Hybrid scale-free skin effect in non-Hermitian systems: A transfer matrix approach

Abstract

Surpassing the individual characteristics of the non-Hermitian skin effect (NHSE) and the scale-free (SF) effect observed recently, we systematically exploit the exponential decay behavior of bulk eigenstates via the transfer matrix approach in non-Hermitian systems. We concentrate on one-dimensional (1D) finite-size non-Hermitian systems with 2*2 transfer matrices in either the absence or presence of the boundary impurity. We analytically unveil that the unidirectional SF effect emerges with the singular transfer matrices, while the hybrid scale-free skin (SFS) effect appears with the nonsingular transfer matrices even when an open boundary condition (OBC) is imposed. The unidirectional SF effect exceeds the scope of the SF effect in previous works, while the hybrid SFS effect is an interesting interplay between the skin effect and the SF effect in finite-size systems. Our results reveal that the skin effect under the OBC prevails when it coexists with the SF effect as the system approaches the thermodynamic limit in the presence of the hybrid SFS effect. Our approach paves the way for rigorous and unified explorations of the skin and SF effects in both Hermitian and non-Hermitian systems with generic boundary conditions.

20 pages, 9 figures

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Cited by in corpus (12)

• Observation of scale-free localized states induced by non-Hermitian defects
• Braiding Topology of Non-Hermitian Open-Boundary Bands
• Observation of Impurity-Induced Scale-Free Localization in a Disordered Non-Hermitian Electrical Circuit
• Constraints of internal symmetry on the non-Hermitian skin effect and bidirectional skin effect under the action of the Hermitian conjugate of time-reversal symmetry
• From scale-free to Anderson localization: a size-dependent transition
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• General theory for infernal points in non-Hermitian systems
• Theory for the spectral splitting exponent of exceptional points
• Non-Hermitian off-diagonal disordered optical lattices
• Defect-driven incoherent skin localization
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Winding-control mechanism of non-Hermitian systems