One-particle Green Research Articles

Nonequilibrium superoperator GW equations

Hedin's equations [Phys. Rev. 139, 796 (1965)] for the one-particle equilibrium Green's function of a many-electron system are generalized to nonequilibrium open systems using two fields that separately control the evolution of the bra and the ket of the density matrix. A closed hierarchy is derived for the Green's function, the self-energy, the screened potential, the polarization, and the vertex function, all expressed as Keldysh matrices in Liouville space.

Calculating molecular Rydberg states using the one-particle Green’s function: Application to HCO and C(NH2)3

A simple but accurate and computationally efficient method for routine ab initio calculations of molecular Rydberg states is described. The method, which can be applied to Rydberg states associated with a nondegenerate ion core, consists in the self-consistent solution of an effective one-electron problem. First, the restricted Hartree-Fock problem of the ion core is solved. The orbital energies and certain two-electron Coulomb matrix elements with respect to the molecular orbital basis are then used to construct an energy-dependent many-body correction to the Hartree-Fock mean field. This correction is derived from the Dyson equation satisfied by the one-particle Green's function. The method is applied to calculate Rydberg potential-energy curves of HCO. The presented data confirm and extend recent large-scale multireference configuration-interaction calculations and help develop a detailed theoretical description of the astrophysically important dissociative recombination of a low-energy electron with HCO(+). As further illustration of the utility of the method, the first ab initio calculations of the excited states of an electron bound to the guanidinium cation [C(NH(2))(3)](+) are reported.

Probing the Shape and Stereochemistry of Molecular Orbitals in Locally Flexible Aromatic Chains: A Penning Ionization Electron Spectroscopy and Green's Function Study of the Electronic Structure of Biphenyl

We report on the results of an exhaustive study of the interplay between the valence electronic structure, the topology and reactivity of orbitals, and the molecular structure of biphenyl by means of Penning ionization electron spectroscopy in the gas phase upon collision with metastable He*(2(3)S) atoms. The measurements are compared with one-particle Green's function calculations of one-electron and shake-up valence ionization spectra employing the third-order algebraic diagrammatic construction scheme [ADC(3)]. Penning ionization intensities are also analyzed by means of the exterior electron-density model and comparison with photoelectron spectra: in contrast with the lines originating from sigma orbitals, ionization lines belonging to the pi-band system have large Penning ionization cross sections due to their greater extent outside the molecular van der Waals surface. The involved chemi-ionization processes are further experimentally investigated using collision-energy-resolved Penning ionization electron spectroscopy. The cross sections of pi-ionization bands exhibit a markedly negative collision-energy dependence and indicate that the interaction potential that prevails between the molecule and the He*(2(3)S) atom is strongly attractive in the pi-orbital region. On the other hand, the partial ionization cross sections pertaining to sigma-ionization channels are characterized by more limited collision-energy dependencies, as a consequence of rather repulsive interactions within the sigma-orbital region. A comparison of ADC(3) simulations with the Penning ionization electron spectra and UV photoelectron spectra measured by Kubota et al. [Chem. Phys. Lett. 1980, 74, 409] on thin films of biphenyl deposited at 170 and 109 K on copper demonstrates that biphenyl molecules lying at the surface of polycrystalline layers adopt predominantly a planar configuration, whereas within an amorphous sample most molecules have twisted structures similar to those prevailing in the gas phase.

Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach

An earlier proposed propagator method for the treatment of molecular ionization is tested in first applications. The method referred to as the non-Dyson third-order algebraic-diagrammatic construction [nD-ADC(3)] approximation for the electron propagator represents a computationally promising alternative to the existing Dyson ADC(3) method. The advantage of the nD-ADC(3) scheme is that the (N+/-1)-electronic parts of the one-particle Green's function are decoupled from each other and the corresponding equations can be solved separately. For a test of the method the nD-ADC(3) results for the vertical ionization transitions in C(2)H(4), CO, CS, F(2), H(2)CO, H(2)O, HF, N(2), and Ne are compared with available experimental and theoretical data including results of full configuration interaction (FCI) and coupled cluster computations. The mean error of the nD-ADC(3) ionization energies relative to the experimental and FCI results is about 0.2 eV. The nD-ADC(3) method, scaling as n(5) with the number of orbitals, requires the solution of a relatively simple Hermitian eigenvalue problem. The method renders access to ground-state properties such as dipole moments. Moreover, also one-electron properties of (N+/-1) electron states can now be studied as a consequence of a specific intermediate-state representation (ISR) formulation of the nD-ADC approach. Corresponding second-order ISR equations are presented.

