One-particle Green Function Research Articles

POLARONIC MECHANISM OF SUPERCONDUCTIVITY IN DOPED FULLERIDE SYSTEMS

A polaronic model of superconductivity in doped fulleride systems is presented. The normal and anomalous one-particle Green's functions are derived for a system with strong electron phonon coupling. The study of collapse of the electron band and the phonon vacuum is presented within the mean-field approximation. Self-consistent equation for the superconductivity order parameter (Δ) is derived using Green's fucntion technique and following Lang and Firsov transformations. Expressions for specific heat, density of states, free energy and critical field based on this model have been derived. The theory is applied to explain the experimental results in the systems K 3 C 60 and Rb 3 C 60. These results are in good agreement with the available experimental data.

Investigation of the molecular conformations of ethanol using electron momentum spectroscopy

The valence electronic structure and momentum-space electron density distributions of ethanol have been investigated with our newly constructed high-resolution electron momentum spectrometer. The measurements are compared to thermally averaged simulations based on Kohn–Sham (B3LYP) orbital densities as well as one-particle Green's function calculations of ionization spectra and Dyson orbital densities, assuming Boltzmann's statistical distribution of the molecular structure over the two energy minima defining the anti and gauche conformers. One-electron ionization energies and momentum distributions in the outer-valence region were found to be highly dependent upon the molecular conformation. Calculated momentum distributions indeed very sensitively reflect the distortions and topological changes that molecular orbitals undergo due to the internal rotation of the hydroxyl group, and thereby exhibit variations which can be traced experimentally. The B3LYP model Kohn–Sham orbital densities are overall in good agreement with the experimental distributions, and closely resemble benchmark ADC(3) Dyson orbital densities. Both approaches fail to quantitatively reproduce the experimental momentum distributions characterizing the highest occupied molecular orbital. Since electron momentum spectroscopy measurements at various electron impact energies indicate that the plane wave impulse approximation is valid, this discrepancy between theory and experiment is tentatively ascribed to thermal disorder, i.e. large-amplitude and thermally induced dynamical distortions of the molecular structure in the gas phase.

Implementation and use of a direct, partially integral‐driven non‐Dyson propagator method for molecular ionization

The Green's function ADC(3) scheme has been for many years a successful method to predict theoretically the ionization (and electron affinity) spectrum of molecules. However, a dramatic enhancement of the method's power has come only recently, with the development of an approximation method to the one-particle Green's function which does not make direct use of the Dyson equation. In the present work, we present an efficient computer implementation of this novel approach, with first comparative tests demonstrating its enormous computational advantage over the conventional approach.

Phonon-assisted tunneling and shot noise in double barrier structures in a longitudinal magnetic field

The phonon-assisted resonant tunneling is studied for the double barrier structures in a longitudinal magnetic field. Using the scattering matrix approach with an appropriate one-particle Green's function we are able to calculate the current and the zero frequency shot noise power spectrum in a large range of the magnetic field and to any order of the electron–phonon interaction. Obtained results describe well the relevant experimental data and provide new suggestions for further examinations.

Plasmons and the spectral function of graphene

We report a theoretical study of the influence of electron-electron interactions on the one-particle Green's function of a doped graphene sheet based on the random-phase approximation and on graphene's massless Dirac equation continuum model. We find that states near the Dirac point interact strongly with plasmons with a characteristic frequency ${\ensuremath{\omega}}_{\mathrm{pl}}^{\ensuremath{\star}}$ that scales with the sheet's Fermi energy and depends on its interaction coupling constant ${\ensuremath{\alpha}}_{\mathrm{gr}}$, partially explaining prominent features of recent angle-resolved photoemission spectroscopy data.

Recursion and Growth Estimates in Renormalizable Quantum Field Theory

In this paper we show that there is a Lipatov bound for the radius of convergence for superficially divergent one-particle irreducible Green functions in a renormalizable quantum field theory if there is such a bound for the superficially convergent ones. In the nonnegative case the radius of convergence turns out to be min{ρ,1/b 1}, where ρ is the bound on the convergent ones, the instanton radius, and b 1 the first coefficient of the β-function, while in general it is bounded by the above.

