One-particle Green Function Research Articles

First principles investigation of the C-terminatedβ−SiC(001)−c(2×2)surface

The structural and electronic properties of the c(2×2) reconstruction of the C-terminated β-SiC(001) surface have been investigated by ab initio calculations based on density functional theory. Employing the generalized gradient approximation, the top layer of this surface is found to consist of triple-bonded C dimers bridging Si atoms in the second layer. The electronic structure of the surface has been calculated on the basis of a semi-infinite geometry using our scattering theoretical method together with one-particle Green's functions. The resulting surface band structure is in good agreement with angle-resolved photoelectron spectroscopy data. Furthermore, our investigations show that compressive stress along the dimer direction induces a tilt of the surface C dimers. The calculated filled- and empty-state scanning microscopy topographs show virtually symmetric and asymmetric height profiles, respectively. These findings are in good agreement with recent experimental observations.

Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference $\epsilon$ and the strength of the interaction $\beta$. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility $\kappa$. In particular $\kappa$ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition.

Optical conductivity in a 2D model of the pseudogap state

We consider a two-dimensional model of the pseudogap state, based on the scenario of strong electron scattering by fluctuations of ``dielectric'' (AFM, CDW) short-range order. We construct a system of recurrence equations both for one-particle Green's function and vertex part, describing electron interaction with an external field, which take into account all Feynman graphs for electron scattering by short-range order fluctuations. The results of detailed calculations of optical conductivity are presented for different geometries (topologies) of the Fermi surface, demonstrating both the effects of pseudogap formation and localization effects. These results are in qualitative agreement with experimental data obtained for high-temperature superconducting cuprates.

Scattering from open-shell many-body targets

The standard one-particle Green function (GF) is extended to account for scattering from open-shell many-body targets. This extended GF possesses a self-energy which is an exact optical potential (OP) for scattering from open-shell targets. Furthermore, to each scattering process with well-defined quantum numbers there is a specific OP, thus reducing the multichannel problem to single-channel ones. As an explicit example we work out, in detail, the scattering of spin-½ projectiles from open-shell targets.

Valence One-Electron and Shake-Up Ionization Bands of Carbon Clusters. III. The Cn(n = 5,7,9,11) Rings

The 1h (one-hole) and 2h-1p (two-hole; one-particle) shake-up bands in the valence ionization spectrum of odd-membered carbon rings (C5, C7, C9, C11) are investigated by means of the third-order algebraic diagrammatic construction [ADC(3)] scheme for the one-particle Green's function. Despite a severe dispersion of the σ- and π- ionization intensity over intricately dense sets of satellites, the present study undoubtedly confirms that structural fingerprints in ionization spectra could be usefully exploited to discriminate the cyclic C5, C7, C9, and C11 species from their linear counterparts in plasma conditions. Such spectra could also be used to indirectly trace very fine details of the molecular structure, such as bond length alternations, out-of-plane distortions, or the strength of cyclic strains. Both structurally and electronically, the cyclic isomers of the C5 and C9 clusters must be described as even-twisted cumulenic tori, whereas the C7 and C11 cyclic species are simply planar polyynic rings. In comparison with their linear counterparts, all species display an intrinsically lower propensity to electronic excitations, marked by a rather significant increase of the fundamental HOMO−LUMO band gap. On the other hand, the lower symmetry of the cyclic clusters, C5 and C9 in particular, permits many more configuration interactions in the cation. The ultimate outcome of these two opposite factors is, overall, a severe enhancement of the shake-up fragmentation of ionization bands, compared with the linear isomers.

Shift in the absorption edge due toexchange interaction in ferromagnetic semiconductors

We develop the theory of the shift in the band edge caused by astrong exchange interaction between charge carrier spins andthe spins of the localized magnetic electrons in ferromagneticsemiconductors. The one-particle Green function is derived by usingMatsubara's temperature Green functions, and then an infinite-order correction to the band edge due to the exchangeinteraction is determined from the poles of the Green function. With the aid of the temperature- and magnetic field-dependentspin polarization of the magnetic moments and the spincorrelation functions, the band edge can be calculated as afunction of temperature in various magnetic fields. Thecalculated results are compared to experimental data in the cases of the ferromagnetic semiconductors EuO and Ga1-xMnxAs over a wide temperature range. For these materialsthe values 0.223 and 1.4 eV are evaluated for the exchangeinteraction parameter, respectively. A new feature is found in the ferromagnetic region, as a result of theexceptionally strong exchange interaction in Ga1-xMnxAs, i.e., a blue-shift in the band edge with decreasingtemperature or with increasing magnetic field.

