Configurable localized states in non-Hermitian extended Su–Schrieffer–Heeger model

Abstract We study the one-dimensional non-Hermitian Su–Schrieffer–Heeger model with gain and loss at two different sublattices and tuned hopping amplitudes between nearest-neighboring sites based on periodic, linear, or exponential functions. A periodic function introduces an additional periodicity while preserving the topological features, offering further opportunities to design topological edge states by adjusting the function period, the system size, and the gain/loss rate. For linear and exponential function tuning, edge states are observed although the periodicity is destroyed. In particular, we find that compared to linear tuning, exponential tuning can lead to high inverse participation ratio and a spatial aggregation trend for a large portion of eigenstates. Our results suggest that introducing functionally tuned hopping amplitudes offers an approach to designing new types of topological edge states or other localized states. Given the high experimental feasibility of various functional modulations, these localized states have great potential in studying cavity quantum electrodynamics and designing optical devices, such as high-output-power lasers.