Higher-order Green's Functions Research Articles

Variation of Transmission Probability Spectrum with the Number of Dots in T-shaped Topology of Quantum Dot System

We analyze the transmission coefficient for T-shaped configuration for quantum dot systems by increasing the number of dots side coupled to the active dot. Analytical expressions for the transmission coefficient have been calculated, in the presence of on-dot Coulomb interaction, using non-equilibrium Green function techniques. The higher-order Green functions containing Coulomb interaction terms have been decoupled using the mean-field approximation. Numerical results show a systematic variation in the transmission peak structure as the number of quantum dots side coupled to the active dot increases. The energy levels of dots available for electron transport have been identified in terms of the internal parameters of quantum dot systems. It is found that the number of transmission probability peaks is directly related to the number of dots in the T-shaped quantum dot system.

Effect of biquadratic exchange and anisotropy on the critical temperature of antiferromagnet

The existence of biquadratic exchange had been well established by Anderson, Huang and Allen. Early investigations indicated that the biquadratic exchange term in spin Hamiltonian was found to have significant effects on the magnetic properties of compounds containing iron-group ions or rare-earth metal ions. Recently, studying the anisotropic magnetic excitation of iron-based superconducting materials indicated that the experimental phenomenon cannot be explained well only by a simple collinear Heisenberg antiferromagnetic model. However, if the nearest neighbor biquadratic spin coupling is introduced, the experiment can be well explained. Similar results had also been obtained in the investigation of the superconducting material FeSe. As a result, exploring the effect of biquadratic exchange interactions on the magnetic properties of magnetic systems is significance. In this paper, we use the double-time Green's function method to study the properties of the spin-1 Heisenberg antiferromagnets with biquadratic exchange interactions and anisotropy on a three-dimensional lattice. We derive the equation of motion of the Green's function by a standard procedure. In the course of this, the higher order Green functions have to be decoupled. For the higher order Green functions of different lattice points, a Tyablikov or random phase approximation decoupling are used to decuple. For the higher order Green functions of the same lattice points, we adopt the Anderson-Callen decoupling to decouple. Based on the above procedures, the analytic expressions of the magnetization and critical temperature are obtained. The effects of biquadratic exchange interactions and anisotropy on the critical temperature are discussed in detailed. Our results show that the critical temperature increases with the increase of the anisotropy for a given biquadratic interaction. Regardless of the value of the anisotropy, the critical temperature always decreases with the increase of the biquadratic interaction. As the value of anisotropic parameter <inline-formula><tex-math id="M1">\begin{document}$\eta = 0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200077_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20200077_M1.png"/></alternatives></inline-formula>, there is an obvious linear relationship between the critical temperature and the biquadratic interaction. However, when the anisotropy of the system becomes weaker, there is no such linear relationship between them. By comparing similar ferromagnetic models, it is found that the results of this paper are significantly different from those of the ferromagnetic model. When the biquadratic interaction is equal to 0, our results agree with other theoretical results.

Low bias negative differential conductance and reversal of current in coupled quantum dots in different topological configurations

Electronic transport through asymmetric parallel coupled quantum dot system hybridized between normal leads has been investigated theoretically in the Coulomb blockade regime by using Non-Equilibrium Green Function formalism. A new decoupling scheme proposed by Rabani and his co-workers has been adopted to close the chain of higher order Green's functions appearing in the equations of motion. For resonant tunneling case; the calculations of current and differential conductance have been presented during transition of coupled quantum dot system from series to symmetric parallel configuration. It has been found that during this transition, increase in current and differential conductance of the system occurs. Furthermore, clear signatures of negative differential conductance and negative current appear in series case, both of which disappear when topology of system is tuned to asymmetric parallel configuration.

Blow-up Solution for $4$-dimensional Generalized Emden-Fowler Equation with Exponential Nonlinearity

Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of generalized Emden-Fowler equation with exponential nonlinearity in fourth-dimensional given by \[ \begin{cases} \Delta (a(x) \Delta u) - V(x) \operatorname{div}(a(x) \nabla u) = \rho^{4} a(x) e^{u} & \textrm{in $\Omega \subset \mathbb{R}^{4}$}, u = \Delta u = 0 & \textrm{on $\partial \Omega$}. \end{cases} \] The leading part $\Delta$ is, usually, called Laplacian operator. The potential $V(x)$ belongs to $L^{\infty}_{\operatorname{loc}}(\mathbb{R}^{4})$ it is smooth and bounded and $a = a(x)$ is a given smooth function over $\overline{\Omega}$, called the Schrodinger wave function. Namely, we are still looking for solutions which concentrate at the points $x^j \in \Omega$, $j = 1,\ldots,m$ as the parameter $\rho$ tends to $0$. We find sufficient conditions under which, as $\rho$ tend to $0$, there exists an explicit class of solutions which admit a concentration behavior with a prescribed bubble profile around some given $m$-points in $\Omega$, for any given integer $m$. These are the so-called singular limits. The candidate $m$-points of concentration must be nondegenerate (in essential way) critical points of a suitable finite dimensional functional explicitly and the higher order Green's function with respect to the imposed boundary conditions.

