Optical spectra of strong-coupling polarons

The photodissociation spectra of Landau-Pekar polarons are calculated using the theory of quantum coherent states. It is shown that the number of phonons emitted in one dissociation event can differ and that their energy is equal to the doubled polaron binding energy E _p only on the average. It is established that the absorption spectrum is a superposition of bands corresponding to different numbers of phonons emitted during the dissociation of one polaron and that the half-width of each of the bands is much greater than the distance between the bands (which is equal to the phonon energy ?θ). Therefore, the absorption spectrum looks like a very wide unstructured band with the low-frequency edge lying at E _p + ?θ, a maximum at an energy of about 5E _p (for the band carrier mass equal to (1–3)m _e ), and the half-width being of the order of the energy corresponding to the maximum.     

Interface polarons in a realistic heterojunction potential

The ground states of interface polarons in a realistic heterojunction potential are investigated by considering the bulk and the interface optical phonon influence. A self-consistent heterojunction potential is used and an LLP-like method is adopted to obtain the polaron effect. The numerical computation has been done for the Zn_1-xCd_xSe/ZnSe system to obtain the polaron ground state energy, self energy and effective mass parallel to the interface. A simplified coherent potential approximation is developed to obtain the parameters of the ternary mixed crystal and the energy band offset of the heterojunction. It is found that at small Cd concentration the bulk longitudinal optical phonons give the main contribution for lower areal electron densities, whereas the interface phonon contribution is dominant for higher areal electron densities. The interface polaron effect is weaker than the effect obtained by the three dimensional bulk phonon and by the two dimensional interface phonon models. Received 17 September 1998     

Properties of nonadiabatic quantum fluctuations of the strongly coupled electron-phonon systems

A new variational-ansatz of states of electrons and phonons was proposed on the basis of the Holstein model in strongly coupled electron-phonon systems for studying the influence of nonadiabatic phonon fluctuation, arising from the motion and density fluctuation of electrons, on the properties of ground state, uncertainty relation, stability of polarons, charge density wave (CDW) and phonon staggered ordering. The new ansatz represents the correlation among the displacement and squeezing states of phonons and polaron’s state of electrons as well as the squeezing-antisqueezing effect. The correlation and squeezing-antisqueezing effect result in the decrease of ground state energy, enhancement of stability of the systems, increase of binding energy of the polarons, weakening of the growing speed of polaron narrowing of the electron band, increase of the charge density wave order and suppression of the increased tendency of anomalous quantum fluctuation of the phonons in such a case, when compared with the uncorrelated case in the systems. The results obtained show that the ground state determined by the new state ansatz is most stable, thus the new ansatz describing the properties of the coupled electron phonon systems is very relevant and available, especially in strongly coupled and largely squeezed cases. Supported by the National “973” Project of China (Grant No. 2007CB6103)     

一维分子晶体系统的极化子-孤子压缩态、系统基态性质和量子涨落

基于一维分子晶体系统的 Holstein 模型,采用压缩-相干态展开方法,计及电子-声子间量子关联和重整化平移修正,分析和研究电子-双声子相互作用对极化子-孤子系统基态性质和量子涨落的影响.推导了一维极化子-孤子系统的封闭形式非线性方程.应用非线性项展开方法,给出非线性方程的解析解和相关基态特性结果.研究表明,仅当电子-双声子耦合强度 g₁<0时非线性方程才有孤波解,此时声子量子涨落效应随着压缩的增加,极化子-孤子系统基态能量变得更负,孤子局域减少,孤子态更加稳定;另一方面,电子密度涨落〈Δ²n〉和声子坐标-动量的不确定量〈Δ²p〉〈Δ²q〉比无声子压缩效应的大,极化子结合能变得更负.特别是,当g₁<0时,双声子效应的量子涨落〈Δ²n〉与〈Δ²p〉〈Δ²q〉的值比单声子情况有明显增加. 关键词： 压缩-相干态展开 极化子-孤子态与量子涨落 电子-双声子相互作用 非线性薛定谔方程     

