Dynamics Of Polaron Formation Research Articles

Dynamics of polaron formation in 1D Bose gases in the strong-coupling regime

We discuss the dynamics of the formation of a Bose polaron when an impurity is injected into a weakly interacting one-dimensional Bose condensate. While for small impurity-boson couplings this process can be described within the Froehlich model as generation, emission and binding of Bogoliubov phonons, this is no longer adequate if the coupling becomes strong. To treat this regime we consider a mean-field approach beyond the Froehlich model which accounts for the backaction to the condensate, complemented with Truncated Wigner simulations to include quantum fluctuation. For the stationary polaron we find a periodic energy-momentum relation and non-monotonous relation between impurity velocity and polaron momentum including regions of negative impurity velocity. Studying the polaron formation after turning on the impurity-boson coupling quasi-adiabatically and in a sudden quench, we find a very rich scenario of dynamical regimes. Due to the build-up of an effective mass, the impurity is slowed down even if its initial velocity is below the Landau critical value. For larger initial velocities we find deceleration and even backscattering caused by emission of density waves or grey solitons and subsequent formation of stationary polaron states in different momentum sectors. In order to analyze the effect of quantum fluctuations we consider a trapped condensate to avoid 1D infrared divergencies. Using Truncated Wigner simulations in this case we show under what conditions the influence of quantum fluctuations is small.

Real-time observation of the buildup of polaron in α-FAPbI3

The formation of polaron, i.e., the strong coupling process between the carrier and lattice, is considered to play a crucial role in benefiting the photoelectric performance of hybrid organic-inorganic halide perovskites. However, direct observation of the dynamical formation of polarons occurring at time scales within hundreds of femtoseconds remains a technical challenge. Here, by terahertz emission spectroscopy, we demonstrate the real-time observation of polaron formation process in FAPbI3 films. Two different polaron resonances interpreted with the anharmonic coupling emission model have been studied: P1 at ~1 THz relates to the inorganic sublattice vibration mode and the P2 at ~0.4 THz peak relates to the FA+ cation rotation mode. Moreover, P2 could be further strengthened than P1 by pumping the hot carriers to the higher sub-conduction band. Our observations could open a door for THz emission spectroscopy to be a powerful tool in studying polaron formation dynamics in perovskites.

Controlling polaron formation at hematite surfaces by molecular functionalization probed by XUV reflection-absorption spectroscopy.

Small polaron formation is known to limit the photocatalytic charge transport efficiency of hematite via ultrafast carrier self-trapping. While small polaron formation is known to occur in bulk hematite, a complete description of surface polaron formation in this material is not fully understood. Theoretical predictions indicate that the kinetics and thermodynamics of surface polaron formation are different than those in bulk. However, to test these predictions requires the ability to experimentally differentiate polaron formation dynamics at the surface. Near grazing angle extreme ultraviolet reflection-absorption (XUV-RA) spectroscopy is surface sensitive and provides element and oxidation state specific information on a femtosecond time scale. Using XUV-RA, we provide a systematic comparison between surface and bulk polaron formation kinetics and energetics in photoexcited hematite. We find that the rate of surface polaron formation (250 ± 40 fs) is about three times slower than bulk polaron formation (90 ± 5 fs) in photoexcited hematite. Additionally, we show that the surface polaron formation rate can be systematically tuned by surface molecular functionalization. Within the framework of a Marcus type model, the kinetics and energetics of polaron formation are discussed. The slower polaron formation rate observed at the surface is found to result from a greater lattice reorganization relative to bulk hematite, while surface functionalization is shown to tune both the lattice reorganization as well as the polaron stabilization energies. The ability to tune the kinetics and energetics of polaron formation and hopping by molecular functionalization provides the opportunity to synthetically control electron transport in hematite.

Quantifying Polaron Formation and Charge Carrier Cooling in Lead-Iodide Perovskites.

Notwithstanding the success of lead-halide perovskites in emerging solar energy conversion technologies, many of the fundamental photophysical phenomena in this material remain debated. Here, the initial steps following photogeneration of free charge carriers in lead-iodide perovskites are studied, and timescales of charge carrier cooling and polaron formation, as a function of temperature and charge carrier excess energy, are quantified. It is found, using terahertz time-domain spectroscopy (THz-TDS), that the observed femtosecond rise in the photoconductivity can be described very well using a simple model of sequential charge carrier cooling and polaron formation. For excitation above the bandgap, the carrier cooling time depends on the charge carrier excess energy and lattice temperature, with cooling rates varying between 1 and 6 meV fs-1 , depending on the cation. While carrier cooling depends on the cation, polaron formation occurs within ≈400 fs in CH3 NH3 PbI3 (MAPbI3 ), CH(NH2 )2 PbI3 (FAPbI3 ), and CsPbI3 . Its formation time is independent of temperature between 160 and 295 K. The very similar polaron formation dynamics observed for the three perovskites points to the critical role of the inorganic lattice, rather than the cations, for polaron formation.