Green's function approach of an anisotropic Heisenberg ferrimagnetic system

We have investigated the influence of the exchange anisotropy parameter on the magnetization, critical and compensation temperatures and susceptibility of the anisotropic Heisenberg ferrimagnetic system with the single-ion anisotropy under an external magnetic field using the double-time temperature-dependent Green's function theory. In order to decouple the higher order Green's functions, Anderson-Callen's decoupling and random phase approximations have been used. This model is useful for understanding the temperature dependence of total magnetization of Lithium-chromium ferrites Li0.5Fe1.25Cr1.25O4 for which negative magnetization is characteristic. We observe that the critical temperature increases when the exchange anisotropy increases. When the system is under an external magnetic field, one obtains the first-order phase transition where the magnetization jumps for all the values of the exchange anisotropy parameters.

Equation of motion solutions to Hubbard model retaining Kondo effect

We propose a new way of analyzing the Hubbard model using equations of motion (EOM) for the higher-order Green's functions approach within the DMFT scheme. In calculating the higher order Green function we will differentiate over both times (t) and (t′). This allows us to obtain the metallic Fermi liquid at nonzero Coulomb interaction, where the three center DOS structure with two Hubbard bands and the quasiparticle resonance peak is obtained. At small Coulomb interactions and zero temperature the height of the quasiparticle resonance peak on the Fermi energy is constant similarly as in the full DMFT method with numerical (Quantum Monte Carlo) or with analytical (e.g. iterative perturbation theory) calculations.

Green's function study of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system

The magnetic properties of a mixed spin-1 and spin-3/2 Heisenberg ferrimagnetic system on a square lattice are investigated by using the double-time temperature-dependent Green's function technique. In order to decouple the higher order Green's functions, Anderson and Callen's decoupling and random phase approximations have been used. The nearest- and next-nearest-neighbor interactions and the single-ion anisotropies are considered and their effects on compensation and critical temperature are studied.

Dirichlet problem for a generalized inhomogeneous polyharmonic equation in an annular domain

In this article, we investigate the solvability of the Dirichlet problems in ring domains for elliptic linear complex partial differential equations having polyharmonic operators as main parts. First, we give higher order Green functions as fundamental solutions of the homogeneous problems using the iteration of harmonic Green functions for ring domains. Second, we introduce some classes of operators related to Dirichlet problems together with their basic properties. Next, we transform the original problems into equivalent singular integral equations. Finally, solvability of the problems is discussed by defining the adjoint problems and using Fredholm alternative.

MAGNETIZATION AND MAGNON EXCITATION ENERGIES OF THE MAGNETIC SEMICONDUCTOR EuTe

We present analytic expressions for the temperature dependent magnetization and magnon dispersion relation of the antiferromagnetic (AFM) EuTe . This bulk semiconductor represent a concentrated spin system for which the interaction between magnons has to be taken into account. We do this using the renormalized spin wave theory. A higher order Green's function according to Tjablikov is used for their description. As a result, we obtain a modified Bloch-T3/2 law, for low temperatures and high magnetic fields. A full analytic expression is given for the sublattice magnetization of the AFM EuTe (B0 = 0), with a Néel temperature of TN = 9.81 K. In the case of EuTe , the magnon excitation energies exhibit a characteristic maximum. For q = 0, an energy gap Eg occurs in the spin wave spectrum, a consequence of the AFM exchange interaction J2(T). Such energy gaps exist in the spectrum of magnon excitation energies only in systems with AFM interactions.

