Dynamics of an Acoustic Polaron in One-Dimensional Electron-Lattice System

Abstract

The dynamical behavior of an acoustic polaron in typical non-degenerate conjugated polymer, polydiacetylene, is numerically studied by using Su-Schrieffer-Heeger's model for the one dimensional electron-lattice system. It is confirmed that the velocity of a polaron accelerated by a constant electric field shows a saturation to a velocity close to the sound velocity of the system, and that the width of a moving polaron decreases as a monotonic function of the velocity tending to zero at the saturation velocity. The effective mass of a polaron is estimated to be about one hundred times as heavy as the bare electron mass. Furthermore the linear mode analysis in the presence of a polaron is carried out, leading to the conclusion that there is only one localized mode, i.e. the translational mode. This is confirmed also from the phase shift of extended modes. There is no localized mode corresponding to the amplitude mode in the case of the soliton in polyacetylene. Nevertheless the width of a moving polaron shows small oscillations in time. This is found to be related to the lowest odd symmetry extended mode and to be due to the finite size effect.

Dynamical Simulations of Polaron Transport in Conjugated Polymers with the Inclusion of Electron−Electron Interactions

“…Basko and Conwell [11] have also analyzed the dynamics of a polaron and found that the speed of a steadily moving polaron cannot exceed the sound speed (V S ). These conclusions are consistent with those from the numerical results presented by Arikabe et al [12] but inconsistent with those given by Johansson and Stafström [13,14], who performed a nonadiabatic simulation in which transitions between instantaneous eigenstates are allowed. In…”

“…So far, there have been many extensive theoretical studies on polaron dynamics in conjugated polymers [9,10,11,12,13,14,15,16,17,18,19,20] based on the Su-Schrieffer-Heeger (SSH) model [21,22], an improved Hückel molecular orbital model, in which π-electrons are coupled to distortions in the polymer backbone by the electron-phonon interaction.…”

Drift of charge carriers in crystalline organic semiconductors

“…Similar phenomenon has been found in the hopping transport [49] and the dynamics of the polarons. [50,51] However, the ability of electron motion can still be reflected by the mean-square displacement for diffusion, which is calculated as…”

The screened polarons

“…Equations (12)(13)(14)(15)(16)(17)(18)(19) are the dynamical equations of our model. We consider polaronic states whose electronic wave function is of the form:…”