Versatile Control of Nonlinear Topological States in Non-Hermitian Systems

The non-Hermitian skin effect (NHSE) and nonlinearity can both delocalize topological modes (TMs) from the interface. However, the NHSE requires precise parameter tuning, while nonlinearity in Hermitian systems results in partial delocalization with limited mode capacity. To overcome these limitations, we propose a non-Hermitian nonlinear topological interface model that integrates Hermitian and non-Hermitian lattices with nonreciprocal hopping and nonlinearity. This system enables the complete delocalization of TMs across the entire lattice without fine-tuning, while allowing precise control over the wavefunction profile and spatial distribution through the intrinsic configuration and intensity of the nonlinearity. Using the spectral localizer, we demonstrate the topological protection and robustness of these extended non-Hermitian TMs against disorder. Furthermore, we show that under external pumping, localized excitations evolve into predefined profiles and generate long-range patterns, an effect unattainable in Hermitian systems. These findings reveal how the interplay of nonlinearity and NHSE shapes topological states, paving the way for compact topological devices.