Polaron Dynamics Research Articles

Dynamics of photogenerated polarons and polaron pairs in P3HT thin films

On the basis of the analysis of the experimental data of the transient absorption spectroscopy of thin films of regioregular poly(3-hexyl thiophene) we suggest a mechanism of the polaron pairs decay based on the coherent up and down conversion cycling between hot polaron pairs and free polarons. Compared to previously adopted models, based on single molecular processes or bimolecular collisions, the suggested model reproduced well both the polaron pairs and polaron population kinetics at short time after photoexcitation. For longer times, when the polaron pairs are already thermalized, they decay via 1-D diffusion limited bi-molecular collision processes.

Electrical structure, magnetic polaron and lithium ion dynamics in four mixed-metal oxide multiple-phase electrode cathode material for Li ion batteries from density functional theory study

This study present results derived from first-principles calculations, at density functional level, and molecular dynamics simulations. Calculations of perfect LiMO2 (M=Mn, Co and Ni) and their mixed-metal oxide (LiMn1/3Co1/3Ni1/3O2) were performed by PBE with the GGA method in the VASP Package. Atomistic simulation calculation was used for searching the electrical structure, magnetic polaron and lithium ion dynamics properties. The results were suitable for the measured valence-band structure, also with the magnetic and electrical properties of the Li-transition metal oxide. The band gap is determined by the charge-transfer and the main contributions from the magnetic polaron produced spin electron−hole pairs that were smaller than that of the states of the M3d and O2p orbitals. When anisotropic O2p-M3d orbital hybridization occurs, a highly-delocalized characteristic was shown in the M3d hole state owing to the states mixing. The extended M4p orbital improved the exchange interaction between Mn3d and Op which led to an asymmetric charge distribution in the MO bonds. The delocalized characteristic of Mn3d holes is a vital part of the mechanism of spin-dependent ligand (O2−) hybridization. Due to the decrease in inter-molecular attractive forces, a decrease in the order parameter of crystalline was derived from the increase of temperature. Moreover, the transition metal-oxygen and lithium-oxygen radial distribution functions (RDF) at temperatures of 300 and 900K were compared to each other. The results indicate that the height of the peaks decrease and the system becomes more stable due to increasing temperature. Overall, because of the increase of thermal motion with increasing temperature, lithium ions showed a gradual evolution of mobility.

Dynamics of Polarons in Organic Conjugated Polymers with Side Radicals.

Based on the one-dimensional tight-binding Su-Schrieffer-Heeger (SSH) model, and using the molecular dynamics method, we discuss the dynamics of electron and hole polarons propagating along a polymer chain, as a function of the distance between side radicals and the magnitude of the transfer integrals between the main chain and the side radicals. We first discuss the average velocities of electron and hole polarons as a function of the distance between side radicals. It is found that the average velocities of the electron polarons remain almost unchanged, while the average velocities of hole polarons decrease significantly when the radical distance is comparable to the polaron width. Second, we have found that the average velocities of electron polarons decrease with increasing transfer integral, but the average velocities of hole polarons increase. These results may provide a theoretical basis for understanding carriers transport properties in polymers chain with side radicals.

Transient dynamics of a one‐dimensional Holstein polaron under the influence of an external electric field

Following the Dirac‐Frenkel time‐dependent variational principle, transient dynamics of a one‐dimensional Holstein polaron with diagonal and off‐diagonal exciton‐phonon coupling in an external electric field is studied by employing the multi‐D2 Ansatz, also known as a superposition of the usual Davydov D2 trial states. Resultant polaron dynamics has significantly enhanced accuracy, and is in perfect agreement with that derived from the hierarchy equations of motion method. Starting from an initial broad wave packet, the exciton undergoes typical Bloch oscillations. Adding weak exciton‐phonon coupling leads to a broadened exciton wave packet and a reduced current amplitude. Using a narrow wave packet as the initial state, the bare exciton oscillates in a symmetric breathing mode, but the symmetry is easily broken by weak coupling to phonons, resulting in a non‐zero exciton current. For both scenarios, temporal periodicity is unchanged by exciton‐phonon coupling. In particular, at variance with the case of an infinite linear chain, no steady state is found in a finite‐sized ring within the anti‐adiabatic regime. For strong diagonal coupling, the multi‐ Anstaz is found to be highly accurate, and the phonon confinement gives rise to exciton localization and decay of the Bloch oscillations. image

Polaron and bipolaron stability on paraphenylene polymers.

