Critical temperature of metallic hydrogen sulfide at 225-GPa pressure

The Eliashberg theory generalized for electron—phonon systems with a nonconstant density of electron states and with allowance made for the frequency behavior of the electron mass and chemical potential renormalizations is used to study T _c in the SH₃ phase of hydrogen sulfide under pressure. The phonon contribution to the anomalous electron Green’s function is considered. The pairing within the total width of the electron band and not only in a narrow layer near the Fermi surface is taken into account. The frequency and temperature dependences of the complex mass renormalization ReZ(ω), the density of states N(ε) renormalized by the electron—phonon interactions, and the electron—phonon spectral function obtained computationally are used to calculate the anomalous electron Green’s function. A generalized Eliashberg equation with a variable density of electron states has been solved. The frequency dependence of the real and imaginary parts of the order parameter in the SH₃ phase has been obtained. The value of T _c ≈ 177 K in the SH₃ phase of hydrogen sulfide at pressure P = 225 GPa has been determined by solving the system of Eliashberg equations.     

Doping dependent tunneling conductance in SDW ordered copper oxide superconductors

It is observed that doping suppresses the long range anti-ferromagnetic order and induces superconducting phase for a suitable doping. In order to study this effect, we present a model study of the doping dependence of the tunneling conductance in high-T_c systems. The system is described by the Hamiltonian consisting of spin density wave (SDW) and s-wave type superconducting interaction in presence of varying impurity concentrations. The gap equations are calculated by using Green’s functions technique of Zubarev. The gap equations and the chemical potential are solved self-consistently. The imaginary part of the electron Green’s functions shows the quasi-particle density of states which represent the tunneling conductance observed by the scanning tunneling microscopy (STM). We investigate the effect of impurity on the gap equations as well as on the tunneling conductance. The results will be discussed based on the experimental observations.     

A generating functional approach to the Hubbard model

The method of generating functional, suggested for conventional systems by Kadanoff and Baym, is generalized to the case of strongly correlated systems, described by the Hubbard X operators. The method has been applied to the Hubbard model with arbitrary value U of the Coulomb on-site interaction. For the electronic Green’s function constructed for Fermi-like X operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. The Green’s function is characterized by two quantities: the self energy Σ and the terminal part Λ. For them we have derived the equation using variational derivatives, whose iterations generate the perturbation theory near the atomic limit. Corrections for the electronic self-energy Σ are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. This approximation is actually equivalent to the one used in the method of Composite Operators, and it describes an insulator-metal phase transition at half filling reasonably well. The equations for the Bose-like Green’s functions have been derived, describing the collective modes: the magnons and doublons. The main term in this equation represents variational derivatives of the electronic Green’s function with respect to the corresponding fluctuating fields. The properties of the poles of the doublon Green’s functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green’s function has a soft mode at the wave vector Q=(π,π,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering. The generating functional method with the X operators could be extended to the other models of strongly correlated systems.     

Crossing resonance of wave fields in a medium with an inhomogeneous coupling parameter

The dynamic susceptibilities (Green’s functions) of the system of two coupled wave fields of different physical natures in a medium with an arbitrary relation between the mean value ? and rms fluctuation Δ? of the coupling parameter have been examined. The self-consistent approximation involving all diagrams with noncrossing correlation lines has been developed for the case where the initial Green’s function of the homogeneous medium describes the system of coupled wave fields. The analysis has been performed for spin and elastic waves. Expressions have been obtained for the diagonal elements G _mm and G _uu of the matrix Green’s function, which describe spin and elastic waves in the case of magnetic and elastic excitations, and for the off-diagonal elements G _mu and G _um , which describe these waves in the case of cross excitation. Change in the forms of these elements has been numerically studied for the case of one-dimensional inhomogeneities with an increase in Δ? and with a decrease in ? under the condition that the sum of the squares of these quantities is conserved: two peaks in the frequency dependences of imaginary parts of G _mm and G _uu are broadened and then joined into one broad peak; a fine structure appears in the form of narrow resonance at the vertex of the Green’s function of one wave field and narrow antiresonance at the vertex of the Green’s function of the other field; peaks of the fine structure are broadened and then disappear with an increase in the correlation wavenumber of the inhomogeneities of the coupling parameter; and the amplitudes of the off-diagonal elements vanish in the limit ? → 0.     

