Polaron Theory Research Articles

Anisotropic Electron-Phonon Interactions in 2D Lead-Halide Perovskites.

Two-dimensional (2D) hybrid organic-inorganic metal halide perovskites offer enhanced stability for perovskite-based applications. Their crystal structure's soft and ionic nature gives rise to strong interaction between charge carriers and ionic rearrangements. Here, we investigate the interaction of photogenerated electrons and ionic polarizations in single-crystal 2D perovskite butylammonium lead iodide (BAPI), varying the inorganic lamellae thickness in the 2D single crystals. We determine the directionality of the transition dipole moments (TDMs) of the relevant phonon modes (in the 0.3-3 THz range) by the angle- and polarization-dependent THz transmission measurements. We find a clear anisotropy of the in-plane photoconductivity, with a ∼10% reduction along the axis parallel with the transition dipole moment of the most strongly coupled phonon. Detailed calculations, based on Feynman polaron theory, indicate that the anisotropy originates from directional electron-phonon interactions.

Theory of acoustic polarons in the two-dimensional SSH model applied to the layered superatomic semiconductor Re6Se8Cl2.

Layered superatomic semiconductors, whose building blocks are atomically precise molecular clusters, exhibit interesting electronic and vibrational properties. In recent work [Tulyagankhodjaev et al., Science 382, 438 (2023)], transient reflection microscopy revealed quasi-ballistic exciton dynamics in Re6Se8Cl2, which was attributed to the formation of polarons due to coupling with acoustic phonons. Here, we characterize the electronic, excitonic, and phononic properties with periodic density functional theory. We further parameterize a polaron Hamiltonian with nonlocal (Su-Schrieffer-Heeger) coupling to an acoustic phonon to study the polaron ground state binding energy and dispersion relation with variational wavefunctions. We calculate a polaron binding energy of about 10meV at room temperature, and the maximum group velocity of our polaron dispersion relation is 1.5 km/s, which is similar to the experimentally observed exciton transport velocity.

Theory of excitonic polarons: From models to first-principles calculations

Theory of excitonic polarons: From models to first-principles calculations

Physical and electrical properties of Sm2O3 doped Boro-Zinc-Vanadate glasses

Sm2O3 doped boro-zinc-vanadate glass systems were synthesised by following the melt quenching method. XRD patterns indicated largely non-crystalline nature with few nano-crystallites. Room temperature density was measured. Molar volume and various polaron parameters were estimated. Density and molar volume are found to vary non-linearly with samarium concentration. Conductivity has been measured by two probe technique for temperature range 303K - 573K. High temperature conductivity obeyed the small polaron hopping (SPH) theory. Activation energy for conduction in the temperature regime of small polaron theory is found to vary from 0.249 eV to 0.368 eV non-linearly with Sm2O3 concentration. The conductivity data at low temperature deviated has been looked into using Mott’s VRH model and the density of states at Fermi level were determined. Shimakawa’s multiphonon tunnelling model has also been applied to the low temperature conductivity and found linearity between logarithmic conductivity, ln(σ) and logarithmic temperature ln(T) as predicted by the model. The temperature exponent values obtained from Shimakawa’s model fit are found to be in good agreement with literature. Therefore, it is concluded that at low temperature, carrier multiphonon tunnelling is the charge transport mechanism in the present glasses.

