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

TL;DR

This study numerically investigates the dynamics of an acoustic polaron in a one-dimensional electron-lattice system, revealing velocity saturation near sound speed, effective mass estimates, and localized mode characteristics.

Contribution

It provides detailed numerical analysis of polaron behavior, including velocity saturation, effective mass, and mode structure, in a one-dimensional electron-lattice model.

Findings

Polaron velocity saturates near the sound velocity.

Effective mass of polaron is about 100 times the electron mass.

Only one localized translational mode exists for the polaron.

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.