Polaron effect and the dc phonon-assisted hopping conductivity in amorphous semiconductors

A new small parameterW of off-diagonal electron-phonon matrix elements with respect to diagonal ones is introduced. Limiting ourselves to terms of the second order inW, the dc phonon assisted hopping conductivity is calculated to the infinite order in the electron-phonon coupling constant. Result clearly exhibits the polaron effect which is discussed in detail.     

Non-adiabatic polaron hopping conduction in CaMn1−xCrxO3 (0?x?0.3)

DC electrical conductivity (σ_dc) of electron-doped antiferromagnetic CaMn_1−xCr_xO₃ (0?x?0.3) has been discussed elaborately in the light of polaron hopping conduction. The increase in Cr doping concentration increases the conductivity and decreases the activation energy. Non-adiabatic polaron hopping conduction is observed in all the manganites at high temperatures. The analysis of σ_dc data shows that small polarons are formed at lower concentrations (?5%) of Cr doping and undoped samples. However, large polarons are materialized at higher doping (?10%) concentrations. This is consistent with the fact that doped Cr³⁺ has larger ionic size compared to that of Mn⁴⁺. Again, strong electron-phonon (e-ph) interaction is perceived in undoped and 5% Cr-doped samples but not in manganites with larger doping concentration. This also confirms the formation of larger polarons with the increase of x. Mott's variable range hopping (VRH) model can elucidate the dc conductivity at very low temperatures. It has been detected that single phonon-assisted hopping is responsible for the dc conduction in the Cr-doped CaMnO₃ manganites.     

Infrared reflectivity of Cox(SiO2)1−x (x∼0.85, 0.55, 0.38) granular films on SiO2 glass substrates

We report the infrared specular reflectivity of Co_x(SiO₂)_1−x (x∼0.85, 0.55, 0.38) films on SiO₂ glass spanning from a metal-like to insulating behavior. While films for x∼0.85 show carrier metallic shielding and hopping conductivity, for x∼0.65 and lower concentrations, the nanoparticles’ number and size promote a localization edge near the highest longitudinal optical frequency. Such an edge is associated with a reflectivity minimum and a higher frequency band connoting strong electron-phonon interactions, carrier phonon assisted hopping, and polaron formation. Optical conductivity fits with current polaron models provide grounds toward a microscopic understanding of transport properties in these as-prepared granular films.     

Universal crossover from band to hopping conduction in molecular organic semiconductors

The charge transport in a variety of herringbone-stacked organic molecular semiconductors is investigated in the temperature range from 10 to 550 K. A crossover from coherent bandlike charge transport with mobilities up to several thousand cm (2)/V s at low temperature to an incoherent hopping motion at high temperatures is observed. This is attributed to the localization of the charge carrier due to increased electron-phonon interaction and, finally, the formation of a lattice polaron.     

掺杂锰氧化物和极化子行为

掺杂锰氧化物属于强关联材料,实验上明确显示出强电-声子耦合对于材料性质(如输运性质和铁磁性质)的影响.极化子是对氧化物材料中载流子行为的近似描述.顺磁状态的掺杂锰氧化物样品电阻率随温度变化关系可以用极化子理论进行很好的描述,并且数据分析还提供了与材料性质有关的微观参数.利用文章作者提出的跃迁极化子交换相互作用与材料铁磁有序温度TC联系的关系式,对掺杂锰氧化物样品磁场下的测量结果进行了数据拟合.非常好的拟合结果说明,跃迁极化子决定交换耦合及铁磁有序的物理图像和数据拟合中使用的近似是合理的.在数据拟合基础上对掺杂锰氧化物和巨磁电阻(CMR)效应的物理图像进行了讨论.     

Formation of polaron clusters

The formation of spherical polaron clusters is studied within the Fröhlich polaron theory. In a dilute polaron gas, using the non-local statistical approach and the polaron pair interaction obtained within the Pekar strong coupling theory, the homogeneous phase results to be unstable toward the appearance of polaron clusters. The physical conditions of formation for the clusters are determined calculating the critical values of electron-phonon interaction for which bound states in the collective polaron potential develop. Finally the sequence in the filling of the states is found and the stability of the clusters is assessed.Received: 6 May 2004, Published online: 12 October 2004PACS: 71.38.-k Polarons and electron-phonon interactions     

Diagrammatic weak-coupling expansion for the magneto-polaron energy

The problem of a Pekar-Fröhlich polaron in a magnetic field is considered for weak electron-phonon interaction. A diagrammatic technique for zero temperature is developed. Previously obtained results for two dimensions are reproduced. For three dimensions the polaron ground-state energy and the longitudinal effective mass are derived in the first orders of the electron-phonon coupling constant for non-zero values of a magnetic field. In a strong magnetic field the bulk polaron is shown to be equivalent to a one-dimensional polaron with a renormalized electron-phonon coupling constant. This leads to exact results in the strong-coupling limit.     