Development of the self-consistent approximation and its application to the problem of magnetoelastic resonance in an inhomogeneous medium

Our previously proposed approximation involving both the first and second terms of the expansion of the vertex function is generalized to the system of two interacting wavefields of different physical nature. A system of self-consistent equations for the matrix Green’s function and matrix vertex function is derived. On the basis of this matrix generalization of the new self-consistent approximation, a theory of magnetoelastic resonance is developed for a ferromagnetic model, where the magnetoelastic coupling parameter ε(x) is inhomogeneous. Equations for magnetoelastic resonance are analyzed for one-dimensional inhomogeneities of the coupling parameter. The diagonal and off-diagonal elements of the matrix Green’s function of the system of coupled spin and elastic waves are calculated with the change in the ratio between the average value ε and rms fluctuation Δε of the coupling parameter between waves from the homogeneous case (ε ≠ 0, Δε = 0) to the extremely randomized case (ε = 0, Δε ≠ 0) at various correlation wavenumbers of inhomogeneities k _c. For the limiting case of infinite correlation radius (k _c = 0), in addition to approximate expressions, exact analytical expressions corresponding to the summation of all diagrams of elements of the matrix Green’s function are obtained. The results calculated for an arbitrary k _c value in the new self-consistent approximation are compared to the results obtained in the standard self-consistent approximation, where only the first term of the expansion of the vertex function is taken into account. It is shown that the new approximation corrects disadvantages of the Green’s functions calculated in the standard approximation such as the dome shape of resonances and bends on the sides of resonance peaks. The appearance of a fine structure of the spectrum in the form of a narrow resonance on the Green’s function of spin waves and a narrow antiresonance on the Green’s function of elastic waves, which was previously predicted in the standard self-consistent approximation, is confirmed. With an increase in the parameter k _c, the Green’s functions calculated in the standard and new approximations approach each other and almost coincide with each other at k _c/k ≥ 0.5. At the same time, the results of this work indicate that the new self-consistent approximation has a certain advantage for studying the problems of stochastic radiophysics in media with long-wavelength inhomogeneities (small k _c values), because it describes both the shape and width of peaks much better than the standard approximation.     

Microscopic theory of longitudinal sound velocity in CDW and SDW ordered cuprate systems

We address here the self-consistent calculation of the spin density wave and the charge density wave gap parameters for high-T_c cuprates on the basis of the Hubbard model. In order to describe the experimental observations for the velocity of sound, we consider the phonon coupling to the conduction band in the harmonic approximation and then the expression for the temperature dependent velocity of sound is calculated from the real part of the phonon Green’s function. The effects of the electron–phonon coupling, the frequency of the sound wave, the hole doping concentration, the CDW coupling and the SDW coupling parameters on the sound velocity are investigated in the pure CDW phase as well as in the co-existence phase of the CDW and SDW states. The results are discussed to explain the experimental observations.     

Nonmonotonic inelastic tunneling spectra due to surface spin excitations in ferromagnetic junctions

The paper addresses inelastic spin-flip tunneling accompanied by surface spin excitations (magnons) in ferromagnetic junctions. The inelastic tunneling current is proportional to the magnon density of states which is energy-independent for the surface waves and, for this reason, cannot account for the bias-voltage dependence of the observed inelastic tunneling spectra. This paper shows that the bias-voltage dependence of the tunneling spectra can arise from the tunneling matrix elements of the electron-magnon interaction. These matrix elements are derived from the Coulomb exchange interaction using the itinerant-electron model of magnon-assisted tunneling. The results for the inelastic tunneling spectra, based on the nonequilibrium Green’s function calculations, are presented for both parallel and antiparallel magnetizations in the ferromagnetic leads.     

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(ε) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.     

Staggered potential and spin polarization effects on RKKY interaction in armchair graphene nanoribbon

Indirect exchange interaction between two magnetic external atoms, named by Ruderman–Kittle–Kasuya–Yosida (RKKY) interaction, has been presented in the staggered armchair graphene nanoribbon. We have studied RKKY interaction as a function of distance between localized moments. It has been shown that a magnetic ordering along the z-axis mediates an anisotropic interaction which corresponds to a XXZ model interaction between two magnetic moments. The static spin susceptibility components of armchair graphene nanoribbon have been calculated to find exchange interaction between arbitrary components of magnetic moments. We have exploited Green’s function approach in order to calculate spin susceptibility components of electronic gas in nanoribbon structure in the context of tight binding model Hamiltonian. The effects of parameter and ribbon width on the dependence of exchange interaction on distance between moments are investigated. Our results show the spin polarization along perpendicular to the plane leads to anisotropic behavior for exchange interaction between the two magnetic moments. In other words the spatial behavior of RKKY interaction between longitudinal components of magnetic moments is different from that of transverse components.     

Spin current through a tunnel junction

We derive an expression for the spin current through a tunnel barrier in terms of many-body Green’s functions. The spin current has two possible contributions. One is associated with angular momentum transfer due to spin-polarized charge current crossing the junction. If there are magnetic moments on both sides of the tunnel junction, due to spin accumulation or ferromagnetic ordering, then there is a second contribution related to the exchange coupling between the moments.     