Study of the photoelectron and electron momentum spectra of cyclopentene using benchmark Dyson orbital theories

A complete study of the valence electronic structure and related electronic excitation properties of cyclopentene in its C(s) ground state geometry is presented. Ionization spectra obtained from this compound by means of photoelectron spectroscopy (He I and He II) and electron momentum spectroscopy have been analyzed in details up to electron binding energies of 30 eV using one-particle Green's function (1p-GF) theory along with the outer-valence (OVGF) and the third-order algebraic diagrammatic construction [ADC(3)] schemes. The employed geometries derive from DFT/B3LYP calculations in conjunction with the aug-cc-pVTZ basis set, and closely approach the structures inferred from experiments employing microwave spectroscopy or electron diffraction in the gas phase. The 1p-GF/ADC(3) calculations indicate that the orbital picture of ionization breaks down at electron binding energies larger than approximately 17 eV in the inner-valence region, and that the outer-valence 7a' orbital is also subject to a significant dispersion of the ionization intensity over shake-up states. This study confirms further the rule that OVGF pole strengths smaller than 0.85 foretell a breakdown of the orbital picture of ionization at the ADC(3) level. Spherically averaged (e, 2e) electron momentum distributions at an electron impact energy of 1200 eV that were experimentally inferred from an angular analysis of EMS intensities have been interpreted by comparison with accurate simulations employing ADC(3) Dyson orbitals. Very significant discrepancies were observed with momentum distributions obtained from several outer-valence ionization bands using standard Kohn-Sham orbitals.

Form factors and correlation functions of an interacting spinless fermion model

Introducing the fermionic R-operator and solutions of the inverse scattering problem for local fermion operators, we derive a multiple integral representation for zero-temperature correlation functions of a one-dimensional interacting spinless fermion model. Correlation functions particularly considered are the one-particle Green's function and the density–density correlation function both for any interaction strength and for arbitrary particle densities. In particular for the free fermion model, our formulae reproduce the known exact results. Form factors of local fermion operators are also calculated for a finite system.

A general approach to bosonization

We summarize recent developments in the field of higher dimensional bosonization made by Setlur and collaborators and propose a general formula for the field operator in terms of currents and densities in one dimension using a new ingredient known as a ‘singular complex number’. Using this formalism, we compute the Green function of the homogeneous electron gas in one spatial dimension with short-range interaction leading to the Luttinger liquid and also with long-range interactions that lead to a Wigner crystal whose momentum distribution computed recently exhibits essential singularities. We generalize the formalism to finite temperature by combining with the author’s hydrodynamic approach. The one-particle Green function of this system with essential singularities cannot be easily computed using the traditional approach to bosonization which involves the introduction of momentum cutoffs, hence the more general approach of the present formalism is proposed as a suitable alternative.

Influence of defects on the absorption edge of InN thin films: The band gap value

We investigate the optical-absorption spectra of InN thin films whose electron density varies from $\ensuremath{\sim}{10}^{17}\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}\ensuremath{\sim}{10}^{21}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The low-density films are grown by molecular-beam-epitaxy deposition while highly degenerate films are grown by plasma-source molecular-beam epitaxy. The optical-absorption edge is found to increase from $0.61\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1.90\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ as the carrier density of the films is increased from low to high density. Since films are polycrystalline and contain various types of defects, we discuss the band gap values by studying the influence of electron degeneracy, electron-electron, electron-ionized impurities, and electron-LO-phonon interaction self-energies on the spectral absorption coefficients of these films. The quasiparticle self-energies of the valence and conduction bands are calculated using dielectric screening within the random-phase approximation. Using one-particle Green's function analysis, we self-consistently determine the chemical potential for films by coupling equations for the chemical potential and the single-particle scattering rate calculated within the effective-mass approximation for the electron scatterings from ionized impurities and LO phonons. By subtracting the influence of self-energies and chemical potential from the optical-absorption edge energy, we estimate the intrinsic band gap values for the films. We also determine the variations in the calculated band gap values due to the variations in the electron effective mass and static dielectric constant. For the lowest-density film, the estimated band gap energy is $\ensuremath{\sim}0.59\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, while for the highest-density film, it varies from $\ensuremath{\sim}0.60\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}\ensuremath{\sim}0.68\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ depending on the values of electron effective mass and dielectric constant.

