Topological selective non Hermitian skin effect

Topologically protected waveguides have aroused increasing interest due to their robustness against disorder and defects. In parallel, the advent of non-Hermitian physics with its inherent gain-and-loss mechanisms has introduced new tools for manipulating wave localization and transport. However, most attempts to combine non-Hermitian effects with topological systems uniformly impose the non-Hermitian skin effect (NHSE) on all modes, without selectivity targeting topological states. In this work, we propose a scheme thatachieves topologically selective NHSE by combining sub-symmetry-protected boundary modes with long-range non-reciprocal couplings. In an improved Su–Schrieffer–Heeger (SSH) chain, we analytically demonstrate that robust zero-energy edge modes can be preserved even in spectra filled with bulk states, while selectively applying the NHSE to the trivial bulk states to achieve the spatial separation between topological state and bulk state. By adjusting the long-range couplings a non-Hermitian phase transition can be observed in the complex energy spectrum: it transitions from a closed loop (circle) to an open arc, and ultimately to a reversely coiled loop. These transitions correspond respectively to a leftward NHSE, the disappearance of the NHSE, and a rightward NHSE. According to the calculations of the generalized Brillouin zone (GBZ), we confirm this transition by observing the GBZ passing through the unit circle, indicating a change in the direction of NHSE.We further extend our model to a two-dimensional higher-order SSH lattice, where selective non-Hermitian modulation enables clear spatial separation between topological corner states and bulk modes. To quantify this, we compute the local density of states (LDOS) in the complex energy plane for site 0 (a topologically localized corner) and site 288 (a region exhibiting NHSE). The comparison of LDOS between the two sites reveals that the topological states are primarily localized at site 0, while the bulk states affected by NHSE accumulate at site 288.To validate the theoretical predictions, we perform finite-element simulations of optical resonator arrays by using whispering-gallery modes. By adjusting the coupling distances and incorporating gain/loss through refractive index engineering, we replicate the modified SSH model and confirm the selective localization of topological and bulk modes.Our results provide a robust method for selectively exciting and spatially controlling the topological states in non-Hermitian systems, and also lay a foundation for future low-crosstalk high-stability topological photonic devices.