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Physical Review B

Dynamics of polarons in conjugated polymers: An adaptive time-dependent density-matrix renormalization-group study

Hui Chao Zhao, Yao Yao, Zhong An, Chang-Qin Wu

Published Jul 28, 2008• 25 citations
Publisher

Abstract

The motion of polarons, which serve as charge carriers in conjugated polymers, is of fundamental importance for understanding transport properties of organic optoelectronic devices. We investigate the dynamics of a charged polaron in the presence of both electron-phonon and electron-electron interactions under the influence of an external electric field, which is modeled by the one-dimensional tight-binding Su-Schrieffer-Heeger (SSH) model supplemented with a Hubbard on-site repulsion term. For this many-body dynamical evolution problem, we develop an adaptive time-dependent density matrix renormalization group ($t$-DMRG) method in combination with a Newtonian equation of motion for atomic displacements. Our results show that the velocity of the polaron is suppressed by the on-site Coulomb interaction $U$. The polaron moves with a supersonic velocity, about four times the sound velocity at the small $U$ limit, and approaches the sound velocity at the large $U$ limit. Furthermore, the dependence of the polaron velocity and the polaron effective mass on the lattice structures are discussed.

DOI
10.1103/physrevb.78.035209

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•Jan 1, 2005•0 citations
The motion of polarons, which serve as charge carriers in conjugated polymers, is of fundamental importance for understanding transport properties of organic optoelectronic devices. We investigate the dynamics of a charged polaron in the presence of both electron-phonon and electron-electron interactions under the influence of an external electric field, which is modeled by the one-dimensional tight-binding Su-Schrieffer-Heeger (SSH) model supplemented with a Hubbard on-site repulsion term. For this many-body dynamical evolution problem, we develop an adaptive time-dependent density matrix renormalization group (ttt-DMRG) method in combination with a Newtonian equation of motion for atomic displacements. Our results show that the velocity of the polaron is suppressed by the on-site Coulomb interaction UUU. The polaron moves with a supersonic velocity, about four times the sound velocity at the small UUU limit, and approaches the sound velocity at the large UUU limit. Furthermore, the dependence of the polaron velocity and the polaron effective mass on the lattice structures are discussed.
\n\nBy employing an adaptive time-dependent density matrix renormalization group (t-DMRG) method, we investigate the electron-electron correlation effects on the inelastic-scattering processes of oppositely charged-soliton anti-soliton pairs in conjugated polymers under the influence of an external electric field. The simulations are performed based on the Su-Schrieffer-Heeger (SSH) model modified to include electron-electron interactions and an external electric field. The percent yield of product is numerically calculated by a projection method. Our results show that the on-site Coulomb interaction is of fundamental importance and favors the recombination between the pairs of soliton. Additionally, the effects of external electric field and nearest-neighbor electron-electron interaction on the collision processes are also discussed.\n
In this paper, we address the role of electron-electron interactions on the velocities of spin and charge transport in one-dimensional systems typified by conjugated polymers. We employ the Hubbard model to model electron-electron interactions. The recently developed technique of time dependent Density Matrix Renormalization Group (tdDMRG) is used to follow the spin and charge evolution in an initial wavepacket described by a hole doped in the ground state of the neutral system. We find that the charge and spin velocities are different in the presence of correlations and are in accordance with results from earlier studies; the charge and spin move together in the noninteracting picture while interaction slows down only the spin velocity. We also note that dimerization of the chain only weakly affects these velocities.
By employing an adaptive time-dependent density-matrix-renormalization-group method, the spin-flip process of polarons is investigated in a polymer chain with magnetic impurities. Being driven by an external electric field, a polaron carrying both spin 1/2 and charge +/-e moves at a constant speed in the polymer chain. When the polaron passes through a specific site, which couples to a magnetic impurity via spin-exchange interaction, a spin-flip process is observed if its spin is antiparallel to the impurity spin. Our results show that the spin-flip probability is enhanced by the on-site Coulomb interaction and increases with increase in the spin-exchange integral. Additionally, some possible applications of the spin-state swap between the polaron and the impurity are discussed.
