Progress on the morphing of topological modes by non-Hermitian skin effect in classical wave systems
Topological phases of matter have been extensively studied in classical wave systems,generating long-lasting influences.A hallmark of these topological matters is the presence of topological states that are localized at the boundaries of topologically nontrivial systems or the interfaces between two topologically distinct media.Taking advantage of topological protections,various applications can leverage properties like robustness and resistance to backscattering.Nevertheless,since the presence of topological states relies on bulk-band topology,any topological applications must be constructed on a bulk lattice,thereby challenging the miniaturization of these systems.Recent investigations into non-Hermitian band theories have unveiled the non-Hermitian skin effect(NHSE),by which the bulk states collapse to the boundaries as skin modes.Theoretical studies have shown that the non-Hermitian skin effect can be harnessed to reshape the topological modes and even induce their delocalization.Such delocalization effects have recently been experimentally demonstrated in both mechanical and acoustic systems.Notably,these extended topological states remain topologically protected,thereby imbuing them with resilience against disorder or imperfections.In this paper,we review the theoretical and experimental advancements of the NHSE and its significant impact on reshaping topological modes.First,we elaborate on the NHSE by taking the well-studied non-reciprocal Su-Schrieffer-Heeger(SSH)chain as a specific example.The characterization method and the topological origin of the NHSE are introduced.We then showcase some remarkable demonstrations of the NHSE in classical wave systems.After that,we focus on the interaction between the NHSE and the topological modes in various tight-binding models,starting with a topological interface system.We introduce the delocalization effect of the topological interface mode and illustrate the derivation of the critical non-reciprocal strength.Then,we present the first experimental demonstration of the extended topological mode in an active mechanical lattice consisting of coupled rotational oscillators.Expanding on the general mechanism rooted in the delocalization effect,we further show the extension of such effect in two-dimensional topological lattices,including the morphing of the topological edge states into diverse profiles by engineering the non-Hermiticity distribution in stacked topological lattices and the delocalization of second-order topological corner mode in a non-Hermitian quadrupole insulator.Notably,these topological modes not only persist within the band gap but also exist within the bulk continuum,forming bound states in a continuum(BICs).We then introduce the interplay between the NHSE and the topological-state-based BIC,emphasizing the novel wave effect known as the"extended state in a localized continuum".The fundamental principles underpinning the delocalization of topological states exhibit a universal nature,making their realization feasible across different platforms.Subsequently,we showcase the experimental demonstration of the extended topological mode in coupled acoustic cavities.Overall,these studies demonstrate the significant potential of the NHSE in wave control and provide theoretical and experimental foundations for the on-demand control of topological states in diverse systems.We hope this review not only enhances the comprehension of the non-Hermitian skin effect and its interplay with the topological states,but also paves the way for novel topological applications.
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