Motion of Nonlinear Excitations in Quasi-One-Dimensional Electron-Phonon Systems

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In this project, the dynamics of solitons in quasi-one-dimensional electron-phonon systems, typically realized in polyacetylene and similar conducting polymers, are investigated mainly in terms of numerical simulations. The lattice displacement is treated classically, while the electronic wave functions are calculated quantum mechanically. The initial state bearing a static soliton is determined by a set of self-consistent equations which are derived so as to minimize the total energy. The soliton is put in motion by applying a uniform electric field. The motion is determined by equation of motions for the lattice displacements and by the time-dependent Schrodinger equations for the electronic wave functions. The advantage of the present method is that we need not assume the shape of a moving soliton, since it is moved by a physical force in a natural way.The main results are(1)Soliton has a saturation velocity to 3 to 4 times of the sound velocity of the system.(2)The width of a movin … More g soliton is a decreasing function of the velocity and the maximum reduction rate is 10 to 20 % at the saturation velocity.(3)The kinetic energy of the soliton looks to diverge weakly at the saturation velocity.(4)The frequency of the amplitude oscillation mode around a moving soliton increases with the velocity, indicating that the inner structure of the soliton becomes harder with increasing velocity.(5)When there is a site-type short-ranged impurity, the effective potential for a soliton has a width of the same order of magnitude as the soliton width.(6)When there is a bond-type disorder, the effective potential for a soliton is step-like and therefore non-local. This is because the soliton considered in this work is a topological soliton connecting two degenerate ground states.(7)Introducing a phenomenological damping in the equation of motion for the lattice displacements, the soliton velocity takes a stationary value in the presence of a static electric field. From the proportionality relation between the stationary velocity and the electric field, the mobility of a soliton is estimated. It is pointed out that the room-temperature conductivity of an ideal polyacetylene can have a value comparable to those of good metals such as copper.The actibation energy of a soliton in the presence of ionized off-chain dopants is found to decreased rather rapidly with increasing the dopant concentration because of the finite width of the soliton. Less