Instanton method for the electron propagator

A nonperturbative theory of the electron propagator is developed and used to calculate the one-particle Green's function and tunneling density of states in strongly correlated electron systems. The method, which is based on a Hubbard–Stratonovich decoupling of the electron–electron interaction combined with a cumulant expansion of the resulting noninteracting propagator, provides a possible generalization of the instanton technique to the calculation of the electron propagator in a many-body system. Application to the one-dimensional electron gas with short-range interaction is discussed.

Theory of isotope exponent for high critical temperature superconductors

We calculate the isotopic exponent α for a Hubbard Hamiltonian with the presence of local Coulomb interaction U and an attractive BCS type potential V by using a normal state one-particle Green function, G N ( k → , iω n) , which is renormalized by the interactions. The BCS type pairing interaction V acts within a region ℏ ω D around the Fermi energy and it is appropriate to study α as function of the hole density ρ. Our results for α vs ρ for relevant U and V values for some high temperature superconductors reproduce the general main features and are in very good agreement with the experimental data.

The construction of the Green functions for GMR structures of complex geometry

We constructed the one-particle Green functions for two systems exhibiting giant magnetoresistance. The first one is a multilayer with arbitrary magnetization directions of the ferromagnetic layers, exchange splitting of the conducting electron band and intrinsic potential. The second one is a segmented nanowire with spin-dependent electron scattering at the lateral interfaces.

Properties of One-Particle Excitation for Two-Chain Tomonaga–Luttinger Model

The one-particle Green's function for the two-chain Tomonaga–Luttinger (TL) model coupled by interchain hopping including spin degrees of freedom is calculated as a function of distance and time by...

An experimental and theoretical study of the valence shell photoelectron spectra of 2-bromothiophene and 3-bromothiophene

The valence shell photoelectron spectra of 2-bromothiophene and 3-bromothiophene have been studied, both experimentally and theoretically, in order to characterise the main bands due to single-hole states and to assess the importance of electron correlation in the formation of satellite states. Synchrotron radiation has been employed to measure photoelectron angular distributions and branching ratios in the photon energy range 13–115 eV, and the results indicate that the photoionisation dynamics of the (12 a ′) −1 B 2 A ′ , (2 a ″) −1 C 2 A ″ and ( 11 a ′) −1 D 2 A ′ states are affected by Cooper minima. The experimental data demonstrate that the 12a ′ and 2a ″ orbitals, corresponding to the Br 4p lone pairs, retain their atomic properties to a substantial degree, and that the same is true, although to a lesser extent, for the 11a ′ orbital which is related to the S 3p subshell. The results are compared with similar measurements on chlorothiophene and bromobenzene. The vertical ionisation energies and spectral intensities of the entire valence shell photoelectron spectrum have been computed using the third-order algebraic–diagrammatic construction approximation scheme for the one-particle Green's function. These theoretical predictions have allowed assignments to be proposed for all the prominent structure observed in the experimental spectra. The outer valence Green's function method has also been used and the calculated ionisation energies show good agreement with the experimental values. Mulliken atomic populations have been computed for some of the outer valence orbitals, and the calculated Br 4p and S 3p content possessed by the 12a ′, 2a ″ and 11a ′ molecular orbitals is in accordance with the strength of the Cooper minimum observed in the photoelectron asymmetry parameters associated with these orbitals.

Optical Potentials and Propagators for Elastic and Inelastic Scattering from Many-Body Targets

The usual textbook one-particle Green's function possesses a self-energy that is known to be an optical potential for elastic scattering. The introduction of an optical potential reduces the complex many-body scattering problem into a tractable one-body problem. In this work the definition of Green's functions is extended. The defined inelastic functions are shown to possess self-energies that can be expressed in closed form in terms of the target states. It is proven that these self-energies are optical potentials for inelastic scattering. The properties of these potentials and working equations for the scattering wave functions are discussed. Particular emphasis is put on elucidating the substantial differences arising in the scattering of a projectile distinguishable from the target's particles and in the scattering of indistinguishable particles.

