Diagrammatic theory for periodic anderson model

Diagrammatic theory for Periodic Anderson Model has been developed, supposing the Coulomb repulsion of f — localized electrons as a main parameter of the theory. f-Electrons are strongly correlated and c-conduction electrons are uncorrelated. Correlation function for f- and mass operator for c-electrons are determined. The Dyson equation for c- and Dyson-type equation for f-electrons are formulated for their propagators. The skeleton diagrams are defined for correlation function and thermodynamic functional. The stationary property of renormalized thermodynamic potential with respect to, the variation of the mass operator is established. The result is appropriate both for the normal and for the superconducting states of the system.     

Superconducting gap anomaly in heavy fermion systems

The heavy fermion system (HFS) is described by the periodic Anderson model (PAM), treating the Coulomb correlation between the f-electrons in the meanfield Hartree-Fock approximation. Superconductivity is introduced by a BCS-type pairing term among the conduction electrons. Within this approximation the equation for the superconducting gap is derived, which depends on the effective position of the energy level of the f-electrons relative to the Fermi level. The latter in turn depends on the occupation probability n ^f of the f-electrons. The gap equation is solved self-consistently with the equation for n ^f; and their temperature dependences are studied for different positions of the bare f-electron energy level, with respect to the Fermi level. The dependence of the superconducting gap on the hybridization leads to a re-entrant behaviour with increasing strength. The induced pairing between the f-electrons and the pairing of mixed conduction and f-electrons due to hybridization are also determined. The temperature dependence of the hybridization parameter, which characterizes the number of electrons with mixed character and represents the number of heavy electrons is studied. This number is shown to be small. The quasi-particle density of states (DOS) shows the existence of a pseudo-gap due to superconductivity and the signature of a hybridization gap at the Fermi level. For the choice of the model parameters, the DOS shows that the HFS is a metal and undergoes a transition to the gap-less superconducting state.      

Anisotropic singlet superconductivity for systems with strongly correlated electrons

The periodic Anderson model extended by pairing interactions amongf- and conduction electrons is investigated in the context of the singlet-like superconductivity. We evaluate the transition temperatureT _c and the ratios of superconducting order parameters atT _c as functions of an effective parameter which describes the correlation off-electrons. The relative stability of thes- andd -superconductivity depends on the values of the Fermi wave vector and on the magnitude of . Due to the absence of on-site pairing forf-electrons, the increase of Coulomb correlations makes thes-like superconductivity more favourable than thed -superconductivity. This behaviour is accompanied by crossover effects: with the increase of Coulomb correlations amongf-electrons the superconductivity is taken over by conduction electrons.Supported by PAN, CPBP 01.12     

Coulomb interaction between conduction electrons andf-electrons in the Anderson impurity model

The influence of the Coulomb interaction between localf-electrons and conduction electrons on the dynamical properties off-electrons is investigated for the Anderson impurity model. An equation-of-motion technique is used to treat simultaneously the Coulomb interaction and the hybridization. We find that the Abricosov-Suhl resonance remains sharp but is reduced in size while the charge excitation peak of thef-electrons is broadened.     

Elusive <Emphasis Type="Italic">s-f</Emphasis> intrasite interactions and double exchange in solids: Ferromagnetic versus nonmagnetic ground state

From the theory of many-electron states in atoms, we know that there exists a strong Coulomb repulsion, which results in the electronic term structure of atoms and is responsible for Hund’s rules. By expanding the Coulomb on-site repulsion into a multipolar series, we derive this interaction and show that it is also present in solids as a correlation effect, which means that the interaction requires a multideterminant version of the Hartree-Fock method. Of particular interest is the case where this interaction couples states of localized (f) and delocalized (s) electrons. We show that the interaction is bilinear in the creation/annihilation operators for localized electrons and bilinear in the operators for conduction electrons. To study the coupling, we consider a simple model in the framework of an effective limited configuration interaction method with one localized f-electron and one itinerant s-electron per crystal site. The on-site multipole interaction between the f- and s-electrons is explicitly taken into account. It is shown that depending on the low-lying excitation spectrum imposed by the crystal electric field, the model can lead not only to ferromagnetism but also to a nonmagnetic state. The model is relevant for solids with localized and itinerant electron states.     

Effect of electron-phonon interaction and temperature dependence of resistivity in some heavy fermion systems

Here we have considered the electron-phonon interaction in the Periodic Anderson Model (PAM) to describe the temperature dependence of resistivity in some heavy fermion (HF) systems. Since the resistivity is related to the imaginary part of the electron self energy, the expression of the same is evaluated from electron Green function by the double time temperature dependant Green function technique of the Zubarev type. In order to understand the effect of electron-phonon interaction in these systems, we couple the phonons to both the f-electrons as well as to the electrons of the hybridization band of both conduction and f-electrons. The influence of various model parameters, namely, the position of 4f level E ₀, the electron-phonon coupling strengths f ₁(q) and f ₂(q), the effecting coupling strength g = N(0)γ ₀²/ω ₀ have been studied on the temperature dependence of resistivity in HF systems. The numerical analysis is performed for q = 0 and for finite temperature in the static limit. The analysis of the results gives satisfactorily in comparison to the experimental observations.     

