One-electron Green Research Articles

Improved quasiparticle self-consistent electronic band structure and excitons in β−LiGaO2

The band structure of $\beta$-LiGaO$_2$ is calculated using the quasiparticle self-consistent QS$G\hat W$ method where the screened Coulomb interaction $\hat W$ is evaluated including electron-hole interaction ladder diagrams and $G$ is the one-electron Green's function. Improved convergence compared to previous calculations leads to a significantly larger band gap of about 7.0 eV. However, exciton binding energies are found to be large and lead to an exciton gap of about 6.0 eV if also a zero-point-motion correction of about $-0.4$ eV is included. These results are in excellent agreement with recent experimental results on the onset of absorption. Besides the excitons observed thus far, the calculations indicate the existence of a Rydberg-like series of exciton excited states, which is however modified from the classical Wannier exciton model by the anisotropies of the material and the more complex mixing of Bloch states in the excitons resulting from the Bethe-Salpeter equation. The exciton fine structure and the exciton wave functions are visualized and analyzed in various ways.

AbInitio Multiplet-Plus-Cumulant Approach for Correlation Effects in X-Ray Photoelectron Spectroscopy.

The treatment of electronic correlations in open-shell systems is among the most challenging problems of condensed matter theory. Current approximations are only partly successful. Ligand-field multiplet theory has been widely successful in describing intra-atomic correlation effects in x-ray spectra, but typically ignores itinerant states. The cumulant expansion for the one-electron Green's function has been successful in describing shake-up effects but ignores atomic multiplets. More complete methods, such as dynamic mean-field theory can be computationally demanding. Here, we show that separating the dynamic Coulomb interactions into local and longer-range parts with abinitio parameters yields a combined multiplet-plus-cumulant approach that accounts for both local atomic multiplets and satellite excitations. The approach is illustrated in transition metal oxides and explains the multiplet peaks, charge-transfer satellites, and distributed background features observed in XPS experiment.

Real-Time Equation-of-Motion CCSD Cumulant Green's Function.

Many-body excitations in X-ray photoemission spectra have been difficult to simulate from first principles. We have recently developed a cumulant-based one-electron Green's function method using the real-time coupled-cluster-singles equation-of-motion approach (RT-EOM-CCS) that provides a general framework for treating these problems. Here we extend this approach to include double excitations in the ground-state energy and in the coupled cluster amplitudes, which have been implemented using subroutines generated by the Tensor Contraction Engine (TCE). As in the case of the singles approximation, RT-EOM-CCSD yields a nonperturbative cumulant form of the Green's function in terms of the time-dependent cluster amplitudes, adding nonlinear corrections to the traditional cumulant forms. The extended approach is applied to the core-hole spectral function for small molecular systems. We find that, when core-optimized basis sets are used, the doubles contributions reduce the mean absolute errors in the core binding energies of the 10e systems from 0.8 to 0.3 eV. They also significantly improve the quasiparticle-satellite gap by reducing its overestimation from about 3-5 to about 0-1 eV in CH4, NH3, and H2O, and also improving the overall shape of the satellite features. Finally, we demonstrate the application of the new implementation to the larger, classical XPS ESCA series of molecules and show that the singles approximation can be paired with a modest basis set to study carbon speciation.

Real-Time Coupled-Cluster Approach for the Cumulant Green's Function.

Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states and spectra. Here, we develop the cumulant form of the one-electron Green's function using a real-time coupled-cluster equation-of-motion approach, in an extension of our previous study (Rehr J.; et al. J. Chem. Phys. 2020, 152, 174113). The approach yields a nonperturbative expression for the cumulant in terms of the solution to a set of coupled first-order, nonlinear differential equations. The method thereby adds nonlinear corrections to traditional cumulant methods, which are linear in the self-energy. The approach is applied to the core-hole Green's function and is illustrated for a number of small molecular systems. For these systems, we find that the nonlinear contributions yield significant improvements, both for quasiparticle properties such as core-level binding energies and for inelastic losses that correspond to satellites observed in photoemission spectra.

A Correlated Source-Sink-Potential Model Consistent with the Meir-Wingreen Formula.