Hopping perturbation treatment of the periodic Anderson model around the atomic limit

The periodic Anderson model with two strongly correlated subsystems of d and f electrons and local on-site hybridization is investigated by considering the hopping of d electrons between lattice sites as perturbation. In zero order without the intersite transfer term, the system of correlated d and f electrons can be treated exactly. The delocalization of electrons and the corresponding renormalization of the one-particle Green's functions are analyzed by using a special diagram technique from which the Dyson equations for the Green's functions are established. We discuss the physics of the delocalized electrons in the simplest approximation corresponding to a Hubbard I\char21{}like decoupling giving rise to eight different energy bands, which depend in a non-trivial way on the exact eigenvalues of the local model. These bands are discussed for the symmetrical case in which the energies of doubly occupied d and f states are equal to each other.

Probing molecular conformations with electron momentum spectroscopy: the case of n-butane.

High-resolution (e,2e) measurements of the valence electronic structure and momentum-space electron density distributions of n-butane have been exhaustively reanalyzed in order to cope with the presence of two stable structures in the gas phase, namely the all-staggered and gauche conformers. The measurements are compared to a series of Boltzmann-weighted simulations based on the momentum-space form of Kohn-Sham (B3LYP) orbital densities, and to ionization spectra obtained from high-level [ADC(3)] one-particle Green's Function calculations. Indubitable improvements in the quality of the simulated (e,2e) ionization spectra and electron momentum profiles are seen when the contributions of the gauche form of n-butane are included. Both the one-electron binding energies and momentum distributions consistently image the distortions and topological changes that molecular orbitals undergo due to torsion of the carbon backbone, and thereby exhibit variations which can be traced experimentally. With regard to the intimate relation of (e,2e) cross sections with orbital densities, electron momentum spectroscopy can therefore be viewed as a very powerful, but up to now largely unexploited, conformational probe. The study also emphasizes the influence of thermal agitation in photoionization experiments of all kind.

Fermionic Renormalization Group Flows: Technique and Theory

We give a self-contained derivation of the differential equations for Wilson’s renormalization group for the one-particle irreducible Green functions in fermionic systems. The application of this equation to the (t, t � )-Hubbard model appears in Ref. 9). Here we focus on theoretical aspects. After deriving the equations, we discuss the restrictions imposed by symmetries on the effective action. We discuss scaling properties due to the geometry of the Fermi surface and give precise criteria to determine when they justify the use of one-loop flows. We also discuss the relationship of this approach to other RG treatments, as well as aspects of the practical treatment of truncated equations, such as the projection to the Fermi surface and the calculation of susceptibilities. Renormalization group (RG)studies of fermionic models are important for understanding models of solid-state theory and high-energy physics. In this paper, we set up a system of equations suitable for studying flows for general fermionic systems, in particular those with a Fermi surface at any density, and discuss general, but nontrivial, properties of their solutions. The system of equations applies both to “normal” and to symmetry-broken situations of fermionic systems with short-range interactions for d ≥ 1. By “short-range” we mean that the two-particle interaction decays so fast that its Fourier transform is a regular function. In Ref. 9)we have, together with Furukawa and Rice, applied the RG equations that we derive here to the two-dimensional (t, t � )-Hubbard model in the regime relevant for high-temperature superconductivity. The purpose of the present paper is to give more background on the theoretical aspects of the equations, in particular on a detailed argument which justifies the one-loop flow in a certain scale range, even if the scale-dependent interaction is no longer small. In the following, we give an overview; the details are filled in in the later sections. 1.1. The RG and the three scale regimes The Wilsonian RG organizes the functional integration corresponding to the grand canonical trace as an iterated integral over degrees of freedom with energies in a certain range, i.e. those that belong to a corresponding length scale. As such, it is simply a rewriting of the generating functional of the correlation functions as a function of an energy scale � . In contrast to the situation in other RG schemes, this approach does not require any assumptions about perfect scaling laws as a

Decay properties of the one-particle Green function in real space and imaginary time

The decay properties of the one-particle Green function in real space and imaginary time are systematically studied for solids. I present an analytic solution for the homogeneous electron gas at finite and at zero temperature as well as asymptotic formulas for real metals and insulators that allow an analytic treatment in electronic-structure calculations based on a space-time representation. The generic dependence of the decay constants on known system parameters is used to compare the scaling of reciprocal-space algorithms for the $\mathrm{GW}$ approximation and the space-time method.

