Soliton Transitions Mediated by Skin-Mode Localization and Band Nonreciprocity

Abstract: Solitons, typically resulting from a competition between band dispersion and nonlinearity, occur in lattices featuring the non-Hermitian skin effect as nonlinearity increases, accompanied by a transition in localization from linear skin modes to solitons. However, localization does not disentangle the role of skin modes in the soliton formation from that of band dispersion. Here, in such lattices, we uncover two distinct soliton phases, skin-mode-assisted solitons (SMASs) and nonreciprocity-dressed solitons (NRDSs). Rooted in fundamentally different mechanisms, SMASs originate from skin effect, while NRDSs stem from band nonreciprocity, each exhibiting unique spatial profiles. Using a stacked Su-Schrieffer-Heeger-like model as a prototype, we delineate the phase diagram of SMASs and NRDSs, each having clear phase boundaries. To interpret them, we formulate a Wannier-function-based nonlinear Hamiltonian, showing that soliton formation depends critically on how skin-mode localization and band nonreciprocity suppress or enhance wave dispersion. For SMASs, skin-mode localization reduces wave broadening at the localization sites, thereby lowering the formation threshold. This soliton phase is observable from edge dynamics and accompanied by a dynamical stability reentrance when transitioning from linear skin modes. In contrast, NRDSs, as well as their thresholds, originate from bulk band nonreciprocity and persist under periodic boundary conditions. Our framework offers predictive tools for characterizing and engineering solitons in experimentally realizable non-Hermitian systems, spanning optics to mechanics.