Pressure induced valence transitions in the Anderson lattice model

Abstract We apply the equation of motion method to the Anderson lattice model, which describes the physical properties of heavy fermion compounds. In particular, we focus here on the variation of the number of f electrons with pressure, associated to the crossover from the Kondo regime to the intermediate valence regime. We treat here the non-magnetic case and introduce an improved approximation, which consists of an alloy analogy based decoupling for the Anderson lattice model. It is implemented by partial incorporation of the spatial correlations contained in higher-order Green's functions involved in the problem that have been formerly neglected. As it has been verified in the framework of the Hubbard model, the alloy analogy avoids the breakdown of sum rules and is more appropriate to explore the asymmetric case of the periodic Anderson Hamiltonian. The densities of states for a simple cubic lattice are calculated for various values of the model parameters V , t , E f , and U .

A spectral function for an interacting electron-lattice system

The lattice quasiparticle conserving Hamiltonian for an interacting electron-lattice system is employed in calculating the electromagnetic spectral response function in absorption for an electron located in a deep trap such that the electronic transition energies are much higher than the cutoff of the lattice vibrational spectrum. The zero-order Hamiltonian for the system is then diagonal in electronic quantum numbers and linear in the lattice vibrational mode coordinates. The spectral response is calculated for a dipole mediated transition by employing the temperature-dependent double-time Green's function technique. It is shown that because of the properties of the lattice field operators, the hierarchy of Green's function equations decouples and no higher-order Green's functions are required for obtaining an explicit solution to a given order. An exact solution for the absorption of spectrum in the lowest order in electromagnetic field is given in terms of delta-function lines. Broadening effects, numerical calculation restrictions and applications to molecular vibronic spectra are briefly discussed.

Application of the Green's function method to an easy-plane Heisenberg model

Many-body Green's function method is a powerful tool for theoretical studies of spin systems. In this formalism, a certain decoupling approximation is generally required to terminate the infinite hierarchy of equations of motion for higher-order Green's functions. The so-called "Tyablikov decoupling" or random-phase approximation (RPA) is a very simple yet effective way to perform this operation. In the present work, this procedure is applied to the study of easy-plane ferromagnets in an in-plane magnetic field. We demonstrate that one should pay careful attention in using the RPA scheme for such a complicated system, which does not have rotational symmetry around the direction of the magnetization. By considering all combinations of the Green's functions, we derive two equations for the magnetization, and point out that the two equations contradict each other if one demands that all operator identities (S2 = S(S + 1), πsr=-s[Sμ – r] = 0; μ = x,y, z) are satisfied in the RPA. Then we discuss the cause of the contradiction and attempt to improve the method in a self consistent way. In our procedure, the effect of the anisotropy can be appropriately taken into account, and the results are in good agreement with the quantum Monte Carlo calculations.

Magnetic order and Kondo effect in the Anderson-lattice model

The Anderson-lattice model has been extensively developed to account for the properties of many anomalous rare-earth compounds and in particular for the competition between the Kondo effect and an antiferromagnetic (AF) phase in a cubic lattice. Here we apply the higher-order decoupling of the equations of motion for the Green Functions (GF) introduced in [H.G. Luo, S.J. Wang, Phys. Rev. B 62 (2000) 1485]. We obtain an improved description of the phase diagram, where the AF phase subsists in a smaller range of the model parameters. As higher-order GF are included in the chain of equations, we are able to calculate directly the local spin–flip correlation function 〈 f ↓ † d ↑ † f ↑ d ↓ 〉 . As a further improvement to the previous approximation of [B.H. Bernhard, C. Aguiar, B. Coqblin, Physica B 378–380 (2006) 712], we obtain a reduced range of existence for the AF phase for the symmetric half-filled case and then we discuss the competition between the AF order and the Kondo effect as a function of the band filling.

The magnetic reorientation transition in thin ferromagnetic films treated by many-body Green's function theory

This contribution describes the reorientation of the magnetization of thin ferromagnetic Heisenberg films as function of the temperature and/or an external field. Working in a rotating frame allows an exact treatment of the single-ion anisotropy when going to higher order Green's functions. Terms due to the exchange interaction are treated by a generalized Tyablicov (RPA) decoupling.

Many-body Green’s function theory of ferromagnetic films with arbitrarily arranged single-ion anisotropies

