Temperature Green Functions Research Articles

Investigation of the electron-acoustic phonon interaction via the deformation and piezoelectric potentials in AlN/GaN resonant tunneling nanostructures

The analytical theory of acoustic phonons arising in the layers of a nitride-based nanostructure, taking into account the presence of the piezoelectric effect, was developed. Proposed theory is based on the first obtained exact solutions of the system consisting of equation of motion for a semiconductor medium and Maxwell equation. The theory of the electronic spectrum renormalized by their interaction with acoustic phonons via deformation and piezoelectric potentials was developed using the method of the temperature Green's function and the Dyson equation. Direct calculations of the electron level shifts and their decay rates are performed for geometric and physical parameters of the new experimentally created nanostructure for various temperature values.

Theoretical investigation of temperature and frequency dependent ferroelectric properties in Rochelle salt (RS) crystal

By adding cubic-order and quartic-order phonon anharmonic interactions terms with spin-spin interactions terms, extra interaction term and external electric field has been considered in two-sublattice pseudospin lattice coupled mode (PLCM) model for phase transitions and dielectric properties of order-disorder Rochelle salt (RS) crystal. Using double-time temperature Green function method, we obtain the expression for Soft mode frequency, dielectric constant and tangent loss have been obtained for Rochelle salt crystal. Numerical calculations will be performed by fitting model values of various parameters in the above expressions for RS crystal. Present theoretical results agree well with experimental results of Sandy and Jones.

ANISOTROPY INFLUENCE ON THE STRIPED ANTIFERROMAGNETISM OF A FRUSTRATED HEISENBERG MODEL: AN APPLICATION TO IRON PNICTIDE MATERIALS

Motivated by several experimental studies of magnetic compounds related to iron pnictides, we examine thermodynamic properties of anisotropic J 1a - J 1b - J c - J 2 Heisenberg antiferromagnetic model. Our calculations are based on the two-time temperature Green's functions within several well-known decoupling approximations. We obtain excitation spectrum, correlation functions and the analytic expression for the critical temperature and compare our results to the existing experimental data. Results presented here could be of a great importance in the further investigations of similar magnetic systems.

Finite Temperature Green's Function Approach for Excited State and Thermodynamic Properties of Cool to Warm Dense Matter.

We present a finite-temperature extension of the retarded cumulant Green's function for calculations of exited-state, correlation, and thermodynamic properties of electronic systems. The method incorporates a cumulant to leading order in the screened Coulomb interaction W, and improves on the GW approximation of many-body perturbation theory. Results for the homogeneous electron gas are presented for a wide range of densities and temperatures, from cool to warm dense matter regimes, which reveal several hitherto unexpected properties. For example, correlation effects remain strong at high T while the exchange-correlation energy becomes small; also the spectral function broadens and damping increases with temperature, blurring the usual quasiparticle picture. These effects are evident, e.g., in Compton scattering which exhibits many-body corrections that persist at normal densities and intermediate T. The approach also yields exchange-correlation energies and potentials in good agreement with existing methods.

Study of temperature Green's functions of graphene-like systems in a half-space

Для исследования электронных свойств полубесконечной двумерной решетки графена при заданной температуре рассмотрен формализм температурных функций Грина. При наиболее общих предположениях об устройстве границы графена вычислен пропагатор соответствующей диаграммной техники. Полученный пропагатор выдерживает предельные переходы между физически различными состояниями границы системы - аценовым краем и граничным условием в приближении "бесконечной массы", а также корректно описывает задачу, в которой электрон-дырочная симметрия нарушена вследствие наличия внешнего потенциала, приложенного к границе графена. Использование пропагатора, его аналитические свойства и особенности вычислений с ним проиллюстрированы на примере расчета зависимости электронной плотности от расстояния до границы системы.

Electric transport in three-dimensional skyrmion/monopole crystal

We study theoretically the transport properties of a three-dimensional spin texture made from three orthogonal helices, which is essentially a lattice of monopole-antimonopole pairs connected by Skyrmion strings. This spin structure is proposed for MnGe based on the neutron scattering experiment as well as the Lorentz transmission electron microscopy observation. Equipped with a sophisticated spectral analysis method, we adopt finite temperature Green's function technique to calculate the longitudinal dc electric transport in such system. We consider conduction electrons interacting with spin waves of the topologically nontrivial spin texture, wherein fluctuations of monopolar emergent magnetic field enter. We study in detail the behavior of electric resistivity under the influence of temperature, external magnetic field and a characteristic monopole motion, especially a novel magnetoresistivity effect describing the latest experimental observations in MnGe, wherein a topological phase transition signifying strong correlation is identified.