Zur allgemeinen kinetischen Theorie von partiell ionisierten Plasmen in zeitabhängigen Magnetfeldern und elektromagnetischen Zusatzfeldern

A general method is given for the calculation of the electron distribution function of a weakly ionized plasma in external time-dependent magnetic fields and additional electromagnetic fields. The Boltzmann equation of kinetic theory is solved taking into account elastic collisions between electrons and neutrals. The isotropic part f⁰ of the distribution function follows from a general linear integro-differential equation and contains all known standard distributions (Druyvesteyn, Davydov, Margenau and others) as special cases. The direction-dependent part f¹ gives the transport tensors.     

Allgemeine Berechnung der Elektronenverteilungsfunktion von schwach ionisierten Plasmen in beliebig zeitabhängigen elektromagnetischen Feldern

The behaviour of a weakly ionized plasma in external, arbitrarily time-dependent, electromagnetic fields is treated within the framework of kinetic theory. The Boltzmann kinetic equation is solved using the Lorentz ansatz, taking into account elastic collisions between electrons and neutral particles and assuming that the collision frequency is independent of the electron velocity. The drift velocity of electrons enters into the isotropic part f₀ and into the direction-dependent part f₁ of the electron distribution function. A method is given for the calculation of the drift velocity, which is calculated explicitly for the important but difficult case of a sinusoidal electric field in the presence of a magnetic switching field. f₀ and f₁ are calculated; f₀ is investigated generally. f₀ consists of an expansion in generalized Laguerre polynomials. The influence of the electromagnetic fields on the distribution function and its time variation is discussed and the relaxation behaviour is shown. The following two special cases are calculated explicitly: a linear rising electric field and a sinusoidal electric field, both in the presence of a constant magnetic field.     

On the electrical conductivity for the valence fluctuation model withd-f electron hole attraction

Using the Kubo formula thedc conductivity for the extended Anderson model has been calculated. The model contains the hopping terms for bothf- andd-electrons. The attraction betweenf-holes andd-electrons is also included. The total conductivity consists of 3 terms, all of them are calculated in the small band width approximation. The contributions of these terms to thedc conductivity strongly depend on the model parameters. The increasing of the attraction parameterU _df causes the shift of the conductivity maxima to the lower temperatures.Partly supported by Polish Academy of Science, problem MR I.9     

Bethe-ansatz solution of a model for a mixed valent impurity with two magnetic configurations: II. Numerical solution of the thermodynamic equations

A mixed valence impurity with two magnetic configurations of total angular momentumJ ₂ andJ ₁=J ₂+1/2, respectively, coupled by conduction electrons with total angular momentum 1/2 via a hybridization matrix element is considered. The thermodynamic Bethe-ansatz equations derived previously are solved numerically for various values ofJ ₂. Thef-level occupation, the entropy, the magnetic susceptibility and the specific heat are obtained as a function of temperature for variousf-level positions. The magnetic field dependence is also discussed in the limit of integer valence (exchange model).Supported by the CONICET, Argentina     

Theory of superconductivity in strongly correlated materials: Application to cuprate superconductors

A microscopic theory of superconductivity in systems with strong electron correlations is considered within the Hubbard model. The Dyson equation for the matrix Green function in terms of the Hubbard operators is derived and solved in the noncrossing approximation for the self-energy. Two channels of superconducting pairing are revealed: mediated by antiferromagnetic (AFM) exchange and spin-fluctuations. It is proved that AFM exchange interaction results in pairing of all electrons in the conduction band and high T _c proportional to the Fermi energy. T _c dependence on lattice constants (or pressure) and an oxygen isotope shift of T _c are explained. The text was submitted by the author in English.     

The changes in electronic structure and optical properties of magnetic semiconductors at magnetic phase transitions

The influence of magnetic phase transitions on electronic structure and optical properties of magnetic semiconductors is discussed. Europium chalcogenides and chromium chalcogenide spinels are the main subjects of the investigation. It is shown, that many-body effects are responsible for the changes of optical properties and non-rigid band behavior of electronic structure. Magnetic phase transition leads to energy shift of wide bands and change in density of states of “magnetic” d(f)-electrons without any significant shift of their energies. The influence of fluctuations at T ～ T _c and antiferromagnetic semiconductors are also considered.     

Renormalization of the Lorentz-Abraham-Dirac equation for radiation reaction force in classical electrodynamics

Dirac’s analysis of radiation reaction force in classical electrodynamics suggested that a 4-momentum not collinear with 4-velocity could be introduced for a radiating electron. This would be equivalent to renormalization of the electron mass as an operator relating these 4-vectors. Dirac also pointed to an arbitrary choice made in deriving the Lorentz-Abraham-Dirac (LAD) equation. It was shown that renormalization substantially modifies the LAD equation under the additional requirement that the standard relativistic relation ℰ² = p ² c ² + m ² c ⁴ holds for the renormalized energy and momentum. The renormalized LAD equation is more rigorous than the LAD equation, because the drawbacks of the latter are eliminated, and is simpler than a well-known approximation of the LAD equation. The renormalized LAD equation appears to be better suited for numerical simulations of processes in ultrahigh-intensity laser-pulse fields.     