In the treatment of Heisenberg Hamiltonian containing single-ion anisotropy by means of many-body Green's function method, the decoupling of the anisotropy term in higher order Green's functions usually takes an Anderson-Callen (AC) form. In this paper, possible improvement schemes of AC decoupling are discussed by comparison of the results with those of quantum Monte Carlo and frame rotation methods. We choose one scheme with a factor concerning the effect of the external field. Next, we discuss a possible difficulty of the frame rotation method in treating systems with single-ion anisotropies in more than one direction. Then we extended our method [Phys. Rev. B 70, 134424 (2004)] to treat magnetic films. Some magnetic properties of ultrathin ferromagnetic films with thicknesses up to 16 monolayers are studied. The properties investigated include transition point, effective anisotropy coefficient, field-induced magnetization reorientation, and hysteresis loop. Several cases are investigated for uniaxial anisotropy and external field along different directions. The transition point, the effective anisotropy coefficient, the coercivity, and the loop area increase with increasing film thickness. The coercivity decreases and the loop area reduces with increasing temperature. The hysteresis loop along field direction is different from that along easy-axis direction. The coercivity and the area of the loop obtained in the former case are larger than the latter case. The reasons are analyzed by investigation of the trajectory of magnetization in detail. The influence of dipole interaction on the magnetic properties is discussed.

Direct diagrammatic construction scheme for the inelastic propagator between simply excited states

We develop a direct diagrammatic construction scheme for the inelastic propagator, which describes inelastic scattering processes. Starting from the previously presented 'direct approach' to the inelastic propagator, which involves a higher-order elastic Green's function, we show how one can obtain the inelastic propagator for simple excitations without actually evaluating all the diagrams for the higher-order Green's function. The three cases where either the target molecule itself or its cation or anion is a closed-shell system are discussed. A generalization of the method to obtaining inelastic propagators between higher excitations is briefly addressed.

Extended random phase approximation for layered copper oxides antiferromagnets

The role of interlayer coupling constant on the Neel temperature of layered copper oxides and other magnetic properties have been studied. The theoretical framework is based on anisotropic Heisenberg model and the two sublattice approach. The higher-order Green functions are decoupled using the second random phase approximation. The Green’s function related to the localized spin correlation functions has been exploited. A self consistent expression for the sublattice magnetization and a corrected form for the Neel temperature are obtained. The free-spin-wave results are obtained under a specific approximation. The theoretical results are compared with that of the random phase approximation and existing experimental results.

A completely invariant SUSY transform of supersymmetric QED

We study the SUSY breaking of the covariant gauge-fixing term in SUSY QED and consider its correspondence to a breaking of the Lorentz gauge condition by SUSY. Reasoning by analogy with SUSY's violation of the Wess-Zumino gauge, we argue that the SUSY transformation, already modified to preserve the Wess–Zumino gauge, should be further modified by another gauge transformation which restores the Lorentz gauge condition. We derive this modification and use the resulting transformation to derive a Ward identity relating the photon and photino propagators without using ghost fields. Our transformation also fulfils the SUSY algebra, modulo terms that vanish in the Lorentz gauge. We finish with a discussion of how to circumvent our transform's non-local, non-linear nature when deriving higher-order Green's function Ward identities.

THE FERMIONIC GREEN'S FUNCTION THEORY FOR CALCULATION OF MAGNETIZATION

The fermionic Green's function theory of Heisenberg-like Hamiltonian is presented in this paper. For the case that the Hamiltonian is isotropic and the higher-order Green's function is asymmetrically decoupled, the present theory is equivalent to the bosonic Green's function theory. When the Hamiltonian is anisotropic and the higher-order Green's function is symmetrically decoupled, it gives the universal formula to calculate the three components of statistical average of spin operators which one encountered when dealing with ferromagnetic or ferroelectric systems described by anisotropic Heisenberg model or pseudospin model respectively. Both cases of <Sz> ≠ 0 and <Sz> = 0 are investigated. Explicit expressions are derived for spin value S = 1/2, 1, 3/2, 2, and 5/2. General expressions for any S value are suggested.

Many-body Green's function theory for thin ferromagnetic films: exact treatment of the single-ion anisotropy

A theory for the magnetization of ferromagnetic films is formulated within the framework of many-body Green's function theory which considers all components of the magnetization. The model Hamiltonian includes a Heisenberg term, an external magnetic field, a second- and fourth-order uniaxial single-ion anisotropy, and the magnetic dipole-dipole coupling. The single-ion anisotropy terms can be treated exactlyby introducing higher-order Green's functions and subsequently taking advantage of relations between products of spin operators which leads to an automatic closure of the hierarchy of the equations of motion for the Green's functions with respect to the anisotropy terms. This is an improvement on the method of our previous work, which treated the corresponding terms only approximately by decoupling them at the level of the lowest-order Green's functions. RPA-like approximations are used to decouple the exchange interaction terms in both the low-order and higher-order Green's functions. As a first numerical example we apply the theory to a monolayer for spin S = 1 in order to demonstrate the superiority of the present treatment of the anisotropy terms over the previous approximate decouplings.