Singlet and triplet bipolarons on the triangular lattice

We study the Coulomb-Fröhlich model on a triangular lattice, looking in particular at states with angular momentum. We examine a simplified model of crab bipolarons with angular momentum by projecting onto the low energy subspace of the Coulomb-Fröhlich model with large phonon frequency. Such a projection is consistent with large long-range electron-phonon coupling and large repulsive Hubbard U. Significant differences are found between the band structure of singlet and triplet states: The triplet state (which has a flat band) is found to be significantly heavier than the singlet state (which has mass similar to the polaron). We test whether the heavier triplet states persist to lower electron-phonon coupling using continuous time quantum Monte Carlo (QMC) simulation. The triplet state is both heavier and larger, demonstrating that the heavier mass is due to quantum interference effects on the motion. We also find that retardation effects reduce the differences between singlet and triplet states, since they reintroduce second order terms in the hopping into the inverse effective mass.     

New Energy Spectra Structure of Polaron in Trans-Polyacetylene

In the weakly coupled electron-phonon systems, the existing theory pointed out that the energy spectra of polaron include four electronic bound states. Our work shows that, due to the non-nearest neighbor hopping interactions, the electron-hole symmetry of the energy band structure implied by SSH model is broken, and the numbers of the bound electronic states are changed. For a negative charged polaron, one new bound state is found near the bottom of conduction band, and the original two bound states below the bottom of the valence band and above the top of the conduction band disappear. For a positive charged polaron, five bound states have been found: one of them is an additional bound state at the top of the conduction band, the others are just the states found in the SSH model. Besides, the energy gap 2Δ is slightly shifted by turning on the long-range hopping interactions.     

Generalized adiabatic polaron hopping: Meyer-Neldel compensation and Poole-Frenkel behavior

The commonly employed adiabatic treatment of polaron hopping is extended to treat the continuous alteration of a carrier wave function with the atoms' movements and a carrier's long-range interaction with a polar surrounding. These features, respectively, introduce carrier-induced softening of the atoms' vibrations and a hopping activation energy that depends on hopping distance. The Meyer-Neldel compensation effect results from carrier-induced softening of vibrations. Poole-Frenkel behavior emerges for electric-field driven polaron hopping in ionic and polar media.     

Mass of a lattice polaron from an extended Holstein model using the Yukawa potential

Renormalization of the mass of an electron is studied within the framework of the Extended Holstein model at strong coupling regime and nonadiabatic limit. In order to take into account an effect of screening of an electron-phonon interaction on a polaron it is assumed that the electron-phonon interaction potential has the Yukawa form and screening of the electron-phonon interaction is due to the presence of other electrons in a lattice. The forces are derived from the Yukawa type electron-phonon interaction potential. It is emphasized that the early considered screened force of (Kornilovitch (1998), Spencer et al. (2005), Hague et al. (2006), Hague and Kornilovitch (2009)) Refs. [7], [18], [19] and [22] is a particular case of the force deduced from the Yukawa potential and is approximately valid at large screening radiuses compared to the distances under consideration. The Extended Holstein polaron with the Yukawa type potential is found to be a more mobile than polaron studied in early works at the same screening regime.     

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.     

Holstein极化子能带和有效质量的温度依赖性

使用正则变换方法,考察了一维Holstein极化子能带和有效质量的温度依赖性。结果表明,对于一定的电子声子耦合强度,Holstein极化子能带宽度随温度升高而变窄,有效质量随温度升高而增大。特别是当电子声子耦合强度足够大时,极化子能带宽度在很小的温度范围内会迅速地变为零,我们认为这种情况实际上是极化子从能带状态向自陷局域态的迅速转变,这与通常的相变现象有点相类似。当电子声子耦合常数越大时,极化子有效质量随温度的升高而增加得越快。很显然,研究电子声子相互作用,对理解固体的光学和输运等性质将有重要的意义。     

Effect of electron-phonon interaction on surface states in a ternary mixed crystal