Polyparaphenylene is the prototypical conjugated polymer containing phenyl rings and its properties are good references for a family of derived polymers. We investigate the structure, stability, and dynamics of polarons and bipolarons in polyparaphenylene chains under an applied electric field. To do this, we use a bidimensional SSH Hamiltonian model with the Hubbard extension, i.e., with local and nearest-neighbor Coulomb interaction, which has been designed to work with general hexagonal lattices, from which polyparaphenylene can be seen as a prominent case. Using the time-dependent Hartree-Fock approximation, we calculate the structural characteristics, the maximum field strength, supported before polarons and bipolarons gets unstable, and the maximum velocity achieved by these charge carriers. We obtained the polaron and bipolaron terminal velocity to be 0.51 Å/fs and 1.15 Å/fs, respectively. The maximum field strength determined by our calculations is 0.54 mV/Å and 0.80 mV/Å, respectively. Our results are in good agreement with other theoretical methods and experiments.

Polaron dynamics in anisotropic Holstein-Peierls systems.

Polaron dynamics in anisotropic organic molecular semiconductors is theoretically investigated and simulated in the framework of a semi-classical Holstein-Peierls model. Our computational protocol is presented and applied to studies of a two-dimensional molecular crystal. The intermolecular (Peierls) parameters for a particular crystal direction are systematically changed in order to study the effect of anisotropy in the system. The usefulness of this methodology is highlighted by studying the polaron dynamics on a picosecond timescale, which provides a microscopic insight into the influence of the interplay between different intramolecular parameters on the charge transport mechanism. Our results show that the polaron mobility is substantially reduced in going from an anisotropic to an isotropic relationship between the Peierls parameters for different directions in the crystal. Interestingly, the molecular charge distribution presents three different signatures corresponding to a one-dimensional polaron, a two-dimensional polaron, and an intermediate state for which the polaron localization depends on the degree of anisotropy. Importantly, the two-dimensional polaron, which is present in the essentially isotropic system, is immobile whereas the other two types of polarons are mobile. This, in order for polaron transport to occur in a two-dimensional molecular based system, this system has to be anisotropic.

Unified analysis of transient and steady-state electrophosphorescence using exciton and polaron dynamics modeling

Phosphorescent organic light-emitting devices (OLEDs) can suffer a significant reduction in device efficiency under high current density excitation. This steady-state efficiency roll-off is frequently modeled by including losses from exciton-exciton and exciton-polaron quenching. Despite success in modeling the steady-state efficiency roll-off, the corresponding transient electroluminescence behavior has not been modeled as effectively using the same quenching processes. In this work, both the steady-state and transient electroluminescence behavior of phosphorescent OLEDs based on tris[2-phenylpyridinato-C2,N]Iridium(III) (Ir(ppy)3) are successfully reproduced by considering a dynamic polaron population. Within this model, polarons are able to either form excitons or leak through the device emissive layer, reducing the overall efficiency. This formalism permits a natural and rigorous connection between exciton and polaron dynamics and device charge balance, with the charge balance cast as the efficiency of exciton formation. The full dynamics model reproduces both the rise and decay of transient electroluminescence, as well as the full dependence of the external quantum efficiency on current density. Fit parameters are independently verified using separate studies of transient and steady-state photoluminescence. The model provides a complete picture for the dynamics present during the electrical operation of phosphorescent OLEDs, while also offering a direct route to elucidate exciton formation.

Quantum Dynamics of Ultracold Bose Polarons.

We analyze the dynamics of Bose polarons in the vicinity of a Feshbach resonance between the impurity and host atoms. We compute the radio-frequency absorption spectra for the case when the initial state of the impurity is noninteracting and the final state is strongly interacting with the host atoms. We compare results of different theoretical approaches including a single excitation expansion, a self-consistent T-matrix method, and a time-dependent coherent state approach. Our analysis reveals sharp spectral features arising from metastable states with several Bogoliubov excitations bound to the impurity atom. This surprising result of the interplay of many-body and few-body Efimov type bound state physics can only be obtained by going beyond the commonly used Fröhlich model and including quasiparticle scattering processes. Close to the resonance we find that strong fluctuations lead to a broad, incoherent absorption spectrum where no quasiparticle peak can be assigned.

Photoinduced dynamics in doped Mott insulators with polaronic conduction:Ba2Ti13O22andBaxTi8O16

To clarify the dynamics of polarons in doped Mott insulators, we performed pump-probe reflectivity measurements for two barium titanates, ${\mathrm{Ba}}_{2}{\mathrm{Ti}}_{13}{\mathrm{O}}_{22}$ and ${\mathrm{Ba}}_{x}{\mathrm{Ti}}_{8}{\mathrm{O}}_{16}$, with a noninteger average number of $d$ electrons per Ti. We found that the photoinduced dynamics in ${\mathrm{Ba}}_{2}{\mathrm{Ti}}_{13}{\mathrm{O}}_{22}$ with a three-dimensional electronic structure is characterized by a broadening of the polaron-excitation peak immediately after photoirradiation, whereas that in ${\mathrm{Ba}}_{x}{\mathrm{Ti}}_{8}{\mathrm{O}}_{16}$ with a one-dimensional electronic structure is characterized by a change in the intensities of the polaron-excitation peak and charge-gap-excitation peak with time. This indicates that a difference in dimensionality results in different photoinduced dynamics of polarons in doped Mott insulators.

