Dynamical simulations of charged soliton transport in conjugated polymers with the inclusion of electron-electron interactions

We present numerical studies of the transport dynamics of a charged soliton in conjugated polymers under the influence of an external time-dependent electric field. All relevant electron-phonon and electron-electron interactions are nearly fully taken into account by simulating the monomer displacements with classical molecular dynamics (MD) and evolving the wavefunction for the $\pi$ electrons by virtue of the adaptive time-dependent density matrix renormalization group (TDDMRG) simultaneously and nonadiabatically. It is found that after a smooth turn-on of the external electric field the charged soliton is accelerated at first up to a stationary constant velocity as one entity consisting of both the charge and the lattice deformation. An ohmic region (6 mV/$\text{\AA}$ $\leq E_0\leq$ 12 mV/$\text{\AA}$) where the stationary velocity increases linearly with the electric field strength is observed. The relationship between electron-electron interactions and charged soliton transport is also investigated in detail. We find that the dependence of the stationary velocity of a charged soliton on the on-site Coulomb interactions $U$ and the nearest-neighbor interactions $V$ is due to the extent of delocalization of the charged soliton defect.