Electron-soliton dynamics in chains with cubic nonlinearity

The lattice vibrations and its coupling with the electronic dynamics (the electron-phonon interaction) plays relevant roles on the effective electronic transport. In our work, we consider the problem of electron transport mediated by the coupling with a solitonic wave.
Our model consists of a one-electron moving in an unharmonic lattice and we will focus on the existence of an electro-soliton pair.
In our model, we will consider a one-dimensional unharmonic lattice with a cubic interaction between nearest neighboring sites.
The electron-lattice interaction was introduced by considering the energy hopping
following the (SSH) approximation, i.e. a linear function of the distance between neighboring atoms.
We will solve numerically the dynamics equations for the electron and lattice and compute the dynamics of an initially localized electronic wave-packet.
Our results suggest that the solitonic waves that exist within this nonlinear lattice can control the electron dynamics along the entire lattice.
We will study in details the formation of a electron-soliton state that can move along the chain.
This mobile electron-soliton pair can be a key ingredient to the charge
transport in a nonlinear chain.
Moreover, we will investigate in details which intensity of the electron-lattice interaction necessary to promote the appearance of this electron-soliton pair.
Our calculations suggest that, even for strong electron-lattice coupling, we can find an electronic dynamics non mediated by solitonic waves.