Polaron Formation Process Research Articles

(Invited) Unraveling Electron-Phonon Coupling in 2D Materials in Momentum and Time with Ultrafast Electron Diffuse Scattering (UEDS)

The nature of the couplings within and between lattice and charge degrees of freedom is central to an understanding of electrical and heat transport in materials. These interactions are essential to phenomena as diverse as superconductivity, charge density waves and carrier mobility in semiconductors and metals. Despite their fundamental role, detailed momentum-dependent information on the strength of electron-phonon coupling (EPC) and phonon-phonon coupling (PPC) across the entire Brillouin zone has proved to be very difficult to obtain.I will describe an emerging pump-probe technique, ultrafast electron diffuse scattering (UEDS), that provides such information from the perspective of the phonon system directly. Recent examples of the application of UEDS to layered (2D) materials will be the focus. First, in the thermoelectric material SnSe – a strongly polar semiconductor – we directly observe the phonon dressing processes that yield carrier localization and polaron formation with UEDS. In SnSe these phonon dressing dynamics are profoundly bimodal, with the fast (300 fs) process associated with the formation of a quasi-1D lattice distortion and a relatively large polaron and the slower (4 ps, an order of magnitude slower timescale) process associated with small polaron formation. The observations in SnSe are consistent with electron and hole polarons being different sizes, or the process of polaron formation being instrincially bimodal for both carriers in a manner reminiscent of Lars Onsager’s inverse snowball effect. Second, the extension of UEDS to a MoS2 monolayer heterostructure will be demonstrated. These results reveal substrate dielectric screening of the electron-phonon interaction within the monolayer as well as the monomentum-dependent carrier-phonon equilibration. These results are compared directly against ab-initio simulations of these processes Figure 1

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.

Photoexcitation Dynamics in Electrochemically Charged CdSe Quantum Dots: From Hot Carrier Cooling to Auger Recombination of Negative Trions

Fulfilling the potential of colloidal semiconductor quantum dots (QDs) in electrically driven applications remains a challenge largely since operation of such devices involves charged QDs with drastically different photophysical properties compared to their well-studied neutral counterparts. In this work, the full picture of excited state dynamics in charged CdSe QDs at various time scales has been revealed via transient absorption spectroscopy combined with electrochemistry as a direct manipulation tool to control the negative charging of CdSe QDs. In trions, excited states of single charged QDs, the additional electron in the conduction band speeds up the hot electron cooling by enhanced electron-electron scattering followed by charge redistribution and polaron formation in a picosecond time scale. The trions are finally decayed by the Auger process in a 500 ps time scale. Double charging in QDs, on the other hand, decelerates the polaron formation process while accelerates the following Auger decay. Our work demonstrates the potential of photoelectrochemistry as a platform for ultrafast spectroscopy of charged species and paves the way for further studies to develop comprehensive knowledge of the photophysical processes in charged QDs more than the well-known Auger decay, facilitating their use in future optoelectronic applications. (Less)

First-Principles Study of the Polaron Formation Process in Energy Materials

Polaron formation severely limits the conduction properties of many metal oxides utilized in electrochemical energy storage and conversion applications. Thus, to improve the charge performance of such energy devices, it is essential to understand the fundamental stages of polaron formation. In this work, we utilize the HSE06 hybrid functional to study the initial stage of the polaron formation process in a series of metal oxides. By separating out electronic and lattice energy contribution to the formation of electron polarons, we find that polaron formation barrier heights are directly correlated with an electronic relaxation delay, which is determined by the hybridization of the conduction band minimum. Our results indicate that the formation of polarons may be mitigated by suitably engineering the electronic structure of the material, through a delayed electronic relaxation mechanism. Overall, these results point towards a systematic bottom-up approach for engineering the conductivity and overall electrochemical rate performance of metal oxide energy materials.

From Large to Small Polarons in Lead, Tin, and Mixed Lead-Tin Halide Perovskites.

The origin of the long carrier lifetime in lead halide perovskites is still under debate, and, among different hypotheses, the formation of large polarons preventing the recombination of charge couples is one of the most fascinating. Using state-of-the art ab initio calculations, we report a systematic study of the polaron formation process in metal halide perovskites, focusing on the influence of the chemical composition of the perovskite on the polaron properties. We examine variations in A-site cations (FA, MA, Cs, and Cs-MA), B-site cations (Pb, Sn, and Pb-Sn), and X-site anions (Br, I). Our study confirms that stronger structural distortions occur for Cs than for MA and FA, with the effect of different A-site cations being almost additive. For the same A cation, bromide features stronger distortions than iodide perovskites. The pure Sn phase has an almost double polaron stabilization energy compared with the pure Pb phase. Surprisingly, the trend of polaron stabilization energy is nonmonotonic in mixed Sn-Pb perovskites, with a maximum for small Sn percentages. Polaron formation is found to be promoted by bond asymmetry, ranging from small to large polarons in mixed Sn-Pb perovskites depending on the relative Sn percentage.

Stationary Phonon Squeezing by Optical Polaron Excitation.

We demonstrate that a stationary squeezed phonon state can be prepared by a pulsed optical excitation of a semiconductor quantum well. Unlike previously discussed scenarios for generating squeezed phonons, the corresponding uncertainties become stationary after the excitation and do not oscillate in time. The effect is caused by two-phonon correlations within the excited polaron. We demonstrate by quantum kinetic simulations and by a perturbation analysis that the energetically lowest polaron state comprises two-phonon correlations which, after the pulse, result in an uncertainty of the lattice momentum that is continuously lower than in the ground state of the semiconductor. The simulations show the dynamics of the polaron formation process and the resulting time-dependent lattice uncertainties.