Optical orientation of hole magnetic polarons in (Cd,Mn)Te/(Cd,Mn,Mg)Te quantum wells

The optically induced spin polarization in (Cd,Mn)Te/(Cd,Mn,Mg)Te diluted-magnetic-semiconductor quantum wells is investigated by means of picosecond pump-probe Kerr rotation. At 1.8 K temperature, additionally to the oscillatory signals from photoexcited electrons and Manganese spins precessing about an external magnetic field, a surprisingly long-lived (up to 60 ns) nonoscillating spin polarization is detected. This polarization is related to optical orientation of equilibrium magnetic polarons involving resident holes. The suggested mechanism for the optical orientation of the equilibrium magnetic polarons indicates that the detected polaron dynamics originates from unexcited magnetic polarons. The polaron spin dynamics is controlled by the anisotropic spin structure of the heavy-hole resulting in a freezing of the polaron magnetic moment in one of the two stable states oriented along the structure growth axis. Spin relaxation between these states is prohibited by a potential barrier, which depends on temperature and magnetic field. The magnetic polaron relaxation is accelerated with increasing temperature and in magnetic field.

Impact of the Electron-Phonon Interactions on the Polaron Dynamics in Graphene Nanoribbons.

The influence of the electron-phonon (e-ph) interactions on the filed-included polaron dynamics in armchair graphene nanoribbons (GNRs) is theoretically investigated in the scope of a two-dimensional tight-binding model. The results show that the localization of the polaronic charge increases when the strength of e-ph coupling also increases. Consequently, the polaron saturation velocity decreases for higher e-ph coupling strengths. Interestingly, the interplay between the e-ph coupling strength and the GNR width changes substantially the polaron dynamics properties.

Polaron Dynamics on the Nonlinear Lattice in the Su-Schrieffer-Heeger Approximation. Exact and Approximate Solutions

We investigate the polaron dynamics on the nonlinear lattice with the cubic nonlinearity in the tight-binding approximation. The electron–phonon interaction is accounted in the Su–Schrieffer–Heeger approximation. The system of nonlinear partial differential equations is derived in the continuum approximation. It has an exact solution at a special relation between parameters of lattice nonlinearity α and electron–phonon interaction χ. An approximate analytical solution is obtained at arbitrary parameters α and χ. Results of the numeric simulations are in a good agreement with the analytical predictions in both cases. The range of parameter values, where theoretical formulae are valid, is determined.

Fast, Accurate Simulation of Polaron Dynamics and Multidimensional Spectroscopy by Multiple Davydov Trial States.

By employing the Dirac-Frenkel time-dependent variational principle, we study the dynamical properties of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling. A linear combination of the Davydov D1 (D2) ansatz, referred to as the "multi-D1 ansatz" ("multi-D2 ansatz"), is used as the trial state with enhanced accuracy but without sacrificing efficiency. The time evolution of the exciton probability is found to be in perfect agreement with that of the hierarchy equations of motion, demonstrating the promise the multiple Davydov trial states hold as an efficient, robust description of dynamics of complex quantum systems. In addition to the linear absorption spectra computed for both diagonal and off-diagonal cases, for the first time, 2D spectra have been calculated for systems with off-diagonal exciton-phonon coupling by employing the multiple D2 ansatz to compute the nonlinear response function, testifying to the great potential of the multiple D2 ansatz for fast, accurate implementation of multidimensional spectroscopy. It is found that the signal exhibits a single peak for weak off-diagonal coupling, while a vibronic multipeak structure appears for strong off-diagonal coupling.

Exploring the impact of semicore level electronic relaxation on polaron dynamics: An adiabaticab initiostudy ofFePO4

In the present work, we study the effects of the electronic relaxation of semicore levels on polaron activation energies and dynamics. Within the framework of adiabatic ab initio theory, we utilize both static transition state theory and molecular dynamics methods for an in-depth study of polaronic hopping in delithiated ${\text{LiFePO}}_{4} ({\text{FePO}}_{4})$. Our results show that electronic relaxation of semicore states is significant in ${\text{FePO}}_{4}$, resulting in a lower activation barrier and kinetics that is one to two orders faster compared to the result of calculations that do not incorporate semicore states. In general, the results suggest that the relaxation of states far below the Fermi energy could dramatically impact the ab initio polaronic barrier estimates for many transition metal oxides and phosphates.