Competition Between Hot-Electron Cooling and Large Polaron Screening in CsPbBr3 Perovskite Single Crystals

Lead halide perovskites (LHPs) are solution processable semiconductors characterized by long carrier lifetimes. Recent studies have suggested that electrons and holes in LHPs interact with phonons to form large polarons on subpicosecond time-scales and polaron formation may also slow down hot carrier cooling. Using femtosecond time-resolved two-photon photoemission (TR-2PPE) and transient reflectance (TR) spectroscopies, we follow the initial electron cooling and polaron formation dynamics in single-crystal CsPbBr3 perovskite. We find that the hot electrons cool down initially (≤0.2 ps) with rates of −0.64 ± 0.06 eV/ps and −0.82 ± 0.08 eV/ps at 300 and 80 K, respectively. This weakly temperature-dependent rate is attributed to the initial relaxation of unscreened hot electrons by the emission of longitudinal optical (LO) phonons. On longer time scales, we observe dynamic changes in the photoemission cross-section and in the red-shift of the optical bandgap. We attribute these dynamic changes to large pola...

From two-dimensional electron gas to localized charge: Dynamics of polaron formation in organic semiconductors

Electronic transport in organic semiconductors is mediated by localized polarons. However, the dynamics on how delocalized electrons collapse into polarons through electron-nuclear interaction is not well known. In this work, we use time- and angle-resolved photoemission spectroscopy to study polaron formation in titanyl phthalocyanine deposited on $\mathrm{Au}(111)$ surfaces. Electrons are optically excited from the metal to the organic layer via the image potential state, which evolves from a dispersive to a nondispersive state after photoexcitation. The spatial size of the electrons is determined from the band structure using a tight-binding model. It is observed that the two-dimensional electron wave collapses into a wave packet of size \ensuremath{\sim}3 nm within 100 fs after photoexcitation.

Transmon-based simulator of nonlocal electron-phonon coupling: A platform for observing sharp small-polaron transitions

We propose an analog superconducting quantum simulator for a one-dimensional model featuring momentum-dependent (nonlocal) electron-phonon couplings of Su-Schrieffer-Heeger and "breathing-mode" types. Because its corresponding vertex function depends on both the electron- and phonon quasimomenta, this model does not belong to the realm of validity of the Gerlach-L\"{o}wen theorem that rules out any nonanalyticities in single-particle properties. The superconducting circuit behind the proposed simulator entails an array of transmon qubits and microwave resonators. By applying microwave driving fields to the qubits, a small-polaron Bloch state with an arbitrary quasimomentum can be prepared in this system within times several orders of magnitude shorter than the typical qubit decoherence times. We demonstrate that in this system -- by varying the circuit parameters -- one can readily reach the critical coupling strength required for observing the sharp transition from a nondegenerate (single-particle) ground state corresponding to zero quasimomentum ($K_{\textrm{gs}}=0$) to a twofold-degenerate small-polaron ground state at nonzero quasimomenta $K_{\textrm{gs}}$ and $-K_{\textrm{gs}}$. Through exact numerical diagonalization of our effective Hamiltonian, we show how this nonanalyticity is reflected in the relevant single-particle properties (ground-state energy, quasiparticle residue, average number of phonons). The proposed setup provides an ideal testbed for studying quantum dynamics of polaron formation in systems with strongly momentum-dependent electron-phonon interactions.

Magnetic Polaron Formation Dynamics in Mn2+-Doped Colloidal Nanocrystals up to Room Temperature

Magnetic Polaron Formation Dynamics in Mn2+-Doped Colloidal Nanocrystals up to Room Temperature

Polaron formation dynamics in conducting polymers

In the framework of the extended Su–Schrieffer–Heeger model, the formation mechanism of a polaron is studied by calculating the interaction force between a hot electron and the lattice in a conducting polymer. It is found that the formation of a polaron depends upon the energy of the hot electron. Regardless of whether an electron comes from an injection, doping or a dissociated state of a polaron, it will be trapped by the lattice to form a polaron only when its energy is lower than a critical value. The force field between the lattice and the hot electron with a lower energy has a localized characteristic, which causes polaron formation in a conducting polymer. For a hot electron with much higher energy, the force field is extended over the whole polymer chain, which cannot trap the electron and therefore a polaron does not form in this case.