Renormalization group treatment of spin-charge separation effects

We examine the spin-charge separation effects which are manifest in the Tomonaga-Luttinger model (TLM) in the framework of the field theoretical renormalization group (RG) theory. Initially, it is shown how far one can go with the perturbative RG method. Following that, we take into full account the Ward identities [Phys. Rev. 78, 172 (1950)]. This allows us to calculate the spin and charge velocities exactly. Next, we construct the Callan-Symanzik equation (CSE) [Phys. Rev. D 5, 3202 (1972); Commun. Math. Phys. 23, 49 (1971)] for the renormalized fermionic one-particle Green's function. Finally, making use of those perturbative results for the TLM and taking the two characteristic velocities as basic ingredients, we solve this CSE in qualitative good agreement with the exact result.

Measuring the One-Particle Excitations of Ultracold Fermionic Atoms by Stimulated Raman Spectroscopy

We propose a Raman spectroscopy technique which is able to probe the one-particle Green function, the Fermi surface, and the quasiparticles of a gas of strongly interacting ultracold atoms. We give quantitative examples of experimentally accessible spectra. The efficiency of the method is validated by means of simulated images for the case of a usual Fermi liquid as well as for more exotic states: specific signatures of, e.g., a d-wave pseudogap are clearly visible.

Imaging Momentum Orbital Densities of Conformationally Versatile Molecules: A Benchmark Theoretical Study of the Molecular and Electronic Structures of Dimethoxymethane

The main purpose of the present work is to predict from benchmark many-body quantum mechanical calculations the results of experimental studies of the valence electronic structure of dimethoxymethane employing electron momentum spectroscopy, and to establish once and for all the guidelines that should systematically be followed in order to reliably interpret the results of such experiments on conformationally versatile molecules. In a first step, accurate calculations of the energy differences between stationary points on the potential energy surface of this molecule are performed using Hartree-Fock (HF) theory and post-HF treatments of improving quality (MP2, MP3, CCSD, CCSD(T), along with basis sets of increasing size. This study focuses on the four conformers of this molecule, namely the trans-trans (TT), trans-gauche (TG), gauche-gauche (G+G+), and gauche-gauche (G+G-) structures, belonging to the C2v, C1, C2, and Cs symmetry point groups, respectively. A focal point analysis supplemented by suited extrapolations to the limit of asymptotically complete basis sets is carried out to determine how the conformational energy differences at 0 K approach the full CI limit. In a second step, statistical thermodynamics accounting for hindered rotations is used to calculate Gibbs free energy corrections to the above energy differences, and to evaluate the abundance of each conformer in the gas phase. It is found that, at room temperature, the G+G+ species accounts for 96% of the conformational mixture characterizing dimethoxymethane. In a third step, the valence one-electron and shake-up ionization spectrum of dimethoxymethane is analyzed according to calculations on the G+G+ conformer alone by means of one-particle Green's function [1p-GF] theory along with the benchmark third-order algebraic diagrammatic construction [ADC(3)] scheme. A complete breakdown of the orbital picture of ionization is noted at electron binding energies above 22 eV. A comparison with available (e,2e) ionization spectra enables us to identify specific fingerprints of through-space orbital interactions associated with the anomeric effect. At last, based on our 1p-GF/ADC(3) assignment of spectral bands, accurate and spherically averaged (e,2e) electron momentum distributions at an electron impact energy of 1200 eV are computed from the related Dyson orbitals. Very significant discrepancies are observed with momentum distributions obtained for several outer-valence levels using standard Kohn-Sham orbitals.