Accounting for many-body correlation effects in the calculation of the valence band photoelectron emission spectra of ferromagnets

The influence of dynamical correlation effects on the valence band photoelectron emission of ferromagnetic Fe, Co and Ni has been investigated. Angle-resolved as well as angle-integrated valence band photoelectron emission spectra were calculated on the basis of the one-particle Green's function, which was obtained by using the fully relativistic Korringa–Kohn–Rostoker method. The correlation effects have been included in terms of the electronic self-energy which was calculated self-consistently within Dynamical Mean-Field Theory (DMFT). In addition a theoretical approach to calculate high-energy angle-resolved valence band photoelectron emission spectra is presented.

D-wave pairing in lightly doped Mott insulators

We define a suitable quantity ${Z}_{c}$ that measures the pairing strength of two electrons added to the ground-state wave function by means of the anomalous part of the one-particle Green's function. ${Z}_{c}$ discriminates between systems described by one-electron states, like ordinary metals and band insulators, for which ${Z}_{c}=0$, and systems where the single particle picture does not hold, like superconductors and resonating valence bond insulators, for which ${Z}_{c}\ensuremath{\ne}0$. By using a quantum Monte Carlo projection technique for the Hubbard model at $U∕t=4$, a finite ${Z}_{c}$, with $d$-wave symmetry, is found at half filling and in the lightly doped regime, thus emphasizing a qualitatively new feature coming from electronic correlation.

Resistivity induced by a rough surface of thin gold films deposited on mica

A central question regarding thin metallic films is how does the roughness of the film affect its electrical transport properties, when its thickness is comparable to or smaller than the electron mean free path. The drive to build ever-faster circuits generates the drive for miniaturization and VLSI, which poses a pressing need to reach full understanding of electron–rough surface scattering. We review progress in the field that has taken place over the last 5 years. From the theoretical point of view, the so-called mSXW theory [Munoz et al., J. Phys.: Condens. Matter 11 (1999) L299] was recently published. The increase in resistivity induced by electron–surface scattering is computed using Kubo's linear response theory. The conductivity of the film is determined by the spectral function characterizing the one-particle Green's function describing the electron gas confined within the film. The effect of the rough surface is to modify the self-energy of the electron gas. The conductivity of the film turns out to depend on the height–height autocorrelation function (ACF) that describes the rough surface. It can be written in a closed form if the ACF is described either by a Gaussian or by an exponential. From the experimental point of view, the tendency to use parameters provided by theory as quantities that must be fitted to describe thin-film resistivity data has been replaced by direct measurements of the surface roughness. The first measurement of the ACF of the rough surface of a 70-nm thick gold film deposited on mica was recently published [Munoz et al., Phys. Rev. B 62 (2000) 4686]. The measurement was performed with a scanning tunneling microscope (STM). Using the data recorded with the STM and the mSXW theory, we reproduced the thickness as well as the temperature dependence of the best resistivity data available for gold films on mica. Theory reproduced the data to within a few percent without adjustable parameters. We report also the first measurement of the increase in resistivity induced by electron–surface scattering in gold films deposited on mica, performed at low temperatures and high magnetic fields.

Valence One-Electron and Shake-Up Ionization Bands of Polycyclic Aromatic Hydrocarbons. III. Coronene, 1.2,6.7-Dibenzopyrene, 1.12-Benzoperylene, Anthanthrene

A comprehensive theoretical study of the He(I) UV photoionization spectra of coronene, 1.2,6.7-dibenzopyrene, 1.12-benzoperylene, and anthanthrene up to electron binding energies of ∼18 eV is presented with the aid of one-particle Green's function calculations performed using the outer-valence Green's function (OVGF) approach and the third-order algebraic-diagrammatic construction [ADC(3)] scheme, using Dunning's correlation-consistent polarized valence basis set of double-ζ quality and the 6-31G basis set, respectively. The deviations from the one-electron OVGF/cc-pVDZ binding energies and experimental results most generally do not exceed 0.3 eV. OVGF/cc-pVDZ pole strengths smaller than 0.85 systematically corroborate a breakdown of the orbital (or one-electron) picture of ionization at the ADC(3)/6-31G level. A comparison has been made with calculations of the lowest doublet−doublet excitation energies of the related radical cations, by means of time-dependent density functional theory (TDDFT) and the Becke−Lee−Yang−Parr (BLYP) functional: Because of systematic and significant underestimations of the lowest [π0* ← σ] transition energies in the cations, this approach has led to erroneous identifications of the σ-ionization onset of the neutral molecules.

Density-of-states picture and stability of ferromagnetism in the highly correlated Hubbard model

The problem of stability of saturated and non-saturated ferromagnetism in the Hubbard model is considered in terms of the one-particle Green's functions. Approximations by Edwards and Hertz and some versions of the self-consistent approximations based on the 1/z-expansion are considered. The account of longitudinal fluctuations turns out to be essential for description of the non-saturated state. The corresponding pictures of density of states are obtained. "Kondo" density-of-states singularities owing to spin-flip processes are analyzed. The critical electron concentrations for instabilities of saturated ferromagnetism and paramagnetic state are calculated for various lattices. Drawbacks of various approximations are discussed. A comparison with the results of previous works is performed.