Electron correlations and instability of a two-center bipolaron

The energy of a large bipolaron is calculated for various spacings between the centers of the polarization potential wells of the two polarons with allowance made for electron correlations (i.e., the explicit dependence of the wave function of the system on the distance between the electrons) and for permutation symmetry of the two-electron wave function. The lowest singlet and triplet 2³S states of the bipolaron are considered. The singlet polaron is shown to be stable over the range of ionic-bond parameter values η≤η_m≈0.143 (η=?_∞/?₀, where ?_∞ and ?₀ are the high-frequency and static dielectric constants, respectively). There is a single energy minimum, corresponding to the single-center bipolaron configuration (similar to a helium atom). The binding energy of the bipolaron for η → 0 is J_bp=?0.136512e⁴m^*/?²? _∞ ² (e and m* are the charge and effective mass of a band electron), or 25.8% of the double polaron energy. The triplet bipolaron state (similar to an orthohelium atom) is energetically unfavorable in the system at hand. The single-center configuration of the triplet bipolaron corresponds to a sharp maximum in the distance dependence of the total energy J_bp(R); therefore, a transition of the bipolaron to the orthostate (e.g., due to exchange scattering) will lead to decay of the bound two-particle state. The exchange interaction between polarons is antiferromagnetic (AFM) in character. If the conditions for the Wigner crystallization of a polaron gas are met, the AFM exchange interaction between polarons can lead to AFM ordering in the system of polarons.     

Second order resonant Raman scattering at the E1 and E1 + Δ1 edges of germanium

The resonance of the 2TO phonon second order Raman band of germanium was investigated in the vicinity of the E₁, E₁ + Δ₁ gaps. The peak reported earlier for 2TO phonons at Γ is interpreted as due to a resonant process of the iterative type, involving two first order electron-phonon vertices. The rest of the 2TO band is interpreted as a process involving a second order electron-two phonon interaction vertex. From these measurements three phonon coupling constants for the electron-two phonon interaction are obtained.     

Antiresonance of Raman cross-sections for nonpolar phonons in CdS

The nonpolar optic phonons of E₂ symmetry in CdS are shown to exhibit a pronounced decrease in Raman cross-section at certain excitation energies. For the E₂ phonon branch at 43 cm⁻¹ the minimum cross-section occurs for laser excitation ∼0.18 eV below the band gap, and cross-section vs. excitation energy near this antiresonant minimum can be described by an equation of the form used by Ralston et al. for transverse polar phonon cross-sections. For the E₂ mode at 256 cm⁻¹ the antiresonance occurs at wavelengths longer than 6328 Å.     

Influence of the Diagonal and Off-Diagonal Electron–Phonon Interactions on the Formation of Local Polarons and Their Band Structure in Materials with Strong Electron Correlations

For systems with strong electron correlations and strong electron–phonon interaction, we analyze the electron–phonon interaction in local variables. The effects of the mutual influence of electron–electron and electron–phonon interactions that determine the structure of local Hubbard polarons are described. Using a system containing copper–oxygen layers as an example, we consider the competition between the diagonal and off-diagonal interactions of electrons with the breathing mode as the polaron band structure is formed within a corrected formulation of the polaron version of the generalized tight-binding method. The band structure of Hubbard polarons is shown to depend strongly on the temperature due to the excitation of Franck–Condon resonances. For an undoped La₂CuO₄ compound we have described the evolution of the band structure and the spectral function from the hole dispersion in an antiferromagnetic insulator at low temperatures with the valence band maximum at point (π/2, π/2) to the spectrum with the maximum at point (π, π) typical for the paramagnetic phase. The polaron line width at the valence band top and its temperature dependence agree qualitatively with angle-resolved photoemission spectroscopy for undoped cuprates.     

Dipole reorientation from bound-polaron hopping in single crystal NiO

We report observation of a first order thermal depolarization peak at 190 K in NiO single crystals which we attribute to the reorientation of Ni³⁺Ni_V²⁺ dipoles. Analysis of the data in terms of these bound polarons, using a non-adiabatic hopping model, yields values of activation energy, E = 0.31eV and the polaron band width, J = 8.6 × 10^?6 eV.     

