Topological and fractal defect states in non-Hermitian lattices

Abstract: Higher dimensions provide fertile ground for diverse topological phases and their associated localization phenomena, thanks to the rich geometric features of boundaries and defects. In this paper, we investigate non-Hermitian lattices with defects and establish a correspondence between spectral winding topology, fractal structures, and defect-localized states in arbitrary dimensions. Through analytical derivation and numerical simulations, we demonstrate that defect states emerge only when the spectral winding number exceeds a threshold determined by the defect size, which is linked to their fractal characteristics. By utilizing the Green's function, we identify amplified responses at defects under external driving fields, strengthening the physical correspondence between these topological and fractal features. Our findings offer a universal framework for understanding defect-localized states in higher-dimensional non-Hermitian systems.