We model a molecular device as a molecule attached to a set of leads treated at the tight-binding level, with the central molecule described to any desired level of electronic structure theory. Within this model, in the absence of electron-phonon interactions, the Landauer-Büttiker part of the Meir-Wingreen formula is shown to be sufficient to describe the transmission factor of the correlated device. The key to this demonstration is to ensure that the correlation self-energy has the same functional form as the exact correlation self-energy. This form implies that nonsymmetric contributions to the Meir-Wingreen formula vanish, and hence, conservation of current is achieved without the need for Green's Function self-consistency. An extension of the Source-Sink-Potential (SSP) approach gives a computational route to the calculation and interpretation of electron transmission in correlated systems. In this picture, current passes through internal molecular channels via resonance states with complex-valued energies. Each resonance state arises from one of the states in the Lehmann expansion of the one-electron Green's function, hole conduction derived from ionized states, and particle conduction from attached states. In the correlated device, the dependence of transmission on electron energy is determined by four structural polynomials, as it was in the tight-binding (Hückel) version of the SSP method. Hence, there are active and inert conduction channels (in the correlated case, linked to Dyson orbitals) governed by a set of selection rules that map smoothly onto the simplest picture.

Satellite band structure in silicon caused by electron-plasmon coupling

We report the first angle-resolved photoemission measurement of the wave-vector dependent plasmon satellite structure of a three-dimensional solid, crystalline silicon. In sharp contrast to nanomaterials, which typically exhibit strongly wave-vector dependent, low-energy plasmons, the large plasmon energy of silicon facilitates the search for a plasmaron state consisting of resonantly bound holes and plasmons and its distinction from a weakly interacting plasmon-hole pair. Employing a first-principles theory, which is based on a cumulant expansion of the one-electron Green's function and contains significant electron correlation effects, we obtain good agreement with the measured photoemission spectrum for the wave-vector dependent dispersion of the satellite feature, but without observing the existence of plasmarons in the calculations.

Cumulant expansion for phonon contributions to the electron spectral function

We describe an approach for calculations of phonon contributions to the electron spectral function, including both quasiparticle properties and satellites. The method is based on a cumulant expansion for the retarded one-electron Green's function and a many-pole model for the electron self-energy. The electron-phonon couplings are calculated from the Eliashberg functions, and the phonon density of states is obtained from a Lanczos representation of the phonon Green's function. Our calculations incorporate ab initio dynamical matrices and electron-phonon couplings from the density functional theory code ABINIT. Illustrative results are presented for several elemental metals and for Einstein and Debye models with a range of coupling constants. These are compared with experiment and other theoretical models. Estimates of corrections to Migdal's theorem are obtained by comparing with leading order contributions to the self-energy, and are found to be significant only for large electron-phonon couplings at low temperatures.

Cumulant expansion of the retarded one-electron Green function

The cumulant expansion is a powerful approach for including correlation effects in electronic structure calculations beyond the $GW$ approximation. However, the expansion is not generally valid, as current implementations ignore terms that mix particle and hole states and lead to partial occupation numbers of one-electron states. These limitations are corrected here using a cumulant expansion of the retarded one-electron Green's function that includes both particle and hole contributions. The approach provides a consistent framework that improves on the $GW$ approximation to the spectral function without additional computational effort. The method is illustrated with results for the homogeneous electron gas and comparisons to experiment and other methods.

Extension of many-body theory and approximate density functionals to fractional charges and fractional spins

The exact conditions for density functionals and density matrix functionals in terms of fractional charges and fractional spins are known, and their violation in commonly used functionals has been shown to be the root of many major failures in practical applications. However, approximate functionals are designed for physical systems with integer charges and spins, not in terms of the fractional variables. Here we develop a general framework for extending approximate density functionals and many-electron theory to fractional-charge and fractional-spin systems. Our development allows for the fractional extension of any approximate theory that is a functional of G(0), the one-electron Green's function of the non-interacting reference system. The extension to fractional charge and fractional spin systems is based on the ensemble average of the basic variable, G(0). We demonstrate the fractional extension for the following theories: (1) any explicit functional of the one-electron density, such as the local density approximation and generalized gradient approximations; (2) any explicit functional of the one-electron density matrix of the non-interacting reference system, such as the exact exchange functional (or Hartree-Fock theory) and hybrid functionals; (3) many-body perturbation theory; and (4) random-phase approximations. A general rule for such an extension has also been derived through scaling the orbitals and should be useful for functionals where the link to the Green's function is not obvious. The development thus enables the examination of approximate theories against known exact conditions on the fractional variables and the analysis of their failures in chemical and physical applications in terms of violations of exact conditions of the energy functionals. The present work should facilitate the calculation of chemical potentials and fundamental bandgaps with approximate functionals and many-electron theories through the energy derivatives with respect to the fractional charge. It should play an important role in developing accurate approximate density functionals and many-body theory.

