Effects of e-e interactions on the dynamics of polarons in conjugated polymers

Combining the one-dimensional tight-binding Su-Schrieffer-Heeger (SSH) model and the extended Hubbard model (EHM), we investigate the effect of electron-electron interactions on the dynamics of a charged polaron in a conjugated polymer chain, by using a nonadiabatic dynamical method. Both the localization and the velocity of the polaron will vary with the on-site Coulomb interactions U and the nearest-neighbor interactions V . It is found that the local extremum of the stationary velocity of the polaron occurs at U ≈ 2V (U, V > 0). Additionally, the relation between the velocity and the lattice structure of the polaron is shown qualitatively. Copyright c © EPLA, 2007 There is currently great interest in the use of semiconducting electroluminescent polymers for the feasibility of constructing light-emitting diodes (LEDs) based on conjugated polymers [1]. In these devices, the electrons and/or holes are injected from metal electrodes, and transported under the influence of an external electric field. It has been generally accepted that the charge carriers are charged polarons in conjugated polymers, due to the strong electron-lattice interaction. Obviously, the transportation and the recombination of polarons play an important role in these optoelectronic devices based on conjugated polymers. There have been extensive studies on dynamics of polarons in conjugated polymers [2–9] under the influence of an external electric field, based on the one-dimensional tight-binding Su-Schrieffer-Heeger (SSH) Hamiltonian [10,11]. The polaron velocity is one of the major issues of interest. Arikabe et al. found that a polaron has a saturation velocity just below the sound velocity by using an adiabatic simulation in which the electronic energy is treated within the Born-Oppenheimer approximation [6]. In contrast to the result, based on a nonadiabatic simulation in which the transitions between instantaneous eigenstates are allowed, Johansson et al. [7,8] showed that the polaron can move with a supersonic velocity when (a)E-mail: [email protected] the electric field strengths are above 0.14mV/Å and the maximum velocity (about four times the sound speed) is reached at a high electric field strength (∼ 3.5mV/Å). At even higher electric field strengths, the polaron becomes unstable and dissociates. However, in the SSH model, only the electron-lattice interactions are considered and the electron-electron interactions are ignored. Therefore, it should be asked, what is the influence of the electron-electron interactions on polarons. The purpose of the present paper is to study how the electron-electron interactions affect the properties of polarons, especially to discuss the dynamics of moving polarons based on the extended Hubbard model (EHM). Indeed, as a prototype model, the static-state properties and the dynamical evolutions of organic polymers have been widely investigated based on the SSH model modified with the consideration of electron-electron interactions via an extended Hubbard Hamiltonian [12–16]. Moreover, the unrestricted Hartree-Fock (UHF) approximation has also been used in weak correlation systems [14–19]. It has been shown that EHM and UHF are good approximations if the electron-electron interactions are not too strong. In this letter, combining the SSH and EHM models, we simulate the motion of polarons under an applied electric field by using a nonadiabatic dynamical method at the UHF level. For simplicity, the lattice is described classically while we solve the time-dependent Schrödinger