Diffusive magnetotransport in a two-dimensional electron gas in the presence of Rashba spin-orbit interaction

An analytical approach to calculation of the conductivity tensor $\ensuremath{\sigma}$ of a two-dimensional electron system with Rashba spin-orbit interaction (SOI) in an orthogonal magnetic field is proposed. The electron momentum relaxation is assumed to be due to electron scattering by a random field of short-range impurities, which is taken into account in the Born approximation. An exact expression for the one-particle Green's function of an electron with Rasba SOI in an arbitrary magnetic field is suggested. This expression allows us to obtain analytical formulas for the density of states and $\ensuremath{\sigma}$ in the self-consistent Born and ladder approximations, respectively, which hold true in a wide range of magnetic fields, from the weak $({\ensuremath{\omega}}_{c}\ensuremath{\tau}\ensuremath{\ll}1)$ up to the quantizing $({\ensuremath{\omega}}_{c}\ensuremath{\tau}\ensuremath{\gtrsim}1)$ ones. It is shown that in the ladder approximation the Rashba SOI has no effect at all on the conductivity magnitude in the whole range of classical (nonquantizing) magnetic fields. The Shubnikov--de Haas oscillation period is shown to be related to the total charge carrier concentration by the conventional formula, irrespective of the SOI magnitude. A simple equation defining the location of the SdH oscillation beating nodes is obtained. The results are in good agreement with the experimental and recent numerical investigations.

A pseudogap model beyond BCS for the cuprates: the effect of order parameter symmetry,cutoff frequency and band structure

We present an extension of the phenomenological pseudogap model proposed by Rodríguez-Núñez et al (2005 J. Phys.: Condens. Matter 17 323) which relies on the assumption that the self-energy is givenby ΣPG(iωn) = −EG2(k) G0(k,−iωn),where G0(k,iωn) is the one-particle free Green function. Going beyond this mean-field model forthe pseudogap we now take into account fluctuations of the pseudogap asΣPG(iωn) = −EG2(k) GPG(k,−iωn),where GPG(k,iωn) is the pseudogap one-particle Green function and is the value of the pseudogap parameter. We study the combined effect ofα′, the second-nearest neighbour in the band structure () and the cutoff frequency, ωD, on the superconducting critical temperature,Tc, as a function of the number of carriers per site,n. The effectof V/t andωD/t is to increasethe value of Tc/t, while α′ displaces Tc,max/t away from half-filling.

The description of the superconductivity in atomic representation for [formula omitted] model

The diagram technique method for Hubbard operators has been used to describe the superconducting (SC) phase of the t – t ′ – t ″ – J * model. The new exact representation for the matrix one-particle Green's function has been derived. The main peculiarity of the obtained representation lies in the fact that not only anomalous components of the mass operator Σ 0 σ , σ ¯ 0 ( k , i ω m ) but also an anomalous components P 0 σ , σ ¯ 0 ( k , i ω m ) of the matrix strength operators P ^ ( k , i ω m ) are taken into account. In the one-loop approximation all analytical contributions of the normal Σ 0 σ , 0 σ ( k , i ω m ) , P 0 σ , 0 σ ( k , i ω m ) and of the anomalous Σ 0 σ , σ ¯ 0 ( k , i ω m ) , P 0 σ , σ ¯ 0 ( k , i ω m ) components mass and strength operators have been calculated. The Matsubara's frequencies dependence of the anomalous strength operator gave rise to description of the SC-phase by an infinite system of integral equations. Taking into account hoppings of electrons between sites situated within the limits of three coordination spheres this system was solved exactly. The influence of three-site interactions and intensity of hoppings on the existence of SC-phase with d x 2 - y 2 -type of the order parameter symmetry have been analyzed. It has been analyzed also the influence of the normal component P 0 σ , 0 σ ( k , i ω m ) on the function distribution of the Fermi-quasiparticles in the normal phase. It is shown that strong electron correlations give rise to degradation of the Fermi function even if the temperature much less than Fermi energy.