Phase fluctuations and single-fermion spectral density in 2d systems with attraction

The effect of static fluctuations in the phase of the order parameter on the normal and superconducting properties of a 2D system with attractive four-fermion interaction is studied. Analytic expressions for the fermion Green’s function, its spectral density, and the density of states are derived in the approximation where the coupling between the spin and charge degrees of freedom is neglected. The resulting single-particle Green’s function clearly demonstrates a non-Fermi-liquid behavior. The results show that as the temperature increases through the 2D critical temperature, the widths of the quasiparticle peaks broaden significantly.     

Path Integral Solution for the Coulomb Potential in a Curved Space of Constant Positive Curvature

A new path integral treatment of a hydrogen-like atom in a uniformly curved space with a constant positive curvature is presented. By converting the radial path integral into a path integral for the modified Pöschl-Teller potential with the help of the space-time transformation technique, the radial Green’s function is expressed in closed form, from which the energy spectrum and the corresponding normalized wave functions of the bound states are extracted. In the limit of vanishing curvature, the Green’s function, the energy spectra and the correctly normalized wave functions of bound and scattering states for a standard hydrogen-like atom are found.     

Spin excitations in granular structures with ferromagnetic nanoparticles

Spin excitations and relaxation in a granular structure which contains metallic ferromagnetic nanoparticles in an insulating amorphous matrix are studied in the framework of the s-d exchange model. As the d system, we consider the granule spins, and the s system is represented by localized electrons in the amorphous matrix. In the one-loop approximation with respect to the s-d exchange interaction for a diagram expansion of the spin Green’s function, the spin excitation spectrum is found, which consists of spin-wave excitations in the granules and of polarized spin excitations. In polarized spin excitations, a change in the granule spin direction is accompanied by an electron transition with a spin flip between two sublevels of a split localized state in the matrix. We considered polarized spin relaxation (relaxation of the granule spins occurring by means of polarized spin excitations) determined by localized deep energy states in the matrix and the thermally activated electronic cloud of the granule. It is found that polarized spin relaxation is efficient over a wide frequency range. Estimates made for structures with cobalt granules showed that this relaxation could be observed in centimetric, millimetric, and submillimetric wavelength ranges.     

Exact solution of the 1D Hubbard model in the atomic limit with inter-site magnetic coupling

In this paper, we present for the first time the exact solution in the narrow-band limit of the 1D extended Hubbard model with nearest-neighbour spin-spin interactions described by an exchange constant J. An external magnetic field h is also taken into account. This result has been obtained in the framework of the Green’s functions formalism, using the composite operator method. By means of this theoretical background, we have studied some relevant features such as double occupancy, magnetization, spin-spin and charge-charge correlation functions and derived a phase diagram for both ferro (J > 0) and anti-ferro (J < 0) coupling in the limit of zero temperature. We also report a study on density of states, specific heat, charge and spin susceptibilities. In the limit of zero temperature, we show that the model exhibits a very rich phase diagram characterized by different magnetic orders and by the coexistence of charge and spin orderings at commensurate filling. Moreover, our analysis at finite temperature of density of states and response functions shows the presence of low-temperature charge and spin excitations near the phase boundaries.     

Exact relations for correlation functions in the general Ising model

The exact relations for the correlation functions in the Ising model are obtained in the simplest form by the Green functions method for the arbitrary spin S and for the arbitrary coordination lattice number P.     

Influence of a narrow conduction band on a Heisenberg spin system

We consider an idealized model, represented by a Heisenberg spin system, which is influenced by a narrow conduction band via ans-d-exchange interaction. By calculating and decoupling the equation of motion of double-time Green's functions by RPA, we derive the magnon dispersion law. The result is a separation of the spectrum into two magnon bands of different shape, similar to the band structure found by Hubbard in his system. We discuss our result by variation of the system parameters, as there are interactions, polarization, temperature, and external field.     

A Wigner-function formulation of finite-state quantum mechanics

For a non-relativistic system with only continous degrees of freedom (no spin, for example), the original Wigner function can be used as an alternative to the density matrix to represent an arbitrary quantum state. Indeed, the quantum mechanics of such systems can be formulated entirely in terms of the Wigner function and other functions on phase space, with no mention of state vectors or operators. In the present paper this Wigner-function formulation is extended to systems having only a finite number of orthogonal states. The “phase space” for such a system is taken to be not continuous but discrete. In the simplest cases it can be pictured as an N×N array of points, where N is the number of orthogonal states. The Wigner function is a real function on this phase space, defined so that its properties are closely analogous to those of the original Wigner function. In this formulation, observables, like states, are represented by real functions on the discrete phase space. The complex numbers still play an important role: they appear in an essential way in the rule for forming composite systems.