Optical conductivity in the “hot spots” 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, dominating within the regions around “hot spots” on the Fermi surface. A system of recurrence equations is constructed both for one-particle Green's function and vertex part, describing electron interaction with an external field, which takes into account all Feynman graphs for electron scattering these (Gaussian) 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.

Metal-insulator transition in the Hubbard model: a simple description including the Kondo effect

The electron spectrum structure in the half-filled Hubbard model is considered in terms of the one-particle Green's functions within many-electron representation. A simple analytical generalization of the single-site Hubbard-III approximation is obtained, which takes into account the Fermi excitations (Kondo terms). The problem of the metal-insulator transition is investigated. The occurrence of a three-peak density-of-states structure including the "Kondo" peak at the Fermi level is discussed. A comparison with large-d calculations is performed.

The one-particle Green's function method in the Dirac-Hartree-Fock framework. I. Second-order valence ionization energies of Ne through Xe.

The one-particle Green's function theory in its various implementations is a well-established many-body approach for the calculation of electron ionization and attachment energies in atoms and molecules. In order to describe not only scalar-relativistic effects but also spin-orbit splitting on an equal footing an embedding of this theory in the four-component framework was carried out and fully relativistic ionization energies of the noble gas atoms Ne through Xe were calculated using the second-order algebraic diagrammatic construction [ADC2] approximation scheme. Comparison with nonrelativistic ADC2 results and experimental data was made.

Spectral moments in the homogeneous electron gas

We present calculations of the lowest three moments of the spectral function of the one-particle Green's function of the unpolarized three-dimensional homogeneous electron gas, which are related to the exact ground-state properties via commutation relations. The moments are, in turn, related to the coefficients in the expansion of the self-energy in inverse powers of the frequency. The zeroth-order term in this expansion can be written in terms of the momentum distribution function, while the first-order term consists of a local term which can be written in terms of the pair correlation function or static structure factor, and a nonlocal term. We use data from diffusion quantum Monte Carlo calculations to evaluate the zeroth-order term and the local part of the first-order term. We have also examined local-field approximations to the self-energy, finding that they do not affect the zeroth-order term in the high-energy expansion, but they substantially alter the first-order term. The nonlocal part of the second-order term has been evaluated using a wave function consisting of a single determinant of plane waves. Our results provide additional benchmarks for self-energy theories of the homogeneous electron gas.

One-Dimensional Proton Conductor with Strong Short-Range Interactions

The energy spectrum of one-dimensional proton conductor described by fermionic model is investigated. The method that allows short-range proton interactions to be taken into account exactly is developed. One-particle proton Green's function is obtained by solving the Larkin equation, while the irreducible Larkin part is calculated in approximation which takes into account the simplest proton scattering processes. It appears that the proton energy spectrum has a band structure and consists of the four groups of the bands. Investigation of the edges of the energy bands and the chemical potential behaviour at different proton concentrations is performed.

Poor screening and nonadiabatic superconductivity in correlated systems

In this paper we investigate the role of the electronic correlation on the hole doping dependence of electron-phonon and superconducting properties of cuprates. We introduce a simple analytical expression for the one-particle Green's function in the presence of electronic correlation and we evaluate the reduction of the screening properties as the electronic correlation increases by approaching half filling. The poor screening properties play an important role within the context of the nonadiabatic theory of superconductivity. We show that a consistent inclusion of the reduced screening properties in the nonadiabatic theory can account in a natural way for the ${T}_{c}\ensuremath{-}\ensuremath{\delta}$ phase diagram of cuprates. Experimental evidences are also discussed.

Recursion method and one-hole spectral function of the Majumdar-Ghosh model

We consider the application of the recursion method to the calculation of one-particle Green's functions for strongly correlated systems and propose a new way how to extract the information about the infinite system from the exact diagonalisation of small clusters. Comparing the results for several cluster sizes allows us to establish those Lanczos coefficients that are not affected by the finite size effects and provide the information about the Green's function of the macroscopic system. The analysis of this 'bulk-related' subset of coefficients supplemented by alternative analytic approaches allows to infer their asymptotic behaviour and to propose an approximate analytical form for the 'terminator' of the Green's function continued fraction expansion for the infinite system. As a result, the Green's function acquires the branch cut singularity corresponding to the incoherent part of the spectrum. The method is applied to the spectral function of one-hole in the Majumdar-Ghosh model (the one-dimensional $ t-J-J^{\prime}$ model at $J^{\prime}/J=1/2$). For this model, the branch cut starts at finite energy $\omega_0$, but there is no upper bound of the spectrum, corresponding to a linear increase of the recursion coefficients. Further characteristics of the spectral function are band gaps in the middle of the band and bound states below $\omega_0$ or within the gaps. The band gaps arise due to the period doubling of the unit cell and show up as characteristic oscillations of the recursion coefficients on top of the linear increase.

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.

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.