Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system

Abstract

We study the topological physics in nonlinear Schrödinger systems on lattices. We employ the quench dynamics to explore the phase diagram, where a pulse is given to a lattice point and we analyze its time evolution. There are two system parameters $\lambda$ and $\xi$, where $\lambda$ controls the hoppings between the neighboring links and $\xi$ controls the nonlinearity. The dynamics crucially depends on these system parameters. Based on analytical and numerical studies, we derive the phase diagram of the nonlinear Su-Schrieffer-Heeger (SSH) model in the ($\lambda ,\xi$) plane. It consists of four phases. The topological and trivial phases emerge when the nonlinearity $\xi$ is small. The nonlinearity-induced localization phase emerges when $\xi$ is large. We also find a dimer phase as a result of a cooperation between the hopping and nonlinear terms. A similar analysis is made of the nonlinear second-order topological system on the breathing Kagome lattice, where a trimer phase appears instead of the dimer phase.

11 pages, 8 figures

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• Supersymmetric non-Hermitian topological interface laser
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Nonlinear dynamics of topological helicity wave in a frustrated skyrmion string
• Nonlinear topological Toda quasicrystal
• Nonlinear dynamical topological phases in Cooper-pair box array