Topological edge solitons and their stability in a nonlinear Su-Schrieffer-Heeger model

Abstract

We study continuations of topological edge states in the Su-Schrieffer-Heeger model with on-site cubic (Kerr) nonlinearity, which is a 1D nonlinear photonic topological insulator (TI). Based on the topology of the underlying spatial dynamical system, we establish the existence of nonlinear edge states (edge solitons) for all positive energies in the topological band gap. We discover that these edge solitons are stable at any energy when the ratio between the weak and strong couplings is below a critical value. Above the critical coupling ratio, there are energy intervals where the edge solitons experience an oscillatory instability. Though our paper focuses on a photonic system, we also discuss the broader relevance of our methods and results to 1D nonlinear mechanical TIs.

7 pages, 6 figures; accepted version in Physical Review E after addressing referee comments

References in corpus (7)

• Nonlinear topological photonics
• Chirality of topological gap solitons in bosonic dimer chains
• Nonlinearity induced topological physics in momentum space and real space
• Stability of topological edge states under strong nonlinear effects
• Weakly nonlinear topological gap solitons in Su-Schrieffer-Heeger photonic lattices
• Topological Protection in a Strongly Nonlinear Interface Lattice
• Bright solitons in a PT-symmetric chain of dimers

Cited by in corpus (15)

• Nonlinear optical waveguide lattices: Asymptotic analysis, solitons, and topological insulators
• Transition from topological to chaos in the nonlinear Su-Schrieffer-Heeger model
• Insensitive edge solitons in a non-Hermitian topological lattice
• Vector valley Hall edge solitons in superhoneycomb lattices
• Optical control of topological end states via soliton formation in a 1D lattice
• Topological Phases of Tight-Binding Trimer Lattice in the BDI Symmetry Class
• Nonlinear Corner States in Topologically Nontrivial Kagome Lattice
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{P}\mathcal{T}$ symmetry
• Wave-packet spreading in the disordered and nonlinear Su-Schrieffer-Heeger chain
• Nonlinear Topological Edge States: from Dynamic Delocalization to Thermalization
• Dirac Solitons and Topological Edge States in the $\beta$-Fermi-Pasta-Ulam-Tsingou dimer lattice
• Solitons induced by an in-plane magnetic field in rhombohedral multilayer graphene
• Insensitive nonreciprocal edge breathers
• Thresholdless nonlinearity-induced edge solitons in trimer arrays
• Dark solitons in nonlinear Su-Schrieffer-Heeger lattices