Quantum Dynamics of Attractive and Repulsive Polarons in a Doped MoSe2 Monolayer

When mobile impurities are introduced and coupled to a Fermi sea, new quasiparticles known as Fermi polarons are formed. There are two interesting, yet drastically different regimes of the Fermi polaron problem: (i) the attractive polaron (AP) branch connected to pairing phenomena spanning the crossover from BCS superfluidity to the Bose-Einstein condensation of molecules and (ii) the repulsive branch (RP), which underlies the physics responsible for Stoner’s itinerant ferromagnetism. Here, we study Fermi polarons in two-dimensional systems, where many questions and debates regarding their nature persist. The model system we investigate is a doped MoSe2 monolayer. We find the observed AP-RP energy splitting and the quantum dynamics of attractive polarons agree with the predictions of polaron theory. As the doping density increases, the quantum dephasing of the attractive polarons remains constant, indicative of stable quasiparticles, while the repulsive polaron dephasing rate increases nearly quadratically. The dynamics of Fermi polarons are of critical importance for understanding the pairing and magnetic instabilities that lead to the formation of rich quantum phases found in a wide range of physical systems including nuclei, cold atomic gases, and solids.Received 17 July 2022Revised 12 November 2022Accepted 23 January 2023DOI:https://doi.org/10.1103/PhysRevX.13.011029Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFermionsOptical & microwave phenomenaPolaronsQuantum coherence & coherence measuresPhysical SystemsTransition metal dichalcogenidesTechniquesFour-wave mixingCondensed Matter, Materials & Applied Physics

Polarons in two-dimensional atomic crystals

The polaron is the archetypal example of a quasiparticle emerging from the interaction between fermionic and bosonic fields in quantum field theory. In crystalline solids, polarons are formed when electrons and holes become dressed by the quanta of lattice vibrations. While experimental signatures of polarons in bulk three-dimensional materials abound, only rarely have polarons been observed in two-dimensional atomic crystals. Here, we shed light on this asymmetry by developing a quantitative ab initio theory of polarons in atomically-thin crystals. Using this conceptual framework, we unravel the real-space structure of the recently-observed hole polaron in hexagonal boron nitride, we discover an unexpected critical condition for the existence of polarons in two-dimensional crystals, and we establish the key materials descriptors and the universal laws that underpin polaron physics in two dimensions.

Charge carrier mobilities of organic semiconductors: ab initio simulations with mode-specific treatment of molecular vibrations

The modeling of charge transport in organic semiconductors usually relies on the treatment of molecular vibrations by assuming a certain limiting case for all vibration modes, such as the dynamic limit in polaron theory or the quasi-static limit in transient localization theory. These opposite limits are each suitable for only a subset of modes. Here, we present a model that combines these different approaches. It is based on a separation of the vibrational spectrum and a quantum-mechanical treatment in which the slow modes generate a disorder landscape, while the fast modes generate polaron band narrowing. We apply the combined method to 20 organic crystals, including prototypical acenes, thiophenes, benzothiophenes, and their derivatives. Their mobilities span several orders of magnitude and we find a close agreement to the experimental mobilities. Further analysis reveals clear correlations to simple mobility predictors and a combination of them can be used to identify high-mobility materials.

Correlation between crystal defects and room temperature ferromagnetism of hydrothermally grown Eu substituted ZnO nanorods

The hydrothermal method has been used to grow zinc oxide nanorods on a glass substrate with different Europium (Eu) concentrations. The Eu doping effect on the structural, optical, and magnetic properties of the samples was systematically investigated. The undoped sample exhibited diamagnetic behaviour, while soft room temperature ferromagnetism was observed in all the Eu substituted samples. With regard to the hysteresis loops, the highest coercivity, saturated magnetic moment, and retentive magnetic moment values were observed to be 41.64 Oe, 18.86 × 10−6 emu, and 2.17 × 10−6 emu, respectively, for ZnO:Eu 7%. According to the relationships between the magnetic properties, Eu doping levels, and defects concentrations, it can be concluded that the room temperature ferromagnetism observed in the samples is caused by crystal point defects including oxygen vacancies and zinc interstitials, rather than carrier-mediated exchange interactions, which is also consistent with the bound magnetic polarons theory.

Polaron induced ferromagnetism in ZnO

The odd phenomenon of the ferromagnetic moment of n-type ZnO increasing with temperature has been observed in experiments. We proposed an impurity model accompanying the polaron theory to explain this result because the electron-phonon interaction plays a critical role in inducing ferromagnetism in n-type ZnOs. Thus, we propose that the ferromagnetism of ZnOs comes from the polarons in the impurity states, and the strong Coulomb interaction in these states causes the spin of electrons to split. In addition, the proper hybridization interaction between the conduction band and the impurity states promotes the increase of electron density in the impurity states as well as the ferromagnetism. In contrast, a too strong hybridization interaction will delocalize the electrons in the impurity states to suppress the ferromagnetism. The polarons induce the ferromagnetism by the Coulomb excitation in the impurity states. The electron thermal excitation produces the polarons in the impurity states near the ZnO conduction band edge coupling with the phonon. Based on the model, the ferromagnetism increases with the temperature consistent with the experimental results.