Bound polaron in a wurtzite GaN/AlxGa1 − xN ellipsoidal finite-potential quantum dot

A variational method is used to study the ground state of a bound polaron in a weakly oblate wurtzite GaN/Al_xGa_1 − xN ellipsoidal quantum dot. The binding energy of the bound polaron is calculated by taking the electron couples with both branches of LO-like and TO-like phonons due to the anisotropic effect into account. The interaction between impurity and phonons has also been considered to obtain the binding energy of a bound polaron. The results show that the binding energy of bound polaron reaches a peak value as the quantum dot radius increases and then diminishes for the finite potential well. We found that the binding energy of bound polaron is reduced by the phonons effect on the impurity states, the contribution of LO-like phonon to the binding energy is dominant, the anisotropic angle and ellipticity influence on the binding energy are small.     

Cyclotron resonance of polarons in AgBr at high microwave fields

A cyclotron resonance experiment on polarons in pure AgBr has been extended to the microwave field of 3 kV cm^?1 by using a pulsed magnetron at 35 GHz at lattice temperatures of 4.2 and 17 K in magnetic fields up to 58 kOe. It was established that the ground state polaron mass is m¹_p(0)=(0.287±0.003)m_e. From microwave field dependences of the peak position and the width of resonance lines, it was established that the electron polaron follows the streaming motion repetitively emitting LO-phonons in the microwave field region above 80 V cm^?1. Further, it was also suggested that, when streaming, the polaron has an enhanced effective mass of (0.353±0.006)m_e rather than the ground state mass m¹_p(0).     

Dynamical properties of the Peierls-Fröhlich state on the many-phonon-coupling model

The amplitude and phase phonons and the frequency dependent conductivity below the mean-field Peierls-Fröhlich transition temperature T_c, and the Kohn anomaly and fluctuation induced charge-density-wave conductivity above T_c, are discussed on the basis of the many-phonon-coupling model recently introduced by Rice, Duke and Lipari. For dominant intramolecular phonon coupling an isotope effect in T_c is related to the isotopic shift in the small polaron binding energy.     

Intersublevel transitions in self-assembled quantum dots

Intersublevel transitions in semiconductor quantum dots are transitions of a charge carrier between quantum dot confined states. In InAs/GaAs self-assembled quantum dots, optically active intersublevel transitions occur in the mid-infrared spectral range. These transitions can provide a new insight on the physics of semiconductor quantum dots and offer new opportunities to develop mid-infrared devices. A key feature characterizing intersublevel transitions is the coupling of the confined carriers to phonons. We show that the effect of the strong coupling regime for the electron–optical phonon interaction and the formation of mixed electron–phonon quasi-particles called polarons drastically affect and control the dynamical properties of quantum dots. The engineering of quantum dot relaxation rates through phonon coupling opens the route to the realization of new devices like mid-infrared polaron lasers. We finally show that the measurement of intersublevel absorption is not limited to quantum dot ensembles and that the intersublevel ultrasmall absorption of a single quantum dot can be measured with a nanometer scale resolution by using phonon emission as a signature of the absorption. To cite this article: P. Boucaud et al., C. R. Physique 9 (2008).     

Combined polaron states in magnetooptical effects in a quantum well

Combined polaron states in a rectangular quantum well in a strong magnetic field perpendicular to the well plane are discussed. These states are due to interaction between two discrete electron levels with different Landau quantum numbers (n and n ₁) and different size-quantization quantum numbers (m and m ₁) on the one hand and a confined LO phonon on the other under conditions of low temperature when the energy difference between the electronic levelsis equal or close to the energy of the confined LO phonon. The expression for the resonant magnetic field H _res at which a combined polaron is formed contains the energy difference between size-quantized levels, so it is a function of quantum well parameters. The separation ΔE _res between branches in the energy spectrum of a combined polaron and H _res has been calculated as a function of the quantum well width d. The resonant field H _res can be reduced dramatically in comparison with the case m=m ₁. The case of size-quantization with n=n ₁ has been analyzed. The energy difference ΔE _res is in the range (1–5)· 10⁻³ eV. The damping of combined polaron states due to the effect of anharmonicity on the LO phonon has been studied. Interband absorption and features in the reflection spectrum due to interband transitions have been calculated for an arbitrary ratio between the radiative and “phonon” lifetime of a combined polaron have been investigated. Zh. éksp. Teor. Fiz. 116, 1419–1439 (October 1999)     

