Double-time Green Research Articles

Theoretical investigation of the impact of intra‐ and inter‐layer coupling of high TC superconductor Nd2‐xCexCuO4

AbstractThe aim of the current study is to investigate the impact of layer coupling on the characteristics of high TC superconductor Nd2‐xCexCuO4 (NCCO). In this study, the intra‐ and inter‐layer couplings are taken into consideration. By applying the double time Green's function (GF) technique and formulating a model Hamiltonian, the transition temperature (TC) of superconductor Nd2‐xCexCuO4 is computed quantitatively by considering the intra‐ and inter‐layer interactions as independent variables. By increasing the layer interactions, the increase in TC is observed. Furthermore, TC is calculated by taking into consideration different number of interlayer interactions as independent variables which subsequently resulted in the enhancement of TC. Besides, TC has been computed as a function of electron doping as a result of which a dome shaped figure has been perceived in the temperature versus doping phase diagram. The superconducting order parameter (Δ) has been also reckoned as a function of temperature and is observed to gradually decrease as temperature increases and eventually vanishes at TC. A slight increment in TC is observed as the doping values of charge carriers increase. Our findings are discussed in connection with the experimental studies of superconductivity (SC) in Nd2CuO4 based layered compounds.

Two-dimensional intrinsic ferromagnetism in CrBr3 monolayer

The CrBr3 monolayer provides an ideal experimental platform to study the two-dimensional ferromagnetism. In this work, we theoretically study the intrinsic ferromagnetism of CrBr3 monolayer based on the anisotropic Heisenberg model with exchange interactions beyond the nearest neighbor and employing the double-time Green's function method. The Hamiltonian parameter values of the model are taken from the recently reported first-principles calculations. The spontaneous magnetization, Curie temperature, hysteresis loop, and magnon energy spectrum are calculated numerically, and the theoretical results are compared with the available experimental results as much as possible. The calculated Curie temperature of 30.5 K is well consistent with the two experimental measurements of 27 K and 34 K, which in turn support the magnetic parameters obtained from the first-principles calculations. Moreover, the theoretically calculated results of critical exponent describing the critical behavior of spontaneous magnetization and hysteresis loops agree qualitatively well with the experimental measurements.

Jahn–Teller Distortion in Two-Orbital Model for s±-Wave Iron-Based Superconductors

The theoretical aspects of research on the role of Jahn–Teller (JT) interactions in quasi-two-dimensional iron-based high-[Formula: see text] superconductors are analyzed. A model Hamiltonian for the JT distortion in iron-based superconductors is proposed by a tight-binding two-orbital model. We have proposed here a [Formula: see text]-wave pairing symmetry of the form [Formula: see text] in the model in mean-field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find the self-consistent gap equation and is solved self-consistently. The lattice strain energy, specific heat, conduction electron density of states and energy band structure for the system are calculated.

Superconductivity in Two-Orbital Model for s±-Wave Iron-Based Superconductors

In high-[Formula: see text] superconductors, electrons form pairs and electric transport becomes dissipation-less at low temperatures. The iron-based superconductors (FeSCs) have the highest superconducting (SC) transition temperature next to copper oxides. The gap structure and pairing mechanism for FeSCs are hotly discussed as a central issue since their discovery. A model Hamiltonian for the superconductivity in FeSCs is proposed by a tight-binding two-orbital model. The SC gap, conduction electron density of states, specific heat and energy band structure for the system are calculated. We have proposed here a [Formula: see text]-wave pairing symmetry of the form [Formula: see text] in the model in the mean-field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find the self-consistent gap equation and is solved self-consistently.

Superconductivity and Jahn-Teller Distortion in s±-Wave Iron-Based Superconductors

We discuss here a few possibilities of gap structure and pairing mechanism for iron-based superconductors with more than one orbital symmetry contributing to the pairing. We have proposed a two-orbital tight-binding model for the coexistence of superconductivity and Jahn-Teller distortion in s±-wave pairing symmetry of the form coskx × cosky in the mean-field approximation. The self-consistent gap equations are calculated by Zubarev’s double-time Green’s function technique which are solved numerically and self-consistently. The specific heat, density of states and band energies are also studied for the proposed model.

Coexistence of Jahn-Teller effect and AFM in two-orbital model for s[formula omitted]-wave iron based superconductors

The origin of pairing mechanism and the coexisting order parameters in Fe-based superconductors have been attracting increasing attention. The tetragonal to orthorhombic phase transition which leads the antiferromagnetic phase transition in many Fe-based superconductors is one of the current heat discussions of electronic order. The distortion and antiferromagnetism coexist in the phase diagrams of such superconductors. A tight-binding two band model with the coexistence of Jahn-Teller distortion and antiferromagnetism is being proposed here for s±-wave pairing symmetry of the form coskx×cosky in the mean field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find their self-consistent gap equations. Then these gap equations are solved self-consistently numerically and the specific heat, density of states and band energies are studied for the system.