ANISOTROPY INFLUENCE ON THE STRIPED ANTIFERROMAGNETISM OF A FRUSTRATED HEISENBERG MODEL: AN APPLICATION TO IRON PNICTIDE MATERIALS

Motivated by several experimental studies of magnetic compounds related to iron pnictides, we examine thermodynamic properties of anisotropic J1a - J1b - Jc - J2 Heisenberg antiferromagnetic model. Our calculations are based on the two-time temperature Green's functions within several well-known decoupling approximations. We obtain excitation spectrum, correlation functions and the analytic expression for the critical temperature and compare our results to the existing experimental data. Results presented here could be of a great importance in the further investigations of similar magnetic systems.

Efficient Temperature-Dependent Green's Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green's Functions.

The popular, stable, robust, and computationally inexpensive cubic spline interpolation algorithm is adopted and used for finite temperature Green's function calculations of realistic systems. We demonstrate that with appropriate modifications the temperature dependence can be preserved while the Green's function grid size can be reduced by about 2 orders of magnitude by replacing the standard Matsubara frequency grid with a sparser grid and a set of interpolation coefficients. We benchmarked the accuracy of our algorithm as a function of a single parameter sensitive to the shape of the Green's function. Through numerous examples, we confirmed that our algorithm can be utilized in a systematically improvable, controlled, and black-box manner and highly accurate one- and two-body energies and one-particle density matrices can be obtained using only around 5% of the original grid points. Additionally, we established that to improve accuracy by an order of magnitude, the number of grid points needs to be doubled, whereas for the Matsubara frequency grid, an order of magnitude more grid points must be used. This suggests that realistic calculations with large basis sets that were previously out of reach because they required enormous grid sizes may now become feasible.

Theory of Green functions of free Dirac fermions in graphene

This work is the beginning of our research on graphene quantum electrodynamics (GQED), based on the application of the methods of traditional quantum field theory to the study of the interacting system of quantized electromagnetic field and Dirac fermions in single-layer graphene. After a brief review of the known results concerning the lattice and electronic structures of single-layer graphene we perform the construction of the quantum fields of free Dirac fermions and the establishment of the corresponding Heisenberg quantum equations of these fields. We then elaborate the theory of Green functions of Dirac fermions in a free Dirac fermion gas at vanishing absolute temperature T = 0, the theory of Matsubara temperature Green functions and the Keldysh theory of non-equilibrium Green functions.

Spin and dispersion of a massive Dirac neutrino in a magnetized plasma

The total energy shift of a polarized massive Dirac neutrino in an electron–positron plasma in a constant magnetic field is investigated. The calculation in the Feynman gauge is performed for the first time by using the Matsubara temperature Green functions. The dependence of the dispersion relation and the anomalous magnetic moment of the neutrino on the magnetic field strength, spin, energy, direction of motion, neutrino mass, and the plasma parameters is analyzed. The results of investigations for the massive neutrino in the limiting case are compared with those obtained earlier by other authors for the massless left neutrino.

Modified Heisenberg model for the zig-zag structure in multiferroic RMn2O5

The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn4+ and Mn3+ magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.

Electron self-energy and generalized Drude formula for infrared conductivity of metals

Goetze and Woelfle (GW) wrote the conductivity in terms of a memory function M as (ine2/m)/(omega+M(omega)), where M=i/tau in the Drude limit. The analytic properties of -M are the same as those of the self-energy of a retarded Green's function. In the approximate treatment of GW, -M closely resembles a self-energy, with differences, e.g., the imaginary part is twice too large. The correct relation between -M and the self-energy is known for the electron-phonon case and is conjectured to be similar for other perturbations. When vertex corrections are ignored there is a known relation. A derivation using Matsubara temperature Green's functions is given.

Josephson current in Fe-based superconducting junctions: Theory and experiment

We present theory of dc Josephson effect in contacts between Fe-based and spin-singlet $s$-wave superconductors. The method is based on the calculation of temperature Green's function in the junction within the tight-binding model. We calculate the phase dependencies of the Josephson current for different orientations of the junction relative to the crystallographic axes of Fe-based superconductor. Further, we consider the dependence of the Josephson current on the thickness of an insulating layer and on temperature. Experimental data for PbIn/Ba$_{1-x}$K$_{x}$(FeAs)$_2$ point-contact Josephson junctions are consistent with theoretical predictions for $s_{\pm}$ symmetry of an order parameter in this material. The proposed method can be further applied to calculations of the dc Josephson current in contacts with other new unconventional multiorbital superconductors, such as $Sr_2RuO_4$ and superconducting topological insulator $Cu_xBi_2Se_3$.