Fermi arcs and hidden zeros of the Green function in the pseudogap state

We investigate the low-energy properties of a correlated metal in the proximity of a Mott insulator within the Hubbard model in two dimensions. We introduce a version of the cellular dynamical mean-field theory using cumulants as the basic irreducible objects. The cumulants are used for reconstructing the lattice quantities from their cluster counterparts. The zero-temperature one-particle Green function is characterized by the appearance of lines of zeros, in addition to a Fermi surface which changes topology as a function of doping. We show that these features are intimately connected to the opening of a pseudogap in the one-particle spectrum and provide a simple picture for the appearance of Fermi arcs.

Green's function study of the one‐electron and shake‐up ionization spectra of unsaturated hydrocarbon cage compounds

The valence one-electron and shake-up ionization spectra of stella-2,6-diene, stella-2,6-dione, bicyclo-[2.2.2]-octane-2,5-dione, and bicyclo-[2.2.1]-heptane-2,5-dione have been exhaustively studied, up to the double ionization threshold and beyond, by means of one-particle Green's function theory. This study is based on calculations employing the outer-valence Green's function and the third-order algebraic diagrammatic construction schemes, along with a variety of basis sets. A comparison is made with available ultraviolet (He I) photoelectron and (e, 2e) electron-impact ionization spectra, with main focus on the identification of spectral fingerprints for cyclic strains and through-bond pi-conjugation. As a byproduct, our results demonstrate that it is impossible to reliably assign complex (e, 2e) ionization spectra by resorting only to Hartree-Fock or Kohn-Sham orbital energies and to the related electron momentum distributions.

Field theory renormalization group: the Tomonaga–Luttinger model revisited

We apply field theoretical renormalization group (RG) methods to describe the Tomonaga-Luttinger model as an important test ground to deal with spin-charge separation effects in higher spatial dimensions. We compute the anomalous dimension associated with the one-particle Green's functions $G_{(a)R}$. We calculate the RG equations for the renormalized forward couplings $g_{2R}$ and $g_{4R}$ up to two-loop order and demonstrate that they don't flow in the vicinities of the Fermi points (FPs). We solve the Callan-Symanzik equation for $G_{(a)R}$ in the neighborhood of the FPs. We calculate the related spectral function and the momentum distribution function at $p=k_{F},p_{0}=\omega$. We compute the renormalized one-particle irreducible function $\Gamma_{(+)R}^{(2)}(p,p_{0}=0;\Lambda)$ and show it carries important spin-charge separation effects in agreement with well known results. Finally we discuss the implementation of the RG scheme taking into account the important simplifications produced by the Ward identities.

A d-wave pseudogap model beyond BCS for the cuprates

One of the most intriguing aspects of high-temperature superconductors is the presence of the pseudogap in the normal and the superconducting phases of the cuprate compounds. Several pseudogap models have been proposed to explain the abnormal properties of the cuprates. One of the recent models (J.J. Rodríguez-Núñez, A.A. Schmidt, H. Beck, J. Phys.: Condens. Matter 17 (2005) 323) relies on the assumption that the self energy is given by ∑ PG ( i ω n ) = - E g 2 ( k ) G 0 ( k ,- i ω n ) , where G 0 ( k , i ω n ) is the one-particle free Green function. Going beyond this mean field model for the pseudogap we now take into account fluctuations of the pseudogap as ∑ PG ( i ω n ) = - E g 2 ( k ) G PG ( k ,- i ω n ) , where G PG ( k , i ω n ) is the one-particle full Green function. We study the combined effect of the band structure and the Debye frequency, ω D , on the superconducting critical temperature, T c , as a function of the number of carriers per site, n.