Universal scalefree non-Hermitian skin effect near the Bloch point

Abstract

The scalefree non-Hermitian skin effect (NHSE) refers to the phenomenon that the localization length of skin modes scales proportionally with system size in non-Hermitian systems. Authors of recent studies have demonstrated that the scalefree NHSE can be induced through various mechanisms, including the critical NHSE, local non-Hermiticity, and the boundary impurity effect. Nevertheless, these methods require careful modeling and precise parameter tuning. In contrast, in this paper, we suggest that the scalefree NHSE is a universal phenomenon, observable in extensive systems if these systems can be described by non-Bloch band theory and host Bloch points on the energy spectrum in the thermodynamic limit. Crucially, we discover that the geometry of the generalized Brillouin zone determines the scaling rule of the localization length, which can scale either linearly or quadratically with the system size. In this paper, we enriches the phenomenon of the scalefree NHSE.

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• Floquet engineering of point-gapped topological superconductors
• Observation of scale-free localized states induced by non-Hermitian defects
• From scale-free to Anderson localization: a size-dependent transition
• Scale-free localization versus Anderson localization in unidirectional quasiperiodic lattices
• Non-Hermitian off-diagonal disordered optical lattices
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• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
• Geometric origin of self-intersection points in non-Hermitian energy spectra