Self-consistent Green Function Research Articles

Self-consistent Green's functions calculation of the nucleon mean-free path

Transport coefficients provide a unique insight into the near-equilibrium behavior of quantum many-body systems. The mean-free path, λ, of a particle within a dense medium is a basic transport coefficient, at the basis of several theoretical concepts and closely related to experimentally measured quantities. Green's functions techniques are particularly well suited to study such transport properties, since they are naturally formulated in the time domain. We present a calculation of the mean-free path of a nucleon in symmetric nuclear matter using self-consistent ladder self-energies extended to the complex energy plane. Our results indicate that, for energies above 50 MeV at densities close to saturation, a nucleon has a mean-free path of 4 to 5 femtometers.

Disordered topological metals

Topological behavior can be masked when disorder is present. A topological insulator, either intrinsic or interaction induced, may turn gapless when sufficiently disordered. Nevertheless, the metallic phase that emerges once a topological gap closes retains several topological characteristics. By considering the self-consistent disorder-averaged Green function of a topological insulator, we derive the condition for gaplessness. We show that the edge states survive in the gapless phase as edge resonances and that, similar to a doped topological insulator, the disordered topological metal also has a finite, but non-quantized topological index. We then consider the disordered Mott topological insulator. We show that within mean-field theory, the disordered Mott topological insulator admits a phase where the symmetry-breaking order parameter remains non-zero but the gap is closed, in complete analogy to 'gapless superconductivity' due to magnetic disorder.

Structural, electronic, magnetic and spin dependent transport properties of Fe/CaS/Fe (001) heterostructures

Structural, electronic, and magnetic properties of Fe/CaS (001) interfaces and Fe/CaS/Fe (001) heterostructures have been studied by means of a self-consistent Green's function technique for surface and interfaces implemented within the tight-binding linear muffin-tin orbital formalism. Spin dependent transport properties of the Fe/CaS/Fe (001) tunnel junctions with thin and intermediate barriers, in the current-perpendicular-to-plane geometry, have been determined by means of Kubo-Landauer approach implemented within the tight-binding linear muffin-tin orbital formalism. A small charge rearrangement is evidenced at the Fe/CaS (001) interfaces. The iron interfacial magnetic moments are enhanced over the bulk value. A small exchange coupling with the sign depending on the Fe/CaS (001) interface geometric structure and the strength decaying exponentially with the barrier is evidenced. Interfacial charge transfer, interface iron magnetic moments, and tunneling currents are sensitive to the interfacial structure. Interface resonant states have a decisive role in the tunneling process and the main contribution to the current in the ferromagnetic state of the junction is given by the minority-spin electrons.

Comparative study of neutron and nuclear matter with simplified Argonne nucleon-nucleon potentials

We present calculations of the energy per particle of pure neutron and symmetric nuclear matter with simplified Argonne nucleon-nucleon potentials for different many-body theories. We compare critically the Brueckner-Hartree-Fock results to other formalisms, such as the Brueckner-Bethe-Goldstone expansion up to third order, self-consistent Green's functions, auxiliary field diffusion Monte Carlo, and Fermi hypernetted chain. We evaluate the importance of spin-orbit and tensor correlations in the equation of state and find these to be important in a wide range of densities.

Self-consistent supercell approach to alloys with local environment effects

We present an efficient and accurate method for calculating electronic structure and related properties of random alloys with a proper treatment of local environment effects. The method is a generalization of the locally self-consistent Green's function (LSGF) technique for the exact muffin-tin orbital (EMTO) method. An alloy system in the calculations is represented by a supercell with a certain set of atomic distribution correlation functions. The Green's function for each atom in the supercell is obtained by embedding the cluster of neighboring atoms lying within a local interaction zone (LIZ) into an effective medium and solving the cluster Dyson equation exactly. The key ingredients of the method are locality, which makes it linearly scaling with the number of atoms in the supercell, and coherent-potential self-consistency of the effective medium, which results in a fast convergence of the electronic structure with respect to the LIZ size. To test the performance and accuracy of the method, we apply it to two systems: Fe-rich bcc-FeCr random alloy with and without a short-range order, and a Cr-impurity on the Fe surface. Both cases demonstrate the importance of taking into account the local environment effects for correct description of magnetic and bulk properties.

Self-consistent Green function equations and the hierarchy of approximations for the four-point propagator

The equation of motion for the Green function is combined with the Bethe-Salpeter equation for the scattering amplitude yielding a concise and formally closed system of three equations that encapsulates the essence of Green function theory. Two of the three equations formally resemble a Dyson-like relation. We prove that this formally simple set is exactly equivalent to Hedin’s equations. Our derivation therefore constitutes an alternative to Hedin’s derivation which is based on functional derivatives. Furthermore, we briefly discuss how approximations can be introduced as a hierarchy of approximations to the four-point Green function.

