Abstract
We study the nonlinear effect on topological edge states by including a nonlinear term to a Chern insulator which has two chiral edge states with opposite chiralities. We explore quench dynamics by giving a pulse to one site on an edge and by analyzing its time evolution. Without the nonlinearity, an initial pulse spreads symmetrically and diffuses. On the other hand, with the nonlinearity present, unexpectedly a solitonlike edge state is formed, undergoes a unidirectional propagation along the edge, and turns at a corner without backscattering or diffraction. Furthermore, its wave function is well fitted by $\ensuremath{\propto}\text{sech}[{k}_{x}(x\ensuremath{-}{v}_{x}t)]$. A further increase of the nonlinearity induces a self-trapping transition, where the pulse is trapped to the initial site.
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