Optical sum rule in metals with strong electron-phonon interaction

The properties of a superconductor featuring strong electron-phonon and electron-impurity interactions have been studied in a single-band approximation. It is shown that the elastic scattering of electrons on static impurities decreases the electron-phonon interaction constant in proportion to the ratio of the electron-impurity relaxation rate and the seeding band width. The optical spectral weight (integral of the real part of the optical conductivity) in various energy intervals of a metal in the normal and superconducting states has been calculated as a function of the temperature and the superconducting gap. In the region of large (compared to the phonon) energies, the dependence of the spectral weight on the superconducting gap is weak, while the dependence on the temperature is completely determined by the corresponding dependence of the relaxation rate due to the elastic electron-phonon scattering far from the Fermi surface. It is shown that a difference in behavior of the spectral weight between the normal and superconducting states at lower energies is determined by so-called Holstein’s shift of the feature in the optical conductivity spectrum (rather than by the gap width, as it is commonly believed) and sharply decreases upon the introduction of impurities.     

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.     

Strings in charge-transfer Mott insulators: Effects of lattice vibrations and the Coulomb interaction

Applying the canonical transformation with the 1/λ perturbation expansion in the nonadiabatic and intermediate regime and the discrete generalization of Pekar’s continuous nonlinear equation in the extreme adiabatic regime, we show that there are no strings in narrow-band ionic insulators due to the Fröhlich electron-phonon interaction alone. The multipolaron system is a homogeneous state in a wide range of physically interesting parameters, no matter how strong the correlations are. At the same time, the Fröhlich interaction allows the antiferromagnetic interactions and/or short-range electron-phonon interactions to form short strings in doped antiferromagnetic insulators if the static dielectric constant is large enough.     

Multivariate analysis of single-molecule spectra: surpassing spectral diffusion

The full exploitation of single-molecule spectroscopy in disordered systems is often hampered by spectral diffusion processes of the optical transitions due to structural fluctuations in the local environment of the probe molecule which leads to temporal averaging of the signal. Multivariate statistical pattern recognition techniques, originally developed for single-molecule cryoelectron microscopy, allow us to retrieve detailed information from optical single-molecule spectra. As an example, we present the phonon side band of the B800 excitations of the light-harvesting 2 (LH2) complex from Rhodospirillum molischianum, revealing the electron-phonon coupling strength for these transitions. The measured Debye-Waller factors, ranging from 0.4 to 0.9, fall in the regime of weak electron-phonon coupling.     

Effect of interband interaction on isotope effect exponent of MgB2 superconductors

The exact formula of T_c’s equation and the isotope effect exponent of two-band s-wave superconductors in the weak-coupling limit are derived by considering the influence of interband interaction. In each band, our model consists of two pairing interactions: the electron-phonon interaction and non-electron-phonon interaction. We find that the isotope effect exponent of MgB₂, α = 0.3 with T_c ≈ 40 K can be found in the weak coupling regime and interband interaction of electron-phonon shows more effect on the isotope effect exponent than on the interband interaction of non-phonon.     

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。     

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     

Horizontal rolls in convective flow above a partially heated surface

Considering the nonlinearity arising from the interaction between electrons and lattice vibrations, an effective electronic model with a self-interaction cubic term is employed to study the interplay between electron-electron and electron-phonon interactions. Based on numerical solutions of the time-dependent nonlinear Schroedinger equation for an initially localized two-electron singlet state, we show that the magnitude of the electron-phonon coupling χ necessary to promote the self-trapping of the electronic wave packet decreases as a function of the electron-electron interaction U. We show that such dependence is directly linked to the narrowing of the band of bounded two-electron states as U increases. We obtain the transition line in the χ × U parameter space separating the phases of self-trapped and delocalized electronic wave packets. The present results indicates that nonlinear contributions plays a relevant role in the electronic wave packet dynamics, particularly in the regime of strongly correlated electrons.     