Spectral function of one hole in several one-dimensional spin arrangements

The spectral function of one hole in different magnetic states of the one-dimensional $t\ensuremath{-}J$ model including three-site term and frustration ${J}^{\ensuremath{'}}$ is studied. In the strong-coupling limit $\stackrel{\ensuremath{\rightarrow}}{J}0$ (corresponding to $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty}$ of the Hubbard model) a set of eigenoperators of the Liouvillian is found which allows us to derive an exact expression for the one-particle Green's function that is also applicable at finite temperature and in an arbitrary magnetic state. The spinon dispersion of the pure $t\ensuremath{-}J$ model with the ground state of the Heisenberg model can be obtained by treating the corrections due to a small exchange term by means of the projection method. The spectral function for the special frustration ${J}^{\ensuremath{'}}=J/2$ with the Majumdar-Ghosh wave function is discussed in detail. Besides the projection method, a variational ansatz with the set of eigenoperators of the t term is used. We find a symmetric spinon dispersion around the momentum $k=\ensuremath{\pi}/(2a)$ and a strong damping of the holon branch. Below the continuum a bound state is obtained with finite spectral weight and a very small separation from the continuum. Furthermore, the spectral function of the ideal paramagnetic case at a temperature ${k}_{B}T\ensuremath{\gg}J$ is discussed.

Some sum rules for non-Fermi liquids: Applications taking into account the mass renormalization factor

Re-studying the non-fermi liquid one-particle Green function (NFLGF) we have extended the work of A. Balatsky (Phil. Mag. Lett. 68, 251 (1993)) and L. Yin and S. Chakravarty (Int. J. Mod. Phys. B 10, 805 (1996)), among others. We used the moment approach of W. Nolting (Z. Phys. 255, 25 (1972)) to compute the unknown parameters of the NFLGF's in the framework of the Hubbard model. The zeroth order momentum requires that our one-particle Green function describe fermionic degrees of freedom. In order to satisfy the first order sum rule a renormalization, $\gamma\neq 1$, of the free electron mass is called for. The second order sum rule or moment imposes a relation between the non-Fermi liquid parameter, $\alpha$, the Coulomb interaction, U, and the frequency cutoff, $\omega_c$. We have calculated the effect of the mass renormalization factor, $\gamma$, on some physical quantities. As a new class of non-Fermi liquid systems, in Appendix A, we have studied two inequivalent coupled Hubbard layers for which we calculated the one-particle spectral functions on the layers and perpendicular to them. We discuss the new features which appear due to the shift in the two effective chemical potentials and proposed some experiments to detect the features founded from our expressions.

Quasiparticle properties of quantum Hall ferromagnets

We report on a study of the temperature and Zeeman-coupling-strength dependence of the one-particle Green's function of a two-dimensional (2D) electron gas at Landau level filling factor $\nu =1$ where the ground state is a strong ferromagnet. Our work places emphasis on the role played by the itinerancy of the electrons, which carry the spin magnetization and on analogies between this system and conventional itinerant electron ferromagnets. We discuss the application to this system of the self-consistent Hartree-Fock approximation, which is analogous to the band theory description of metallic ferromagnetism and fails badly at finite temperatures because it does not account for spin-wave excitations. We go beyond this level by evaluating the one-particle Green's function using a self-energy, which accounts for quasiparticle spin-wave interactions. We report results for the temperature dependence of the spin magnetization, the nuclear spin relaxation rate, and 2D-2D tunneling conductances. Our calculations predict a sharp peak in the tunneling conductance at large bias voltages with strength proportional to temperature. We compare with experiment, where available, and with predictions based on numerical exact diagonalization and other theoretical approaches.

Anisotropy of the energy gap in the insulating phase of the U-t-t' Hubbard model

We apply a diagrammatic expansion method around the atomic limit (U >> t) for the U-t-t' Hubbard model at half filling and finite temperature by means of a continued fraction representation of the one-particle Green's function. From the analysis of the spectral function A(\vec{k},\omega) we find an energy dispersion relation with a (cos k_x-cos k_y)^2 modulation of the energy gap in the insulating phase. This anisotropy is compared with experimental ARPES results on insulating cuprates.