Chiral edge soliton in nonlinear Chern systems

We study the effect on the chiral edge states by including a nonlinearity to a Chern insulator which has two chiral edge states with opposite chiralities. We explore a quench dynamics by giving a pulse to one site on an edge and analyzing the time evolution of a wave packet. Without the nonlinearity, an initial pulse spreads symmetrically and diffuses. On the other hand, with the nonlinearity present, a solitary wave is formed by the self-trapping effect of the nonlinear term and undergoes a unidirectional propagation along the edge, which we identify as a chiral edge soliton. A further increase of the nonlinearity induces a self-trapping transition, where the chiral wave packet stops its motion. It is intriguing that the nonlinearity is controlled only by changing the initial condition without changing a sample.