外场对π电子能隙调制C==C，C-C伸缩振动的影响

共振拉曼光谱是研究线性多烯分子的主要分子光谱技术。该技术完美地表征了π电子能隙对C==C,C-C伸缩振动的调制规律。这种调制是通过电子-声子耦合完成的。改变外界环境,能隙调制作用将受到影响。测量了溶剂中β-胡萝卜素分子在温度、压力、溶剂效应、相变等不同环境影响下的吸收光谱、共振拉曼光谱,研究了不同外场对π电子能隙调制C==C,C-C伸缩振动的影响机理及规律。结果表明,在外场影响下,体系的能量降低,π电子能隙(π-π*)减小会使调制增强。即电子-声子耦合增强,使拉曼强度增加,谱线红移。对理解共振拉曼物理过程,认识线性多烯分子的结构,性能有重要意义,对研制优质光电器件也有参考价值。     

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.     

Electron-phonon interaction close to a Mott transition

The effect of Holstein electron-phonon interaction on a Hubbard model close to a Mott-Hubbard transition at half filling is investigated by means of dynamical mean-field theory. We observe a reduction of the effective mass that we interpret in terms of a reduced effective repulsion. When the repulsion is rescaled to take into account this effect, the quasiparticle low-energy features are unaffected by the electron-phonon interaction. Phonon features are only observed within the high-energy Hubbard bands. The lack of electron-phonon fingerprints in the quasiparticle physics can be explained interpreting the quasiparticle motion in terms of rare fast processes.     

Electron-phonon renormalization of the direct band gap of diamond

We calculate from first principles the temperature-dependent renormalization of the direct band gap of diamond arising from electron-phonon interactions. The calculated temperature dependence is in good agreement with spectroscopic ellipsometry measurements, and the zero-point renormalization of the band gap is found to be as large as 0.6 eV. We also calculate the temperature-dependent broadening of the direct absorption edge and find good agreement with experiment. Our work calls for a critical revision of the band structures of other carbon-based materials calculated by neglecting electron-phonon interactions.     

Phonon softening and dispersion in the 1D Holstein model of spinless fermions

We investigate the effect of electron-phonon interaction on the phononic properties in the one-dimensional half-filled Holstein model of spinless fermions. By means of determinantal Quantum Monte Carlo simulation we show that the behavior of the phonon dynamics gives a clear signal of the transition to a charge-ordered phase, and the phase diagram obtained in this way is in excellent agreement with previous DMRG results. By analyzing the phonon propagator we extract the renormalized phonon frequency, and study how it first softens as the transition is approached and then subsequently hardens in the charge-ordered phase. We then show how anharmonic features develop in the phonon propagator, and how the interaction induces a sizable dispersion of the dressed phonon in the non-adiabatic regime.     

Electron-phonon interaction at the Si(111)-7 x 7 surface

It is shown that electron-phonon interaction provides a natural explanation for the unusual band dispersion of the metallic surface states at the Si(111)-(7 x 7) surface. Angle-resolved photoemission reveals a discontinuity of the adatom band at a binding energy close to the dominant surface phonon mode at h(omega0) = 70 meV. This mode has been assigned to adatom vibrations by molecular dynamics calculations. A calculation of the spectral function for electron-phonon interaction with this well-defined Einstein mode matches the data. Two independent determinations of the electron-phonon coupling parameter from the band dispersion and from the temperature-dependent phonon broadening yield similar values of lambda = 1.09 and lambda = 1.06.     

带间耦合相互作用对MgB2超导体同位素效应指数的影响

在弱耦合极限下考虑带间相互作用,得到了二带s-波超导体临界温度Tc的公式及同位素效应指数的公式。在此模型中,耦合相互作用在每一带中包括两部分:电子-声子相互作用和非电子-声子相互作用,当Tc≈40K时,在弱耦合机制中得到MgB2的同位素效应指数αB=0.3,并且带间的电子-声子相互作用比非电子-声子作用对同位素效应指数的影响大。     

Theory of 1f noise in medium and far infrared photodetectors

The present report is denoted to the theory of infrared photodiode low frequency noise based on homogeneous and nondegenerate semiconductors. The results of the theoretical calculation are extended to include photodiodes made of elementary semiconductors, as well as of chalcogenides and solid solutions band structures which are described through a two-band Kane model. The kinetic equations of Boltzmann for the system of electrons and phonons are used to calculate the spectral density noise. In the calculation, only the electron-phonon interactions have been taken into consideration. For low frequency noise spectrum an expression is obtained which is well matched with the experimental formula Hooge.     

