A research team led by Prof. Kun Ding from the Department of Physics at Fudan University has addressed these questions theoretically. Using non-Hermitian lattices with nonreciprocal hopping and Kerr nonlinearity as model systems, the researchers combined soliton threshold diagrams with a Wannier-projected effective nonlinear Hamiltonian method. They identified two families of non-Hermitian solitons that differ in both their formation thresholds and the physical mechanisms underlying their formation. The study, titled "Solitons mediated by skin-mode localization and band nonreciprocity," has been published in National Science Review .
The first family, called skin-mode-assisted solitons (SMASs), mainly appear in regions where skin modes accumulate. The second family is called nonreciprocity-dressed solitons (NRDSs), which appear away from the skin-mode accumulation region.
To explain these threshold behaviors, the team developed a Wannier-projected effective nonlinear Hamiltonian approach. Near the formation threshold, the soliton's spatial profile resembles a linear Wannier function. By projecting the nonlinear problem onto a small number of relevant Wannier degrees of freedom, the researchers reduced the original nonlinear system to an effective model that can analytically characterize soliton thresholds. This method clarifies why SMASs arise in skin-mode accumulation regions: skin-mode localization pre-confines the wave packet and suppresses dispersive spreading, so only weak nonlinearity is required for localization. NRDSs follow the opposite route. They appear outside the skin-mode accumulation region, where band nonreciprocity enhances directional spreading, thereby raising the nonlinear threshold required to confine the wave packet. Together, the two soliton families show that skin-mode localization and band nonreciprocity play opposite roles in nonlinear localization: the former suppresses wave spreading, whereas the latter enhances it.
The researchers have further shown that this classification is not limited to a single model. In one- and two-dimensional systems, as well as in the different lattice geometries studied in the work, the spatial distribution of skin modes reshapes the soliton formation threshold and determines where the two soliton families emerge. In conventional Hermitian systems, soliton threshold hierarchies are often controlled by dimensionality and boundary geometry. In non-Hermitian skin systems, this hierarchy is reorganized by the spatial localization of skin modes: regions where skin modes accumulate favor SMAS formation, whereas regions away from skin-mode accumulation favor higher-threshold NRDS formation.
This study distinguishes the roles of skin-mode localization and band nonreciprocity in the formation of non-Hermitian solitons and provides a general theoretical framework for designing nonlinear localized states in non-Hermitian systems. As nonreciprocal couplings and nonlinear effects become increasingly controllable in photonic systems, acoustic and mechanical metamaterials, electrical circuit networks, and ultracold atoms, the framework may offer new ideas for low-threshold nonlinear responses, directional wave transport, and programmable nonlinear states.
The study was conducted by Shanyue Li, Mengying Hu, and Jing Lin of Prof. Kun Ding's group at Fudan University, in collaboration with Chen Fang from the Institute of Physics, Chinese Academy of Sciences, and Zhensheng Tao from Fudan University. Prof. Kun Ding is the corresponding author of the paper.
National Science Review