We investigate the effect of static electron-phonon coupling on real-time dynamics of spin and charge transport in $\ensuremath{\pi}$-conjugated polyene chains. The polyene chain is modeled by the Pariser-Parr-Pople Hamiltonian with dimerized nearest-neighbor parameter ${t}_{0}(1+\ensuremath{\delta})$ for short bonds and ${t}_{0}(1\ensuremath{-}\ensuremath{\delta})$ for long bonds, and long-range electron-electron interactions. We follow the time evolution of the spin and charge using time-dependent density matrix renormalization group technique when a hole is injected at one end of the chain in its ground state. We find that spin and charge dynamics followed through spin and charge velocities depend both on chain length and extent of dimerization $\ensuremath{\delta}$. Analysis of the results requires focusing on physical quantities such as average spin and charge polarizations, particularly in the large dimerization limit. In the dimerization range 0.0 $\ensuremath{\le}$ $\ensuremath{\delta}$ $\ensuremath{\le}$ 0.15, spin-charge dynamics is found to have a well-defined behavior, with spin-charge separation (measured as the ratio of charge velocity to spin velocity) as well as the total amount of charge and spin transported in a given time along the chain decreasing as dimerization increases. However, in the range 0.3 $\ensuremath{\le}$ $\ensuremath{\delta}$ $\ensuremath{\le}$ 0.5, it is observed that the dynamics of spin and charge transport becomes complicated. It is observed that, for large $\ensuremath{\delta}$ values, spin-charge separation is suppressed and the injected hole fails to travel the entire length of the chain.
We solve the disordered Holstein model via the density-matrix renormalization group method to investigate the combined roles of electron-phonon coupling and disorder on the localization of a single charge or exciton. The parameter regimes chosen, namely the adiabatic regime, $\ensuremath{\hbar}\ensuremath{\omega}/4{t}_{0}={\ensuremath{\omega}}^{\ensuremath{'}}<1$, and the large polaron regime, $\ensuremath{\lambda}<1$, are applicable to most conjugated polymers. We show that as a consequence of the polaron effective mass diverging in the adiabatic limit (defined as ${\ensuremath{\omega}}^{\ensuremath{'}}\ensuremath{\rightarrow}0$ subject to fixed $\ensuremath{\lambda}$) self-localized, symmetry-breaking solutions are predicted by the quantum Holstein model for infinitesimal disorder, in complete agreement with the predictions of the Born-Oppenheimer Holstein model. For other parts of the (${\ensuremath{\omega}}^{\ensuremath{'}}$, $\ensuremath{\lambda}$) parameter space, however, self-localized Born-Oppenheimer solutions are not expected. If ${\ensuremath{\omega}}^{\ensuremath{'}}$ is not small enough and $\ensuremath{\lambda}$ is not large enough, then the polaron is predominately localized by Anderson disorder, albeit more than for a free particle, because of the enhanced effective mass. Alternatively, for very small electron-phonon coupling ($\ensuremath{\lambda}\ensuremath{\ll}1$) the disorder-induced localization length is always smaller than the classical polaron size, $2/\ensuremath{\lambda}$, so that disorder always dominates. We comment on the implication of our results on the electronic properties of conjugated polymers.
In this work we develop a new numerical method, the adaptive time-dependent density-matrix renormalization-group (adaptive t-DMRG), which turns out to be very well suited to investigate time-dependent phenomena in one-dimensional strongly correlated systems. The method is based on the original density-matrix renormalization group method by White and the time evolving block-decimation procedure by Vidal. We further show the applicability of the new method to different physical systems: bosonic, fermionic, and spin chains. We first discuss the consequences of the presence of an external trapping potential on the static properties of trapped cold bosonic atoms in an optical lattice using the Bose-Hubbard model. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. We note that the superfluid to Mott-insulating transition is seen most directly in the half width of the interference peak. Then we turn to the evolution of density perturbations in these systems. In particular, we discuss the dependence of the velocity and the decay of the amplitude on density, interaction strength, and the extent and height of the perturbation in a numerically exact way, covering a wide range of interaction and perturbation strengths. By comparing our results for the sound velocity to theoretical predictions, we determine the limits of a Gross-Pitaevskii or Bogoliubov type description and the regime where repulsive one-dimensional Bose gases exhibit fermionic behaviour. As a second application of the adaptive t-DMRG, we investigate the phenomenon of spin-charge separation in the Hubbard model and propose an experimental setup for its observation in cold Fermi gases. We show the robustness of this separation beyond the low-energy regime by studying the time evolution of density wave packets of finite strength and at length scales down to a few lattice spacings. A striking signature of spin-charge separation is found in 1D cold Fermi gases in a harmonic trap using the different propagation properties of the liquid and Mott-insulating phases. The third application relates to the area of spintronics. A simplified model for the magnetization transport between two coupled reservoirs with opposite spin polarization is studied. We investigate whether a simple long time limit for the spin transport exists and if so, how it depends on the properties of the system such as integrability and criticality. Time-scales accessible to us are of the order of 100 units of time measured in 1/J while maintaining insignificant error in the observables.