Formation of heavy quasiparticles and singlet superconductivity in the periodic Anderson model

The periodic Anderson model is investigated by the method of equations of motion for the symmetric case. The narrowing of the central peak in the density of states with an increase of Coulomb correlation energyU is derived and the resulting enhancement of the effective mass is scaled by the hybridization strength asV ^–4. An intersite pairing is allowed forf electrons and a Green function for the superconducting state is calculated. One can conclude that the conduction electron mediatedf-f interaction, which manifests itself as an effective pairing mechanism, supports singlet superconductivity off electrons.Supported by Polish Academy of Sciences, CPBP, 01.12     

The Boltzmann Equation for Driven Systems of Inelastic Soft Spheres

We study a generic class of inelastic soft sphere models with a binary collision rate g^ν that depends on the relative velocity g. This includes previously studied inelastic hard spheres (ν = 1) and inelastic Maxwell molecules (ν = 0). We develop a new asymptotic method for analyzing large deviations from Gaussian behavior for the velocity distribution function f(c). The framework is that of the spatially uniform nonlinear Boltzmann equation and special emphasis is put on the situation where the system is driven by white noise. Depending on the value of exponent ν, three different situations are reported. For ν < −2, the non-equilibrium steady state is a repelling fixed point of the dynamics. For ν > −2, it becomes an attractive fixed point, with velocity distributions f(c) having stretched exponential behavior at large c. The corresponding dominant behavior of f(c) is computed together with sub-leading corrections. In the marginally stable case ν = −2, the high energy tail of f(c) is of power law type and the associated exponents are calculated. Our analytical predictions are confronted with Monte Carlo simulations, with a remarkably good agreement.     

Pressure induced phase transition behaviour in f-electron based dialuminides

The rare-earth and actinide based compounds are endowed with several exotic physical and chemical properties due to the presence of f-electrons. These properties exhibit interesting changes under the action of various thermodynamic fields and hence continues to be a subject of extensive research. For instance, under pressure, the nature of f-electrons can be changed from localized to itinerant, leading to a variety of changes in their structural, physical and chemical properties. The present review on the high pressure phase transition behaviour of dialuminides of rare earths and actinides is an outcome of research in our laboratory during the last five years using a unique combination of a Guinier diffractometer and a diamond anvil cell built in-house. To bring out the correlations between the compressibility and structural behaviour with the electronic structure, we have also carried out electronic structure calculation. Further, the usefulness of Villars’ three parameter structure maps in predicting pressure induced structural transitions has been explored and this has been illustrated with the available phase transition data.     

Experimental Evidence of Parametric Instabilities in an Unmagnetized Plasma Subjected to a Strong H.F. Electric Field

Experimental evidence of parametric excitation, by an intense external H.F. field, of an electron surface mode and an ion wave is presented. The pumping electromagnetic energy density is equal to or slightly larger than the thermal energy density of the electrons. The value of f_pc/f₀ (electron plasma frequency/external field frequency) is that for an electron surface wave. Depending on the pressure and field intensity, this decay instability can lead to three types of low frequency oscillations, with frequencies close to the ion plasma frequency. Two of these are described by Aliev and Silin's intense field theory: one is the volume ion plasma oscillation and the other a surface ion plasma oscillation. The third corresponds to no known ion eigenmode. Several other features of the theory by Aliev and co-workers are also confirmed experimentally, such as the harmonic excitation of the instability (nf₀ ≈ f_pe/√2, where n is an integer), the instability amplitude as a function of f_pe/f₀ (above threshold conditions), the value of the mismatch parameter as a function of field strength and ion mass, and the existence of a fine structure corresponding to the symmetric and antisymmetric electron surface oscillations. Even at high pump field strengths, the decay products are nearly monochromatic i.e. the plasma does not become turbulent.     

Nonlinear ion acoustic waves in dissipative and dispersive magneto-rotating relativistic plasmas with two temperature superthermal electrons

A study has been presented for the nonlinear features of ion-acoustic (IA) shock waves in a magnetorotating plasma consisting of warm viscous streaming ions along with kappa-distributed electrons having two different temperatures. In this regard, we have employed the reductive perturbation technique to derive the Zakharov-Kuznetsov-Burgers (ZKB) equation that governs the dynamics of IA shock waves. The solution obtained by the hyperbolic tangent method has been shown to depend on various plasma parameters such as spectral index (κ_c), density fraction (f), effective rotation frequency (Ω_c), ion kinematic viscosity (η_o), and temperature ratio (σ). In the limiting case when dissipative coefficient D → 0 , we have also examined the solitary potential distributions, which are the solutions of Zakharov Kuznetsov (ZK) equation. It is found that both rarefactive and compressive structures exist for the system under consideration. The transition in the nature of such profiles is due to the enhancement in the density of cold electrons. The importance of present theoretical investigations has been carried out with regard to Saturn's magnetosphere, where two temperature superthermal electron populations have been observed by various satellite missions.