Dynamics of polarons in organic conjugated polymers with impurity ions

Based on the one-dimensional tight-binding Su-Schrieffer-Heeger (SSH) model, and using the molecular dynamics method, we discuss the dynamics of electron and hole polarons under the influence of impurity potentials and the distance between impurities. Under an external electric field, the electron or hole polaron can move along the polymer chain with a steady velocity. When the polarons collide with impurities, the velocities of the polarons would be affected by the impurity potentials and the distance between the impurities. 1) Firstly, at a fixed impurity potential strength, the average velocities of the electron and hole polarons as a function of the distance (2-16 times the lattice constant) between impurities have been discussed in polymers. It is found that the average velocities of the electron and hole polarons increase with increasing distance between impurities. It is worth noting that the average velocities of the electron polarons are greater than those of the hole polarons, which results from the fact that the electron and hole polarons have different coulomb interactions with the impurity ions. That is to say, the coulomb repulsion is shown between the electron polarons and impurity ions, which is similar to the potential barriers; while the coulomb attraction appears between the hole polaron and impurity ions, which is similar to a potential well. However, as the distance between the impurity ions becomes large enough, the average speeds of the electron and hole polarons almost remain the same, and show just a few small oscillation. This is due to the different distances between impurity ions which generate the different superposition effects of barrier or potential well on the electron and hole polarons. 2) Next, with a fixed distance between the two impurity ions, we find that with the increase of impurity potential strength, the average velocities of the electron and hole polarons decrease. And the decrease of the average speed of the hole polaron is more obvious. It can be explained as follows: the coulomb attraction interactions between the hole polaron and impurity ions can obviously enhance the localization of the hole polaron. While the coulomb repulsion interactions between electron polaron and impurity ions can only make the electron polaron undergo a small shift in the polymer chain, so that the localization of it is almost unchanged. In view of the average speed of the polaron being closely related to the localization of the polaron, the change of the average speed of the hole polaron is more obvious. The results above may provide some theoretical basis for understanding the conduction properties in doped polymers.

Polaronic effects in one- and two-band quantum systems

In this work we study the formation and dynamics of polarons in a system with a few impurities in a lattice immersed in a Bose-Einstein condensate (BEC). This system has been experimentally realized using ultracold atoms and optical lattices. Here we consider a two-band model for the impurity atoms, along with a Bogoliubov approximation for the BEC, with phonons coupled to impurities via both intra- and inter-band transitions. We decouple this Fr\"ohlich-like term by an extended two-band Lang-Firsov polaron transformation using a variational method. The new effective Hamiltonian with two (polaron) bands differs from the original Hamiltonian by modified coherent transport, polaron energy shifts and induced long-range interaction. A Lindblad master equation approach is used to take into account residual incoherent coupling between polaron and bath. This polaronic treatment yields a renormalized inter-band relaxation rate compared to Fermi's Golden Rule. For a strongly coupled two-band Fr\"ohlich Hamiltonian, the polaron is tightly dressed in each band and can not tunnel between them, leading to an inter-band self-trapping effect.

Dynamics of a One-Dimensional Holstein Polaron with the Hierarchical Equations of Motion Approach.

Dynamics of a one-dimensional Holstein molecular crystal model is investigated by making use of the hierarchical equations of motion (HEOM) introduced by Tanimura and Kubo [J. Phys. Soc. Jpn. 1989, 104, 101]. Our extended, numerically exact HEOM approach is capable of treating exciton-phonon coupling in a nonperturbative manner and is applicable to any temperature. It is revealed that strong exciton phonon coupling leads to excitonic localization, while a large exciton transfer integral facilitates exciton transport. Temperature effects on excitonic scattering have also been examined. A proof of concept, our work also serves as a benchmark for future comparisons with other numerical approaches to Holstein polaron dynamics.

The influence of charge and magnetic order on polaron and acoustic phonon dynamics in LuFe2O4

Femtosecond optical pump-probe spectroscopy is used to reveal the influence of charge and magnetic order on polaron dynamics and coherent acoustic phonon oscillations in single crystals of charge-ordered, ferrimagnetic LuFe2O4. We experimentally observed the influence of magnetic order on polaron dynamics. We also observed a correlation between charge order and the amplitude of the acoustic phonon oscillations, due to photoinduced changes in the lattice constant that originate from the photoexcited electrons. This provides insight into the general behavior of coherent acoustic phonon oscillations in charge-ordered materials.

Polaron dynamics with a multitude of Davydov D2 trial states.

We propose an extension to the Davydov D2 Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D2 Ansatz" is a linear combination of Davydov D2 trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schrödinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D1 and D2 Ansätze. With an increase in the number of the Davydov D2 trial states in the multi-D2 Ansatz, deviation from the exact Schrödinger dynamics is gradually diminished, leading to a numerically exact solution to the Schrödinger equation.

Width Influence on the Polaron Dynamics in Graphene Nanoribbons

Width Influence on the Polaron Dynamics in Graphene Nanoribbons