Antiferromagnetism in two-orbital model for s ± -wave iron based superconductors

In iron based superconductors the superconducting phase occurs near the onset of antiferromagnetism order. Unconventional superconductivity has led to extensive experimental and theoretical studies on the effect of electron correlations and on the nature of magnetism in iron based superconductors. For the study of antiferromagnetism in these superconductors we have proposed a tight-binding two-orbital model Hamiltonian. We have proposed here a s±-wave pairing symmetry of the form coskx × cosky in the model in mean-field approximation. The model is solved by Zubarev’s double-time Green’s function technique to find the self-consistent gap equation and is solved self-consistently numerically. The antiferromagnetism gap, specific heat, conduction electron density of states and energy band structure for the system are calculated.

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.

Coexistence of SC and AFM in two-orbital model for s±-wave iron based superconductors

The gap structure and pairing mechanism for iron based superconductors is hotly discussed as a central issue since their discovery. The long range order parameters, electronic specific heat, conduction electron density of states and energy band structure of iron based superconductors are calculated by a tight-binding two-orbital model with the coexistence of superconductivity and antiferromagnetism. We have proposed here a s±-wave pairing symmetry of the form cos kx × cos ky in a two-orbital model for the coexistence of the two order parameters in the mean-field approximation. The model is solved by Zubarev's double-time Green's function technique to find their self-consistent gap equations and are solved self-consistently numerically.

The theoretical study of the correlation between band filling and Coulomb interaction in the charge gap of graphene-on-substrate in paramagnetic limit

A suitable substrate breaks the sub-lattice symmetry leading to generation of a gap at the Fermi level. We propose here a tight binding model Hamiltonian for graphene on a substrate with nearest neighbour-hopping in presence of symmetry breaking interaction due to substrate effect. The sub-lattice Coulomb interaction between the electrons which produces varieties of magnetic, non-magnetic and collective interactions is considered within mean-field approximation in the paramagnetic limit. The Hamiltonian is solved by Zubarev's double time Green's function technique. The electron occupancies of the two sub-lattices are calculated from the correlation functions. Finally, the expression for the temperature dependent charge gap is derived and calculated numerically. The evolution of the charge gap in graphene is investigated by varying the Coulomb interaction, electron-occupancy and substrate induced gap. The magnitude of the electron occupancy at A-site becomes larger than that at B-site indicating symmetry breaking of the two sub-lattices of graphene.

The theoretical study of the correlation between band filling and Coulomb interaction in the charge gap of graphene-on-substrate in paramagnetic limit

A suitable substrate breaks the sub-lattice symmetry leading to generation of a gap at the Fermi level. We propose here a tight binding model Hamiltonian for graphene on a substrate with nearest neighbour-hopping in presence of symmetry breaking interaction due to substrate effect. The sub-lattice Coulomb interaction between the electrons which produces varieties of magnetic, non-magnetic and collective interactions is considered within mean-field approximation in the paramagnetic limit. The Hamiltonian is solved by Zubarev's double time Green's function technique. The electron occupancies of the two sub-lattices are calculated from the correlation functions. Finally, the expression for the temperature dependent charge gap is derived and calculated numerically. The evolution of the charge gap in graphene is investigated by varying the Coulomb interaction, electron-occupancy and substrate induced gap. The magnitude of the electron occupancy at A-site becomes larger than that at B-site indicating symmetry breaking of the two sub-lattices of graphene.

Effect of external magnetic field on the coexistence of SC and AFM in iron based superconductors

We have studied the interplay of antiferromagnetism and superconductivity in presence of an applied external magnetic field for the iron based superconductors. For the purpose we have proposed a model Hamiltonian and solved it self-consistently by using the Zubarev's technique of double time Green's function technique. The self-consistent gap equations are solved numerically and interpreted the gap values from the of density of states plots.

Magnetism and thermodynamics of the anisotropic frustrated spin-1 Heisenberg antiferromagnet on a body-centered cubic lattice

Abstract The magnetic and thermodynamic properties of anisotropic frustrated spin-1 Heisenberg antiferromagnet on a body-centered cubic lattice for Neel phase (the region of weak frustration) are systematically investigated by use of the double-time Green's function method within the random phase approximation and the Anderson and Callen's decoupling. The zero-temperature sublattice magnetization and Neel temperature increase with spin anisotropy strength and single-ion anisotropy strength, and decrease with frustration strength. This indicates that quantum fluctuation is suppressed by spin anisotropy and single-ion anisotropy, by contrast, is strengthened by frustration. It is possible to tune the quantum fluctuations by the competition of anisotropy strength and frustration strength to change the ground state properties of magnetic materials. Although we find that both the spin anisotropy and the single-ion anisotropy suppress the quantum fluctuations, but their respective effects on the thermodynamic quantities, especially the internal energy and free energy, are different at zero temperature and finite temperature. Furthermore, when these two kinds of anisotropic coexist, the effect of the spin anisotropy on the sublattice magnetization and internal energy is larger than that of the single-ion anisotropy.

Model study of coexistence of Jahn-Teller distortion, antiferromagnetism and superconductivity in iron pnictide superconductors

Abstract We have proposed a theoretical model for the coexistence of superconductivity (SC), antiferromagnetism (AFM) and Jahn-Teller (JT) effect in the mean field approximation for iron based superconductors. The model is solved by using Zubarev's double-time Green's function technique to get their selfconsistent gap equations. Then these gap equations are solved numerically.