Jahn–Teller and the Dynamics of Polaron Formation

We discuss a powerful algorithm for calculating static and dynamic properties of electron–phonon coupled systems with dynamic quantum phonons. The difference between Jahn–Teller polarons present in certain transition metal oxides and simpler Holstein polarons is explored. We calculate the dynamics of polaron formation from a bare injected electron, which has been measured in several recent experiments.

Quantum dynamics of polaron formation with the Wigner-function approach

In compound semiconductor crystals with a substantial degree of ionicity Froelich interaction of charge carriers with longitudinal optical (LO) phonons is strong enough to produce detectable polaron effects. In this paper polaron effects are analysed using a quantum theory of electron transport based on the momentum- and frequency-dependent Wigner function fw(p, ω), defined starting from the G< Green function, simply related to the electron spectral function A(p, ω). The theoretical approach considers the dynamical evolution of the electron Wigner function in the presence of phonon scattering. An elaboration of the quantum dynamical equation in terms of Wigner paths formed by free flights and scattering events is used. These paths are especially suitable for a Monte Carlo solution of the transport equation for the Wigner function very similar to the semiclassical traditional Monte Carlo solution of the Boltzmann equation. Numerical results for GaAs and CdTe in a variety of physical conditions are presented.

Quantum dynamics of polaron formation with the Wigner-function approach

In compound semiconductor crystals with a substantial degree of ionicity Froelich interaction of charge carriers with longitudinal optical phonons is strong enough to produce detectable polaron effects. In this paper polaron effects are analyzed using a quantum theory of electron transport based on the momentum and frequency-dependent Wigner function ${f}_{w}(p,\ensuremath{\omega}),$ defined starting from the ${G}^{l}$ Green function, simply related to the electron spectral function $A(p,\ensuremath{\omega}).$ The theoretical approach considers the dynamical evolution of the electron Wigner function in presence of phonon scattering. An elaboration of the quantum dynamical equation in terms of Wigner paths formed by free flights and scattering events is used. These paths are especially suitable for a Monte Carlo solution of the transport equation for the Wigner function very similar to the semiclassical traditional Monte Carlo solution of the Boltzmann equation. Numerical results for GaAs and CdTe in a variety of physical conditions are presented.

STATICS AND DYNAMICS OF COUPLED ELECTRON–PHONON SYSTEMS

We review recent variational methods that provide extremely accurate solutions for the problem of one and two electrons coupled to dynamical, quantum phonons, including retardation effects. The dynamics of these systems far from equilibrium is explored, including the dynamics of polaron formation after electron injection by an STM. An examination of three-point functions suggests a qualitative modification of the traditional picture of a polaron. Long-range electron–phonon interactions are studied in some generality, including vector and frustrated Fröhlich models, and bounds are obtained on the possible mass enhancement.

Magnetic-field-induced formation of exciton magnetic polarons in ZnSe/Zn1-xMnxSe quantum-well structures.

cw and time-resolved photoluminescence spectroscopy is used to study ZnSe/${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se quantum wells with semimagnetic barriers in an external magnetic field. The data demonstrate a change of the dominant energy relaxation mechanism from disorder localization of light-hole excitons at zero-field to heavy-hole exciton interface magnetic polaron formation at intermediate fields and, again, disorder localization of heavy-hole excitons at large magnetic fields. The formation of the interface magnetic polaron is promoted by a magnetic-field-induced type-I--type-II transition for heavy-hole excitons. Despite the transition, neither the exciton lifetime nor its optical oscillator strength is dramatically altered. This is, as we confirm by numerical solution of the two-particle Schr\odinger equation, a result of the electron-hole Coulomb interaction. The polaron formation time is initially 110 ps, but decreases with growing magnetic field down to 70 ps (B=5 T). A theoretical investigation of the polaron formation dynamics shows that the associated change of the exciton wave function is smaller, the closer the ${\mathrm{Mn}}^{2+}$ spin system is driven into saturation by the external field. As a consequence, the polaron formation time approaches the characteristic ${\mathrm{Mn}}^{2+}$ spin response time. Our measurement uncovers a fast primary localization prior to the polaron process---but also of magnetic origin---that we believe to be necessary to start the polaron formation. \textcopyright{} 1996 The American Physical Society.

On the dynamics of polaron formation in a deformable medium

We consider the standard model for exciton transport in which the energy of interaction between the exciton and the lattice is linear in the lattice coordinates and local in the exciton coordinates. We focus on the dynamics of polaron formation by restricting our analysis to the immobile exciton limit in which the model is exactly solvable. We study the evolution of the many-body system from initial states representing a bare exciton in a quiescent bare lattice and a polaron in a quiescent dressed lattice. The total energy, the dynamical energy content of the bare lattice, the deformation of the bare lattice, and many-body Green’s functions are calculated exactly. The reduced density matrix appropriate to each initial condition is obtained exactly for any temperature.