Ab initio self-consistent many-body theory of polarons at all couplings

A self-consistent many-body theory of polarons is presented. This unifies weak- and strong-coupling approaches to the electron-phonon interaction from first principles, opening the door toward a full characterization of polaronic effects in materials at all coupling strengths.

The time-dependent polaron frame

The single-photon emitters in solid-state photonic devices have become crucial for quantum technology implementations. The exciton–phonon interaction degrades the quality of the photons even when the coherent scattering is dominant. Some models describing an emitter’s trajectory in a phonon bath are the weak-coupling master equation and the standard and variational polaron master equations. The polaron theory based on a steady polaron transformation cannot capture the response of the phonon reservoir upon the exciton creation in its transformed Hamiltonian. Here, a time-dependent phonon displacement leads to the time evolution of the phonon-related energies and correlations. Variables as the phonon-induced energy shift and the phonon first-order correlation function converge to the standard polaron theory results. However, the expectation value of the phonon displacement operator differs. According to the time-dependent polaron master equation, the mitigation of the coupling between the single-photon emitter and the coherent driving field by the phonon reservoir evolves to be worse than predicted in the standard polaron theory. • A time-dependent polaron unitary transformation is derived • Time evolution of the exciton–phonon interaction • The path from the weak-coupling Hamiltonian to the polaron Hamiltonian

Polaron in TiO2 from First‐Principles: A Review

AbstractOften the choice of semiconductor material for light‐chemical energy conversion in solar cell technology is TiO2 polymorphs. However, quantum‐mechanical phenomena of electron self‐trapping (polaron) in these polar semiconductors present a challenge to optimize their performance for absorption of solar radiation. The electron trapped in the defect site of the lattice may suppress the recombination of charge carriers and improve the efficiency of light‐chemical energy conversion. Therefore, it is crucial to study polarons in transition metal oxides and semiconductors using first‐principles methods to elucidate the nature of charge carriers and trapping sites for ameliorating the performance of energy conversion. In this work, a comprehensive review is presented using selected literature of polaron studies in TiO2 from first‐principles methods. Overview of the Landau–Pekar model to the recent development of ab initio theory of polaron is presented. The popular DFT+U approach and hybrid functional method are discussed to show the general way of studying polaron using ab initio methods. Introduction of electron‐phonon interaction and the ab initio theory of polaron are briefly presented Therefore, this review presents the development of first‐principles methods from Landau theory to the state‐of‐the‐art to study polarons using TiO2 as the toy model. Finally, conclusions and future perspectives are outlined.

Recombination of Polaronic Electron-Hole Pairs in Hematite Determined by Nuclear Quantum Tunneling.

Here, we investigate the intrinsic nonradiative recombination mechanism in hematite single crystals that decides the photocarrier lifetime under solar illumination. On the basis of the small polaron theory, we propose that the photogenerated electron-hole pair along with its induced lattice deformation in hematite could be treated as a pseudocoordination-complex (PCC) dispersed in a solid medium. We demonstrate that the nonradiative recombination rate at different temperatures determined from the transient absorption spectroscopy can be excellently described by the nonradiative transition theory developed previously for parallels of the PCC model. Our finding suggests that at room temperature the nonradiative recombination in hematite substantially depends on the probability of quantum tunneling of the nuclear configuration.