Peierls Structural Transition in Q1D Crystals of TTF-TCNQ Type for Different Values of Carrier Concentration

The Peierls structural transition is studied in quasi-one-dimensional (Q1D) organic crystals of the tetrathiofulvalene-tetracyanoquinodimethane (TTF-TCNQ) type in a more complete 2D physical model. Unlike the previous investigations, two electron-phonon interactions are considered: one is of the deformation potential type and the other is similar to that of polaron. The method of temperature Green functions is applied and the analytic expression for the polarization operator is obtained in the random phase approximation. The polarization operator as a function of temperature is calculated numerically for different values of the ratio d of the transfer energy in the direction transversal to conductive chains to the transfer energy along the conductive chains. The Peierls critical temperature Tp is determined for different values of the parameter d in two cases: 1) when the dimensionless Fermi momentum is kF = 0.59π/2, and 2) when the Fermi momentum is kF = 0.59π/2 ± δ, where δ represents the variation of the Fermi momentum, determined by the increase or by the decrease of carrier concentration. It is found that in the first case the Tp strongly decreases with the increase of the parameter d and for a certain value of the parameter d the Peierls transition does not take place on the whole. In the second case, the Tp with the increase of carrier concentration n also decreases and for some value of n the transition disappears too. But with the decrease of carrier concentration the Tp strongly increases. In both these cases the physical interpretations of such behavior of the Peierls transition are presented and discussed.

INTERNAL ENERGY OF HEISENBERG SPIN-1/2 J1 - J2 ANTIFERROMAGNET ON THE BODY-CENTERED-CUBIC LATTICE IN TYABLIKOV APPROXIMATION

Magnetic properties of spin ½ J 1 - J 2 quantum Heisenberg antiferromagnet on body centered cubic lattice are investigated in the paper. By using two-time temperature Green's functions, sublattice magnetization and critical temperature depending on the frustration ratio J 2 / J 1 are obtained in both stripe and Neel phase. The analysis of ground state sublattice magnetization and internal energy indicates the first order phase transition from Neel to stripe phase for 0.7< J 2 / J 1 < 0.8, which is in agreement with previous studies.

Dynamics of Fluctuactions in the BCS-BEC Crossover in Superfluid Fermi Gases

The BCS-BEC crossover phenomenon in a 3D attractive Fermi gas is revisited by using finite temperature Green functions formalism derived from the quantum path integral technique and Mean Field Approximation (MFA). Collective modes for weak and strong coupling particle-particle interaction g are obtained after recovering the dynamical coefficients in the nonlinear Time Dependent Ginzburg Landau (TDGL) equation, and numerically simulated under those particular states for the filling energy g ~ 0 and order parameter Δ(x,τ) ~ Δ0. Explicit formulas for the first order average fluctuations ⟨η2q,ω⟩ and the scaling law for the thermal energy associated to the non-linear collective modes are also reported.

INTERNAL ENERGY OF HEISENBERG SPIN-1/2 J1 - J2 ANTIFERROMAGNET ON THE BODY-CENTERED-CUBIC LATTICE IN TYABLIKOV APPROXIMATION

Magnetic properties of spin ½ J1-J2 quantum Heisenberg antiferromagnet on body centered cubic lattice are investigated in the paper. By using two-time temperature Green's functions, sublattice magnetization and critical temperature depending on the frustration ratio J2/ J1 are obtained in both stripe and Neel phase. The analysis of ground state sublattice magnetization and internal energy indicates the first order phase transition from Neel to stripe phase for 0.7 J2/ J1 0.8, which is in agreement with previous studies.

Microscopic theory for phase-sensitive experiments to determine the symmetry of the order parameter in Fe-based superconductors

We present a microscopic theory for the dc Josephson current, based on the construction of a coherent temperature Green's function in the tight-binding approximation, in junctions with multiband superconductors. This theory is applied to junctions with a multiband Fe-based superconductor (FeBS) described by -wave and -wave order parameter symmetries, which is probably realized in FeBS. For the first time, phase dependences of the Josephson current have been calculated for different directions of an interface with respect to crystallographic axes of FeBS. The present approach is also suitable for a consistent description of the Josephson transport in structures with topological superconductors.

Bose-Einstein condensation beyond perturbation theory: Goldstone singularities and instanton solution

Temperature Green functions are applied to the analysis of Bose-condensation of weakly interacting gas. The character of Goldstone singularities of correlation functions is established to all orders in perturbation theory. These singularities are regularized by the system volume. An anomalous volume dependence of the correlation functions is revealed. Quantum-field perturbation series are studied in the framework of the instanton approach. It is shown that there are no time-dependent instantons and that the time-independent instanton solutions exhibit factorial growth in large orders of the quantum-field perturbation expansion.

Phase diagram of [formula omitted] quantum Heisenberg [formula omitted] antiferromagnet on the body-centered-cubic lattice in random phase approximation

Magnetic properties of spin 12J1–J2 Heisenberg antiferromagnet on the body centered cubic lattice are investigated. By using two-time temperature Green's functions, sublattice magnetization and critical temperature depending on the frustration ratio p=J2/J1 are obtained in both stripe and Néel phases. The analysis of ground state sublattice magnetization and phase diagram indicates the critical end point at J2/J1=0.714, in agreement with previous studies.