Lack of near-sightedness principle in non-Hermitian systems

Abstract

The non-Hermitian skin effect is a phenomenon in which an extensive number of states accumulates at the boundaries of a system. It has been associated to nontrivial topology, with nonzero bulk invariants predicting its appearance and its position in real space. Here, we demonstrate that the non-Hermitian skin effect has weaker bulk-edge correspondence than topological insulators: when translation symmetry is broken by a single non-Hermitian impurity, skin modes are depleted at the boundary and accumulate at the impurity site, without changing any bulk invariant. Similarly, a single non-Hermitian impurity may deplete the states from a region of Hermitian bulk.

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Cited by in corpus (3)

• Localized states and skin effect around non-Hermitian impurities in tight-binding models
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Impurity-induced counter skin-effect and linear modes in non-Hermitian systems