Self-consistent Gorkov Green's function calculations of one-nucleon spectral properties

Results from the newly developed Gorkov self-consistent Green's function approach are presented. Ab-initio spectral strength distributions for one-nucleon addition or removal calculated in doubly-closed shell 40Ca and in semi-magic 44Ca are briefly discussed. The object of the present communication is to illustrate the potential spectroscopic reach of the method.

Ab initioself-consistent Gorkov-Green's function calculations of semimagic nuclei: Formalism at second order with a two-nucleon interaction

An ab initio calculation scheme for finite nuclei based on self-consistent Green's functions in the Gorkov formalism is developed. It aims at describing properties of doubly magic and semimagic nuclei employing state-of-the-art microscopic nuclear interactions and explicitly treating pairing correlations through the breaking of U(1) symmetry associated with particle number conservation. The present paper introduces the formalism necessary to undertake applications at (self-consistent) second order using two-nucleon interactions in a detailed and self-contained fashion. First applications of such a scheme will be reported soon in a forthcoming publication. Future works will extend the present scheme to include three-nucleon interactions and implement more advanced truncation schemes.

Electrical control of ferromagnetism and bias anomaly in Mn-doped semiconductor heterostructures

The interplay of tunneling transport and carrier-mediated ferromagnetism in narrow semiconductor multiquantum well structures containing layers of GaMnAs is investigated within a self-consistent Green's function approach, accounting for disorder in the Mn-doped regions and unwanted spin flips at heterointerfaces on phenomenological ground. We find that the magnetization in GaMnAs layers can be controlled by an external electric bias. The underlying mechanism is identified as spin-selective hole tunneling in and out of the Mn-doped quantum wells, whereby the applied bias determines both hole population and spin polarization in these layers. In particular, we predict that, near resonance, ferromagnetic order in the Mn-doped quantum wells is destroyed. The interplay of both magnetic and transport properties combined with structural design potentially leads to several interrelated physical phenomena, such as dynamic spin filtering, tunneling-induced bias anomaly, electrical control of magnetization in individual magnetic layers, and, under specific bias conditions, to self-sustained current and magnetization oscillations (magnetic multistability). Relevance to recent experimental results is discussed.

Gorkov self-consistent Green's function calculations of semi-magic nuclei

The first nuclear structure application of the newly developed Gorkov self-consistent Green's function method is presented. The approach aims to describe many-nucleon systems from an ab-initio standpoint featuring an explicit treatment of pairing correlations. In the present work calculations of binding energies of calcium isotopes are reported and compared with experimental data and other theoretical references.

Electronic structure of the Ge and Se vacancies in GeSe layered semiconductor

We report the results of a theoretical investigation of electronic properties of ideal cation and anion vacancies in GeSe. The calculations have been performed using self-consistent Green's function method. The bulk electronic structure is described by a tight-binding Hamiltonian in the bases sets of Linear Combinations of Atomic Orbitals (LCAO). The Green's function of the perfect crystal evaluated using an eigenfunction expansion employing wave functions and band structures obtained from a self-consistent, pseudopotential, local-density-functional calculation. The defect potential is calculated using occupied electron states of the perturbed system. Results are obtained in terms of vacancy bound states, vacancy resonances, and vacancy antiresonances. The energy states in energy gaps, their origin, orbital content and resonances due to the localized defects are discussed.

ONE- AND TWO-NUCLEON STRUCTURE FROM GREEN'S FUNCTION THEORY

We review some applications of self-consistent Green's function theory to studies of one- and two-nucleon structure in finite nuclei. Large-scale microscopic calculations that employ realistic nuclear forces are now possible. Effects of long-range correlations are seen to play a dominant role in determining the quenching of absolute spectroscopic factors. They also enhance considerably (e,e' pn ) cross sections in superparallel kinematics, in agreement with observations.

Self-Consistent Green Function Calculations for Isospin Asymmetric Nuclear Matter

(Received September 1, 2009; Revised February 2, 2010)The one-body potentials for protons and neutrons are obtained from the self-consistentGreen-function calculations of asymmetric nuclear matter, in particular their dependence onthe degree of proton/neutron asymmetry. Results of the binding energy per nucleon as afunction of the density and asymmetry parameter are presented for the self-consistent Greenfunction approach using the CD-Bonn potential. For the sake of comparison, the same cal-culations are performed using the Brueckner-Hartree-Fock approximation. The contributionof the hole-hole terms leads to a repulsive contribution to the energy per nucleon whichincreases with the nuclear density. The incompressibility for asymmetric nuclear matter hasbeen also investigated in the framework of the self-consistent Green-function approach usingthe CD-Bonn potential. The behavior of the incompressibility is studied for different valuesof the nuclear density and the neutron excess parameter. The nuclear symmetry potentialat fixed nuclear density is also calculated and its value decreases with increasing the nu-cleon energy. In particular, the nuclear symmetry potential at saturation density changesfrom positive to negative values at nucleon kinetic energy of about 200 MeV. For the sakeof comparison, the same calculations are performed using the Brueckner-Hartree-Fock ap-proximation. The proton/neutron effective mass splitting in neutron-rich matter has beenstudied. The predicted isospin splitting of the proton/neutron effective mass splitting inneutron-rich matter is such that