Charge localization in a layer induced by electron-phonon interaction: application to transient polaron formation

We describe electron transfer and localization in a finite two-dimensional transporting layer (15 × 15) using a tight binding Hamiltonian where each site is coupled to phonons. For a narrow electronic band, a polaron is formed with a population that peaks in the middle of the layer and exhibits a concomitant energy lowering. A “local defect” can be simulated by lowering or raising the corresponding site energy. As an example, if we put the defect in one corner, the consequence is that the electron population builds up a polaron which is repelled from this region. The model has been applied to describe the experimentally observed real time polaron formation process in organic layers and in particular in the surface bands of ice-covered metal. We simulate the polaron formation, population distribution and energy relaxation in time. We also investigate the effect of local fluctuations on polaron formation. The formalism can be generalized to excitonic trapping, and has many potential applications.

Dynamics of polaron formation in Li2O2from density functional perturbation theory

Additional electrons injected into lithium peroxide become self-trapped to form polarons. While the final stage of this self-trapping phenomenon has been examined extensively, the electron-phonon interactions that drive this process remain largely unaddressed in the first-principles literature. In order to understand the dynamical process of polaron formation in lithium peroxide, we examine the initial embryonic stage of this process through first-principles calculations of the electron-phonon interaction between the lithium peroxide lattice and an extra electron injected into the crystal. It is shown that the electron-phonon interaction is perceivably strong with such phonons whose vibration patterns map directly onto the lattice distortions that occur when a polaron is actually formed. These patterns indicate the elongation of the bond length of the O${}_{2}^{2\ensuremath{-}}$ ions and contraction of the surrounding Li${}^{+}$ ions.

Polaron formation: Ehrenfest dynamics vs. exact results

We use a one-dimensional tight binding model with an impurity site characterized by electron-vibration coupling, to describe electron transfer and localization at zero temperature, aiming to examine the process of polaron formation in this system. In particular we focus on comparing a semiclassical approach that describes nuclear motion in this many vibronic-states system on the Ehrenfest dynamics level to a numerically exact fully quantum calculation based on the Bonca-Trugman method [J. Bonča and S. A. Trugman, Phys. Rev. Lett. 75, 2566 (1995)]. In both approaches, thermal relaxation in the nuclear subspace is implemented in equivalent approximate ways: In the Ehrenfest calculation the uncoupled (to the electronic subsystem) motion of the classical (harmonic) oscillator is simply damped as would be implied by coupling to a Markovian zero temperature bath. In the quantum calculation, thermal relaxation is implemented by augmenting the Liouville equation for the oscillator density matrix with kinetic terms that account for the same relaxation. In both cases we calculate the probability to trap the electron by forming a polaron and the probability that it escapes to infinity. Comparing these calculations, we find that while both result in similar long time yields for these processes, the Ehrenfest-dynamics based calculation fails to account for the correct time scale for the polaron formation. This failure results, as usual, from the fact that at the early stage of polaron formation the classical nuclear dynamics takes place on an unphysical average potential surface that reflects the distributed electronic population in the system, while the quantum calculation accounts fully for correlations between the electronic and vibrational subsystems.

Exciton magnetic polarons in short-period CdTe/Cd1-xMnxTe superlattices.

The formation of magnetic polarons in short-period semimagnetic CdTe/${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te superlattices is studied by low-temperature cw and time-resolved photoluminescence and compared to the polaron formation in single quantum wells with the equivalent well width and manganese content. The dependence of the polaron energy on the superlattice period, i.e., quantum-well width, is identical to the dependence on well width in the corresponding single quantum wells. This implies that in the superlattice structures the polaron formation process does not lead to a spatial shift of the center of the hole wave function into the semimagnetic barrier. Temperature and magnetic-field-dependent measurements of the polaron energy reveal a more efficient polaron suppression in superlattices than in single quantum wells. This is attributed to the modification of the magnetic properties in the thin semimagnetic barrier layers of the superlattices. The different mechanisms of magnetic-field-induced polaron suppression in Faraday and Voigt geometries are discussed.

Localized exciton magnetic polarons in Cd1-xMnxTe.

Using the method of selective excitation of the exciton luminescence in ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te epilayers we have measured energies of localized magnetic polarons (LMP's) for alloys with manganese mole fractions x\ensuremath{\le}0.34. The suppression of the LMP energy has been studied in external magnetic fields and with temperature increase. Polaron formation times and exciton lifetimes have been measured by time-resolved photoluminescence. We have found that in alloys with x0.17 the polaron formation process is interrupted by exciton recombination and, as a result, the LMP does not reach its equilibrium energy. This dynamical effect on the polaron energy together with the strong sensitivity of the LMP formation to the conditions of primary exciton localization causes the absence of the LMP formation in layers with x0.1. Antiferromagnetic clustering of Mn ions, which leads to the spin-glass phase formation at low temperatures, affects the polaron energy and results in the increasing stability of LMP's against suppression by temperature increase and magnetic fields. In ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Te with xg0.20 a considerable part of the polaron energy is controlled by the input of clusters of antiferromagnetically coupled Mn spins located in the nonuniform molecular field of localized excitons. The comparison of the exciton Zeeman splitting and the LMP magnetic-field suppression provides insight into the internal structure of LMP's.

Polaron formation in the acoustic chain

Exact calculations are presented which detail the process of polaron formation in the one-dimensional acoustic chain. Exact solution is possible because the limit considered is the transportless limit in which the Hamiltonian matrix elements responsible for the motion of an excitation among site states have been set to zero. The polaron formation process is found to be decomposable into two subprocesses having distinct time scales. A disparity of time scales is possible in the case of long wavelength excitations. The consistency of our conclusions is demonstrated through the consensus of results obtained for the discrete acoustic chain, the Debye model, and the elastic continuum.