Strong interaction of correlated electrons with phonons: Exchange of phonon clouds by polarons

The interaction of strongly correlated electrons with phonons in the framework of the Hubbard-Holstein model is investigated. The electron-phonon interaction is considered to be strong and is an important parameter of the model, in addition to the Coulomb repulsion of electrons and the band filling. This interaction with nondispersive optical phonons is transformed to the problem of mobile polarons using the canonical transformation of Lang and Firsov. We discuss the case where the on-site Coulomb repulsion is exactly canceled by the phonon-mediated attractive interaction. It is suggested that polarons exchanging phonon clouds can lead to polaron pairing and superconductivity. The fact that the frequency of the collective mode of phonon clouds is larger than the bare frequency then determines the superconducting transition temperature.     

Excitonic polaron and phonon assisted photoluminescence of ZnO nanowires

The coupling strength of the radiative transition of hexagonal ZnO nanowires to the longitudinal optic (LO) phonon polarization field is deduced from temperature dependent photoluminescence spectra. An excitonic polaron formation is discussed to explain why the interaction of free excitons with LO phonons in ZnO nanowires is much stronger than that of bound excitons with LO phonons. The strong exciton-phonon coupling in ZnO nanowires affects not only the Haung-Ray S factor but also the FXA-1LO phonon energy spacing, which can be explained by the excitonic polaron formation.     

Effects of squeezing-antisqueezing in strongly coupled electron–phonon systems

The effects of squeezing-antisqueezing resulting from the motion and density fluctuation of the electrons on the properties of both electrons and phonons have been studied by using a new variational ansatz with correlated displacement and squeezing in strongly coupled electron–phonon systems. The effects results in (1) reduction of the ground state energy, and enhancement of stability of the systems, (2) increase of the binding energy of the polaron occurred and weakening of growing speed of polaron narrowing of electron band, (3) increase of the charge density wave order and (4) suppression of increased tendency of anomalous quantum fluctuation of the phonons in the systems. The antisqueezed effect plays an important role in determining the properties of the electrons and phonons in the strongly coupled electron–phonon systems.     

Ab initio calculations of the electron-phonon interaction and characteristics of large polarons in rutile and anatase

The calculations of the electron-phonon interaction and some characteristics of excited electrons near the bottom of the conduction band of titanium dioxide in the structure of anatase and rutile have been performed. The Eliashberg function, the imaginary and real parts of the self-energy potential, as well as the band and polaron masses and width of the photoemission line, have been calculated. It has been shown that the electron-phonon interaction is primarily determined by the interaction with optical photons. Moderate values of the polaron mass (<2m _e ) correspond to large polarons. The calculated values of the spectral line width are significantly less than those observed in the experiment. Arguments have been presented in support of the assumption that the main contribution to the spectral line width corresponds to the interaction of electrons with the potential of randomly arranged oxygen vacancies.     

Angular focusing of acoustoelectrically active phonons in ZnO and CdS at 300K

The energy focusing of a uniform angular distribution of quasi-transverse acoustic phonons has been investigated. It is found that the energy enhancement above the average value in certain crystallographic directions depends strongly on the normalized phonon frequency, v/?_m.     

Polaron transport in quasi-1d organic conductors and in some narrow band systems

A detailed review of large and small polaron transport theory in quasi-1d organic conductors and conducting polymers, and in some narrow band systems including superlattices, superionic conductors and superconductors with heavy fermions is presented. The strong-coupling large polaron mobility is evaluated in 1d and 3d crystals taking account of optical phonon dispersion. The current-voltage characteristics (CVC) for a a 1d acoustic polaron with saturation of the drift velocity V₀(E) in strong fields E→∞ near the sound velocity S is found. This effect has been recently observed by Donovan and Wilson in polydiacetylene PDA TS [8]. The small polaron (SP) spectrum in narrow band conductors is investigated and its strong anisotropy in quasi-1d organic conductors is proved. The CVC for SP is calculated and the characteristic maximum with the negative differential conductivity is found. An exact theory of the Gunn effect in these 1d systems is developed and the explicit analytic expressions for a domain structure are obtained. The domain stability is studied and the possibility of their experimental observing is discussed.