Sm and Er partial alternatives of Co in Co3O4 nanoparticles: Probing the physical properties

In the attempt of producing multifunctional materials, the Sm3+ and Er3+ partial alternatives of Co in Co3O4 nanoparticles were synthesized via the co-precipitation method with the chemical formula Co3-2xSmxErxO4 (0.00 ≤ x ≤ 0.06). The structural analysis by XRD revealed that x = 0.02 at.% is the maximum solubility of Sm and Er in the Co3O4 matrix, which beyond it there are small traces of the Sm2O3 secondary phase. The size of the nanoparticles, obtained from XRD and TEM, decreased with increasing the co-doping percentages, leading to an increase in the surface area, and hence, benefit the magnetic recording density and electron transport efficiency. Moreover, the co-doping changed the morphology from slightly agglomerated spherical-shaped nanoparticles to the highly agglomerated mixed morphology of welded nanorods and nanokernels. The tetrahedral and octahedral functional groups were revealed by FTIR spectroscopy, declaring the successful formation of Co3O4 spinel structure. The UV–vis spectroscopy showed a monotonic decrease in the absorbance with increased codopants concentration accompanied by a widening of the band gap energy that serves photovoltaic materials, solar cells … The defect concentrations were investigated by photoluminescence spectroscopy that assured the presence of cobalt interstitial as the main defect. The intensity is quenched with x = 0.01 at.%, addressing the heterogeneous photocatalysis, and enhanced to reach its maximum with x = 0.06 at.%, fostering the electrochemical supercapacitors. The concentration of these defects directly influences the magnetic behavior as proposed by the Bound Magnetic Polaron theory. The codopants render the nanoparticles softer magnetic materials due to the decrease in their coercivity and retentivity, which is good for data storage applications and electromagnetic materials.

Influence of reducing heat treatment on the structural and magnetic properties of MnO:ZnO ceramics

Polycrystalline MnO:ZnO bulk ceramics with a Mn proportion of 6, 11, 17 and 22 at% are prepared through a solid-state reaction and subjected to a heat treatment in a reducing atmosphere (Ar (95%) and H2 (5%)). The samples are studied with particular emphasis on their composition and structural and magnetic properties. A detailed microstructural and chemical analysis confirms the Mn doping of the wurtzite ZnO structure mainly at the surface of the ZnO grains. For the samples with higher Mn proportions, the secondary phases ZnMn2O4 and Mn1−xZnxO (Zn-doped MnO) are detected for the as-prepared and heat-treated samples, respectively. The structural change of the secondary phases under heat treatment, from ZnMn2O4 to Mn1−xZnxO, confirms the effectiveness of the heat treatment in reducing the valence of the Mn ions and in the formation of oxygen vacancies into the system. In spite of the induced defects, the magnetic analysis presents only a paramagnetic behavior with an antiferromagnetic coupling between the Mn ions. In the context of the bound magnetic polaron theory, it is concluded that oxygen vacancies are not the necessary defect to promote the desired ferromagnetic order at room temperature.

Dirac Polarons and Resistivity Anomaly in ZrTe_{5} and HfTe_{5}.

Resistivity anomaly, a sharp peak of resistivity at finite temperatures, in the transition-metal pentatellurides ZrTe_{5} and HfTe_{5} was observed four decades ago, and more exotic and anomalous behaviors of electric and thermoelectric transport were revealed in recent years. Here, we present a theory of Dirac polarons, composed by massive Dirac electrons and holes in an encircling cloud of lattice displacements or phonons at finite temperatures. The chemical potential of Dirac polarons sweeps the band gap of the topological band structure by increasing the temperature, leading to the resistivity anomaly. Formation of a nearly neutral state of Dirac polarons accounts for the anomalous behaviors of the electric and thermoelectric resistivity around the peak of resistivity.

Contrasting temperature dependence of the band gap in CH3NH3PbX3 (X=I, Br, Cl) : Insight from lattice dilation and electron-phonon coupling