Effect of electron-electron interactions on the Klein paradox in graphene-based double-barrier structures

The effects of Coulomb interactions on the transport properties of the relativistic electron through graphene-based double-barrier structures have been investigated. A self-consistent Green's function method has been developed by solving numerically the Dyson equation in the Hartree-Fock approximation. The transmission probability, conductivity, shot noise, and Fano factor through the structures have been calculated and analyzed. It is shown that Klein tunneling is suppressed strongly by taking into account the electron-electron interaction. In contrast, the Fano factor shows abrupt increase. The shot noise is either improved or suppressed, which depends on the energy of the incident electron and the strength of the electron-electron interaction. The physical originations for these phenomena have been discussed.

Thermodynamic properties of nuclear matter with three-body forces

We calculate thermodynamic quantities in symmetric nuclear matter within the self-consistent Green's functions method including three-body forces. The thermodynamic potential is computed directly from a diagrammatic expansion, implemented with the CD-Bonn and Nijmegen nucleon-nucleon potentials and the Urbana three-body forces. We present results for entropy and pressure up to temperatures of 20 MeV and densities of $0.32 {\mathrm{fm}}^{\ensuremath{-}3}$. While the pressure is sensitive to the inclusion of three-body forces, the entropy is not. The unstable spinodal region is identified and the critical temperature associated to the liquid-gas phase transition is determined. When three-body forces are added we find a strong reduction of the critical temperature, obtaining ${T}_{c}\ensuremath{\simeq}12 \mathrm{MeV}$.

Terahertz Response of Carbon Nanotube Transistors

We present an approach for time-dependent quantum transport based on a self-consistent nonequilibrium Green function formalism. The technique is applied to a ballistic carbon nanotube transistor in the presence of a time-harmonic signal at the gate. In the on state, the dynamic conductance exhibits plasmonic resonant peaks at terahertz frequencies. These vanish in the off state, and the dynamic conductance displays smooth oscillations, a signature of single-particle quantum effects. We show that the nanotube kinetic inductance plays an essential role in the high-frequency behavior.

Entropy of a correlated system of nucleons

The self-consistent Green's function method within the ladder approximation allows for a realistic description of strongly interacting quantum many-body systems. At the microscopic level, the single-particle properties of the system are described in terms of finite-width spectral functions. The connection with the bulk properties at finite temperatures can be established via the Luttinger–Ward formalism. An expression for the entropy that includes the effects of the fragmentation of the quasi-particle peak will be presented. The properties of this dynamical quasi-particle entropy will be discussed and the corresponding results will be compared to other approximations. Even though we shall restrict our discussion to nuclear matter, this formalism can be used to study the thermodynamical properties of other fermionic systems.

Approximate self-consistent green's functions for solids

Three related methods for finding crystal Green's functions are presented. All are related by the use of localized calculations. All have the property that local excitations and correlation effects are adequately described, but long-range correlation effects such as plasmons and certain types of charge transfer excitons are not included.

Quasiparticle and quasihole states of nuclei aroundNi56

The single-particle spectral function of $^{56}\mathrm{Ni}$ has been computed within the framework of self-consistent Green's functions theory. The Faddeev random phase approximation method and the $G$ matrix technique are used to account for the effects of long- and short-range physics on the spectral distribution. Large-scale calculations have been performed in spaces including up to ten oscillator shells. The chiral ${\mathrm{N}}^{3}\mathrm{LO}$ interaction is used together with a monopole correction that accounts for eventual missing three-nucleon forces. The single-particle energies associated with nucleon transfer to valence $1p0f$ orbits are found to be almost converged with respect to both the size of the model space and the oscillator frequency. The results support that $^{56}\mathrm{Ni}$ is a good doubly magic nucleus. The absolute spectroscopic factors to the valence states on $A=55,57$ are also obtained. For the transition between the ground states of $^{57}\mathrm{Ni}$ and $^{56}\mathrm{Ni}$, the calculations nicely agree with heavy-ion knockout experiments.

Depletion of the nuclear Fermi sea

The short-range and tensor components of the bare nucleon-nucleon interaction induce a sizeable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Green's function method within the ladder approximation provides an \textit{ab-initio} description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi sea is clarified. A connection is established between the momentum distribution and the time-ordered components of the self-energy, which allows for an improved interpretation of the results. The dependence on the underlying nucleon-nucleon interaction provides quantitative estimates of the importance of short-range and tensor correlations in nuclear systems.