A variational theory is proposed to study the surface states of electrons in a semi-infinite ternary mixed crystal, by taking the effect of electron-surface optical (SO) phonon interaction into account. The energy and the wave function of the electronic surface-states are calculated. The numerical results of the energies of the surface states of the polarons and the self-trapping energies are obtained as functions of the composition x and surface potential V₀ for several ternary mixed crystal materials. The results show that the electron-phonon interaction lowers the surface-state levels with the energies from several to scores of meV. It is also found that the self-trapping energy of the surface polaron has a minimum at some middle value of the composition x. It is indicated that the electron-phonon coupling effect can not be neglected. Received 4 January 1999 and Received in final form 7 January 2000     

Self-Trapping of Acoustic Polaron in One Dimension

The ground-state energy and effective mass of an acoustic polaron in one dimension are calculated by using an electron-longitudinal-acoustic-phonon interaction Hamiltonian derived here. The self-trapping of the acoustic polaron is discussed. It is found that the critical coupling constant shifts toward weaker electron-phonon interaction with the increasing cutoff wave vector and the products of the critical coupling constant by the cutoff wave vector tend to a certain value. The self-trapping of acoustic polarons in one dimension is easier to be realized than that in three- and two-dimensional systems. The self-trapping transition of acoustic polarons is expected to be observed in the one dimensional systems of alkali halides and wide-band-gap semiconductors.     

On lower bound estimates for the energy spectrum of the Fr?hlich polaron model

Method of intermediate problems was applied to investigation of the energy spectrum of the Fr?hlich polaron model. It was shown that various infinite sequences of non-decreasing improvable lower bound estimates for the low-lying branch of the slow-moving polaron excitation energy spectral curve adjacent to the ground state energy can be derived for arbitrary values of the electron-phonon interaction constant. These bound estimates allow for explicit numerical evaluation at all orders. In conjunction with numerous well-known upper bound estimates for the energy spectral curve of the Fr?hlich polaron as a function of the interaction constant and the polaron total momentum, the aforesaid improvable lower bound estimates might provide one with virtually precise magnitude for the energy of the slow-moving polaron. Possible generalization to the case of the Fr?hlich polaron in external magnetic field is outlined.     

Magnetic transition and polaron crossover in a two-site single polaron model including double exchange interaction

A two-site double exchange model with a single polaron is studied using a perturbation expansion based on the modified Lang-Firsov transformation. The antiferromagnetic to ferromagnetic transition and the crossover from small to large polaron are investigated for different values of the antiferromagnetic interaction (J) between the core spins and the hopping (t) of the itinerant electron. Effect of the external magnetic field on the small to large polaron crossover and on the polaronic kinetic energy are studied. When the magnetic transition and the small to large polaron crossover coincide for some suitable range of J/t, the magnetic field has very pronounced effect on the dynamics of polarons. Received 1 June 2000     

Electron pairing by cooperation of superexchange and polaron effects

This paper proposes a pairing mechanism relevant to high T_c superconductors with strong electron correlations. The Hubbard model is extended to account for a large electron-phonon interaction. It is shown that the band width is much reduced by the polaron effect, but that the superexchange interaction is not reduced. The cooperation of superexchange and polaron effects makes an anisotropic singlet pair a stable bound state, with the largest binding energy in the one-dimensional system.     

非对称量子点中弱耦合极化子的相互作用能

采用改进的线性组合算符和幺正变换方法,研究非对称量子点中弱耦合极化子的性质.导出了非对称量子点中弱耦合极化子的振动频率和相互作用能随量子点的横向和纵向有效受限长度和电子-声子耦合强度的变化关系.数值计算结果表明:非对称量子点中弱耦合极化子的振动频率和相互作用能随量子点的横向和纵向有效受限长度的减小而迅速增大,表现出奇特的量子尺寸效应.     

The phonon effects on the impurity states in cylindrical quantum wire with a finite confining potential

The variational method and the effective mass approximation are applied to calculate the binding energies of the hydrogenic impurity states in a cylindrical quantum wire with finite deep potential well. The phonon effects on the impurity states are considered by taking both the couplings of the electron-phonon and the impurity ion-phonon into account. The numerical results for the GaAs cylindrical quantum wire are given and discussed. It is found that the ion-phonon interaction reduces the impurity binding energy and supplies key contribution to the energy shift, but the electron-phonon coupling enhances the binding energy less. Longitudinal optical (LO) phonons play more important role than interface optical (IO) phonons in the impurity potential screening. The polaron effect caused by LO phonons is more important when the wire is thinner, otherwise the LO phonons are dominant for the thicker wires.