Although hybrid halide perovskites $(\text{MAPb}{X}_{3},$ $\mathrm{MA}={\mathrm{CH}}_{3}{\mathrm{NH}}_{3} \mathrm{and} X=\mathrm{I}, \mathrm{Br}, \mathrm{Cl})$ have been ubiquitously explored from the photovoltaic perspective, there are still a few unanswered questions which require a more fundamental understanding. One such unsettled issue is the puzzling behavior of the band gap. Unlike conventional semiconductors, $\text{MAPb}{X}_{3}$ $(X=\mathrm{I}, \mathrm{Br})$ is found to show a blueshift (increase) in the band gap $({E}_{g})$ with increasing temperature $(T)$, while ${\mathrm{MAPbCl}}_{3}$ shows an unusual redshift (decrease). In order to understand this, we performed a detailed $T$-dependent study of electronic, optical, and structural properties of $\text{MAPb}{X}_{3}$ combined with the state-of-the-art first-principles calculations. With increasing $T$, two dominant mechanisms which come into play are lattice dilation and electron-phonon coupling (EPC). The former (latter) is responsible for an increase (decrease) in ${E}_{g}$. We found that lattice dilation effect dominates in $\text{MAPb}{X}_{3}$ $(X=\mathrm{I}, \mathrm{Br})$, causing an enhancement in ${E}_{g}$. EPC involves various contributions, of which the interaction of charge carriers with the longitudinal optical phonon mode via Fr\ohlich interaction is the most dominant one at room temperature. We quantify this contribution using Fr\ohlich's theory of large polarons and show that the ${E}_{g}$ correction due to this effect in ${\mathrm{MAPbCl}}_{3}$ is almost double as compared to ${\mathrm{MAPbBr}}_{3}$ and thus explain the reduction in ${E}_{g}$ for the former.

A Quantum Theory of Electron Emission from a Metal–Dielectric Structure in High Electric Fields

A generalized formula for electron emission current as a function of temperature, field, and electron work function in a metal–dielectric system has been derived with regard to the quantum nature of image forces. For free electrons, the Fermi–Dirac distribution and a quantum image potential obtained in terms of the electron polaron theory have been used. The well-known Richardson–Schottky formula (for thermionic emission) and Fowler–Nordheim formula (for field emission) have been derived in the limit of the image force classical potential. It has been shown that at high temperatures and electric fields E ≥ 10 MV/cm, the polaron contribution grows with field and declines with rising temperature. The decrease in emission current is associated with the increase in effective work function of electrons, which is due to the electron polaron effect. Extrapolation formulas suitable for theoretical estimation of thermionic and cold emission currents have been obtained.

A polaron theory of quantum thermal transistor in nonequilibrium three-level systems**Project supported by the National Natural Science Foundation of China (Grant Nos. 11704093 and 11705008) and Beijing Institute of Technology Research Fund Program for Young Scholars, China.

We investigate the quantum thermal transistor effect in nonequilibrium three-level systems by applying the polaron-transformed Redfield equation combined with full counting statistics. The steady state heat currents are obtained via this unified approach over a wide region of system–bath coupling, and can be analytically reduced to the Redfield and nonequilibrium noninteracting blip approximation results in the weak and strong coupling limits, respectively. A giant heat amplification phenomenon emerges in the strong system–bath coupling limit, where transitions mediated by the middle thermal bath are found to be crucial to unravel the underlying mechanism. Moreover, the heat amplification is also exhibited with moderate coupling strength, which can be properly explained within the polaron framework.

Going beyond polaronic theories in describing charge transport in rubrene single crystals

We show that the charge transport properties of single crystals of rubrene can be well described without using polaron theories along the two high-mobility axes. The charge carriers can be considered as holes with coupling to the lattice but not to the degree, which requires the use of polaron theories. It is possible to use the Boltzmann Transport Equation (BTE) in the relaxation time approximation (RTA) to evaluate mobilities due to various scattering mechanisms after introducing a transport reduction factor (PTRF). PTRF takes into account the fraction of charge carriers, which have path lengths that are larger than the lattice constant, and permits the use of the BTE in the RTA even when the magnitude of the overall mobility is lower than the value typically required for the use of the BTE. We are then able to calculate mobilities due to various scattering mechanisms. We calculate the effective electron–phonon coupling constant from the published values for various phonon modes. The values of the effective mass from calculations and measurements reported in the literature vary slightly; we assume an intermediate value for the effective mass. With no fitting parameters needed for calculating temperature-dependent mobilities for trap-free crystals, we are able to get excellent agreement with the measured values along the two high-mobility crystallographic directions. In samples, with some trapping, a small density of exponentially distributed trap states is assumed and gives a very good fit to the measured data. Our work provides strong evidence that it is not necessary to invoke polaronic effects to understand charge transport in rubrene crystals.