Highlights
Topological phases of sound enable unconventional confinement of acoustic energy at the corners in higher-order topological insulators
A key feature of the topological insulators is the existence of robust edge states that are immune to backscattering from disorder or interface variations
The edge states were predicted by the bulk-edge correspondence principle, but recently, the concept of Topological insulators (TIs) has been generalized to higher-order topological insulators (HOTIs), at which the conventional bulk-boundary correspondence does not apply[20,21,22,23,24]
Summary
Topological phases of sound enable unconventional confinement of acoustic energy at the corners in higher-order topological insulators. These unique states which go beyond the conventional bulk-boundary correspondence have recently been extended to non-Hermitian wave physics comprising finite crystal structures including loss and gain units. Parity-time PT symmetry on the other hand, describes the invariance of a non-Hermitian system that can have real eigenvalue spectra despite its complex entities Those systems are a special kind of physical configurations invariant upon the combined parity P and time reversal T operations, which have been realized in artificial structures hosting balanced gain and loss constituents. Beyond the excellent agreement between the two techniques permitting us to study topological corner, edge and bulk states, as well as their spatial pressure profiles, we deliberately employ the MST to elaborate the robustness of non-Hermitian corner states in the presence of interstitial cylinder-defects
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