Hierarchy of correlations: Application to Green's functions and interacting topological phases

We study the many-body physics of different quantum systems using a hierarchy of correlations, which corresponds to a generalization of the $1/\mathcal{Z}$ hierarchy. The decoupling scheme obtained from this hierarchy is adapted to calculate double-time Green's functions, and due to its non-perturbative nature, we describe quantum phase transition and topological features characteristic of strongly correlated phases. As concrete examples we consider spinless fermions in a dimers chain and in a honeycomb lattice. We present analytical results which are valid for any dimension and can be generalized to different types of interactions (e.g., long range interactions), which allows us to shed light on the effect of quantum correlations in a very systematic way. Furthermore, we show that this approach provides an efficient framework for the calculation of topological invariants in interacting systems.

Thermodynamic properties of frustrated arbitrary spin-S J1–J2 quantum Heisenberg antiferromagnet on the body-centered-cubic lattice in random phase approximation

Abstract The thermodynamic properties of the frustrated arbitrary spin-S J1–J2 Heisenberg antiferromagnet on the body-centered-cubic lattice for Neel phase are systematically calculated by use of the double-time Green׳s function method within the random phase approximation (RPA). The role of spin quantum number and frustration strength on sublattice magnetization, Neel temperature, internal energy, and free energy are carefully analyzed. The curve of zero-temperature sublattice magnetization 〈 S z ( 0 ) 〉 / S versus frustration strength J2/J1 values are almost flat at the larger spin quantum number S=10. With the increase of normalized temperature T/TN, the larger the spin quantum number S, the faster the 〈 S z 〉 / S drops, and the smaller influence of J2/J1 on the 〈 S z 〉 / S versus T/TN curve. Under the RPA approach, the Neel temperature TN /Sp and the internal energy E/Sp at the Neel point are independent of spin quantum number S. The numerical results show that the internal energy E/Sp at the Neel point seems independent of the frustration strength J2/J1. This indicates that thermodynamic quantities have universal characteristics for large spin quantum number.

Phase transition of anisotropic frustrated Heisenberg model on the square lattice.

We have investigated the J_{1}-J_{2} Heisenberg model with exchange anisotropy on a square lattice and focused on possible AF1-AF2 phase transition below the Néel point and its dependence on the exchange anisotropy, where AF1 and AF2 represent Néel state and collinear state, respectively. We use the double-time Green's-function method and adopt the random-phase approximation. The less the exchange anisotropy, the stronger the quantum fluctuation of the system will be. Both the Néel state and collinear state can exist and have the same Néel temperature for arbitrary anisotropy and spin quantum number S when J_{2}/J_{1}=0.5. Under such parameters, the calculated free energies show that there may occur a first-order phase transition between the Néel state and collinear state for an arbitrary S when anisotropy is not strong.

Equation-of-motion series expansion of double-time Green's functions

Based on the Green's function (GF) equation-of-motion formalism, we develop a method to expand the double time Green's function into Taylor series of the parameter $\lambda$ in the Hamiltonian $H=H_0 + \lambda H_1$. Here $H_0$ is the exactly solvable part and $H_1$ is regarded as the perturbation. To restore the analytical structure of GF, we use the continued fraction to do resummation for the obtained series. The problem of zero-temperature divergence is identified and remedied by the self-consistent series expansion. To demonstrate the implementation of this method, we carry out the weak- as well as the strong-coupling expansion for the Anderson impurity model to order $\lambda^2$. Improved result for the local density of states is obtained by self-consistent second-order strong-coupling expansion and continued fraction resummation.

The magnetic properties of a mixed spin-1/2 and spin-1 Heisenberg ferrimagnetic system on a two-dimensional square lattice

The magnetic properties of a mixed spin-1/2 and spin-1 Heisenberg ferrimagnetic system on a two-dimensional square lattice are investigated by means of the double-time Green's function technique within the random phase decoupling approximation. The role of the nearest-, next-nearest-neighbors interactions and the exchange anisotropy in the Hamiltonian is explored. And their effects on the critical and compensation temperature are discussed in detail. Our investigation indicates that both the next-nearest-neighbor interactions and the anisotropy have a great effect on the phase diagram.

Magnon specific heat and free energy of Heisenberg ferromagnetic single-walled nanotubes: Green's function approach

The effect of magnetic spin correlation on the thermodynamic properties of Heisenberg ferromagnetic single-walled nanotubes are comprehensively investigated by use of the double-time Green's function method. The influence of temperature, spin quantum number, diameter of the tube, anisotropy strength and external magnetic field to internal energy, free energy, and magnon specific heat are carefully calculated. Compared to the mean field approximation, the consideration of the magnetic correlation effect significantly improves the internal energy values at finite temperature, while it does not so near zero temperature, and this effect is related to the diameter of the tube, anisotropy strength, and spin quantum number. The magnetic correlation effect lowers the internal energy at finite temperature. As a natural consequence of the reduction of the internal energy, the specific heat is reduced, and the free energy is elevated.