Many-body effects on the transport properties of single-molecule devices

The conductance through a molecular device including electron-electron and electron-phonon interactions is calculated using the numerical renormalization group method. At low temperatures and weak electron-phonon coupling the properties of the conductance can be explained in terms of the standard Kondo model with renormalized parameters. At large electron-phonon coupling a charge analog of the Kondo effect takes place that can be mapped into an anisotropic Kondo model. In this regime the molecule is strongly polarized by a gate voltage which leads to rectification in the current-voltage characteristics of the molecular junction.     

Magnetism in the single-band Hubbard model

A self-consistent spectral density approach (SDA) is applied to the Hubbard model to investigate the possibility of spontaneous ferro- and antiferromagnetism. The starting point is a two-pole ansatz for the single-electron spectral density, the free parameter of which can be interpreted as energies and spectral weights of respective quasiparticle excitations. They are determined by fitting exactly calculated spectral moments. The resulting self-energy consists of a local and a non-local part. The higher correlation functions entering the spin-dependent local part can be expressed as functionals of the single-electron spectral density. Under certain conditions for the decisive model parameters (Coulomb interaction U, Bloch bandwidth W, band occupation n, temperature T) the local part of the self-energy gives rise to a spin-dependent band shift, thus allowing for spontaneous band magnetism. As a function of temperature, second-order phase transitions are found away from half-filling, but close to half-filling, the system exhibits a tendency towards first-order transitions. The non-local self-energy part is determined by use of proper two-particle spectral densities. Its main influence concerns a (possibly spin-dependent) narrowing of the quasiparticle bands with the tendency to stabilize magnetic solutions. The non-local self-energy part disappears in the limit of infinite dimensions. We present a full evaluation of the Hubbard model in terms of quasiparticle densities of states, quasiparticle dispersions, magnetic phase diagram, critical temperatures (T_c, T_N) as well as spin and particle correlation functions. Special attention is focused on the non-locality of the electronic self-energy, for which some rigorous limiting cases are worked out.     

The Electronic and Lattice Structures of the Groundand the Polaron States of Polymer Poly (Phenylene Vinylene) (PPV)

The electronic and lattice structures of poly (phenylene vinylene) (PPV) are studied theoretically. Both the electron-electron and electron-phonon interactions are taken into account in the Pariser-Parr-Pople model. The electronic band and the lattice structure of the ground state and the polaronic state are calculated by means of the unrestricted Hartree-Fock method. In the ground state, there exist eight bands in PPV including four valence bands and four conduction bands, and the benzenes can be considered to be rigid. The polaron induces the split of energy bands. There are four localized electronic states within the energy gap. The defect of the polaron appears to extend over about 5 units. The benzenes are strongly affected by the electron-phonon interaction. Our calculation for the energy band structure of the ground and polaron states are consistent with experimental absorption spectra. The results of our calculation show that the electron-phonon and inter-site electron-electron interactions play an important role in determining the electronic and lattice structures.     

The Electronic and Lattice Structures of the Ground and the Polaron States of Polymer Poly (Phenylene Vinylene) (PPV)

The electronic and lattice structures of poly (phenylene vinylene) (PPV) are studied theoretically. Both the electron-electron and electron-phonon interactions are taken into account in the Pariser-Parr-Pople model. The electronic band and the lattice structure of the ground state and the polaronic state are calculated by means of the unrestricted Hartree-Fock method. In the ground state, there exist eight bands in PPV including four valence bands and four conduction bands, and the benzenes can be considered to be rigid. The polaron induces the split of energy bands. There are four localized electronic states within the energy gap. The defect of the polaron appears to extend over about 5 units. The benzenes are strongly affected by the electron-phonon interaction. Our calculation for the energy band structure of the ground and polaron states are consistent with experimental absorption spectra. The results of our calculation show that the electron-phonon and inter-site electron-electron interactions play an important role in determining the electronic and lattice structures.