Bipolar non-Hermitian skin effect and enhanced dynamics induced by long-range complex couplings

The non-Hermitian skin effect is a crucial feature in non-Hermitian systems, characterized by the pronounced localization of bulk eigenstates. In this work, we investigate an extended non-Hermitian Su-Schrieffer-Heeger model with power-law-decaying long-range complex couplings, revealing a skin transition from unipolar to bipolar. Specifically, we rigorously validate this skin phase transition by combining the energy spectra, spectral winding numbers, and spatial profiles of eigenstates. Meanwhile, the process of dynamical evolution further corroborates this transition, as wave packets are observed to spread toward both boundaries of the system rather than propagating unidirectionally. Remarkably, we reveal that the complex couplings can accelerate the dynamical evolution while suppressing the localization effect. Furthermore, we demonstrate that the couplings between identical sublattices lead to stronger localization and faster dynamic behaviors compared to those between opposite sublattices. In particular, we show that anti-Hermitian complex couplings, realized through dissipative couplings, can also effectively induce the bipolar non-Hermitian skin effect. Finally, we propose a feasible experimental scheme for realizing our model based on an electric circuit system. These findings provide a deeper understanding of both the directionality of the skin effect and non-Hermitian topological dynamics.