New Method to Deal with Three-Dimensional Electron Gas with a Strong Correlation Effect

Similar to the bosonization method in one dimension, we divide the electron operators in phase space into two component operators, and study three-dimensional homogeneous electron gas with a strong correlation effect. We apply this method to calculate the pair distribution function g(r = 0, rs) and the renormalization coefficient of the one-electron Green's function Z(kF) (ZF), and show that it has great advantages of succinctness and efficiency for studying one- and three-dimensional systems with a strong correlation effect. This method can be applied to investigate interaction quenches in ultracold atomic gases.

General derivation of the Green's functions for the atomic approach of the Anderson model: application to a single electron transistor (SET)

We consider the cumulant expansion of the periodic Anderson model (PAM) in the case of a finite electronic correlation U, employing the hybridization as perturbation, and obtain a formal expression of the exact one-electron Green's function (GF). This expression contains effective cumulants that are as difficult to calculate as the original GF, and the atomic approach consists in substituting the effective cumulants by the ones that correspond to the atomic case, namely by taking a conduction band of zeroth width and local hybridization. In a previous work (T. Lobo, M. S. Figueira, and M. E. Foglio, Nanotechnology 21, 274007 (2010)10.1088/0957-4484/21/27/274007) we developed the atomic approach by considering only one variational parameter that is used to adjust the correct height of the Kondo peak by imposing the satisfaction of the Friedel sum rule. To obtain the correct width of the Kondo peak in the present work, we consider an additional variational parameter that guarantees this quantity. The two constraints now imposed on the formalism are the satisfaction of the Friedel sum rule and the correct Kondo temperature. In the first part of the work, we present a general derivation of the method for the single impurity Anderson model (SIAM), and we calculate several density of states representative of the Kondo regime for finite correlation U, including the symmetrical case. In the second part, we apply the method to study the electronic transport through a quantum dot (QD) embedded in a quantum wire (QW), which is realized experimentally by a single electron transistor (SET). We calculate the conductance of the SET and obtain a good agreement with available experimental and theoretical results.

Transport through small world networks

We numerically investigate the transport properties through a system where small world networks are added to a one-dimensional chain. One-electron Green’s function method is applied to standard tight-binding Hamiltonians on networks, modeled as (i) adding connections between any two nonadjacent random sites in the chain, (ii) introducing finite one-dimensional chains between any pair of such connected sites, and (iii) attaching finite dangling chains at random sites in the chain. Due to the small world bonds and dangling conduction paths, the systems have irregular geometrical shapes, leading to quenched disordered systems. We consider the qualitative influence of the small world bonds and dangling bonds on the transmittance and find that the systems exhibit a strong energy dependence on the transmittance, with strong sample-to-sample fluctuations.

One-electron Green’s function of multilayer magnetic systems

We propose a method for constructing a symmetric one-electron Green’s function of a magnetic multilayer system with an arbitrary direction of homogeneous magnetization of magnetic layers. We show that the constructed Green’s function allows imposing special boundary conditions.

Transport properties of an intermediate-valence model ofTl2Mn2O7

The appearance of colossal magnetoresistance (CMR) in ${\mathrm{Tl}}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ has stimulated many recent studies of the pyrochlore family of compounds ${\mathrm{A}}_{2}{\mathrm{B}}_{2}{\mathrm{O}}_{7}$. The double exchange model of Zener does not describe the CMR in ${\mathrm{Tl}}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$, because its metallic conductivity cannot be explained by doping. Here we employ Hubbard operators to reformulate the intermediate valence model used by Ventura and Alascio [Phys. Rev. B 56, 14533 (1997)] to describe the electronic structure and transport properties of this compound. Following Foglio and Figueira [Phys. Rev. B 62, 7882, (2000)] we use approximate one-electron Green's functions to calculate the thermopower and the static and dynamic conductivity of ${\mathrm{Tl}}_{2}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ for several magnetic fields. A qualitative agreement was obtained with the experimental measurements of those properties. Although the agreement is far from perfect, these quantities are fairly well described by the same set of system parameters.

Relativistic central-field Green's functions for the Ratip package

From perturbation theory, Green’s functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green’s functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green’s functions also for atoms and ions other than the hydrogen-like ions, here we provide an extension to the R ATIP program which supports the computation of relativistic (one-electron) Green’s functions in an—arbitrarily given—central-field potential V(r). Different computational modes have been implemented to define these effective potentials and to generate the radial Green’s functions for all bound-state energies E< 0. In addition, care has been taken to provide a user-friendly component of the RATIP package by utilizing features of the Fortran 90/95 standard such as data structures, allocatable arrays, or a module-oriented design. Program summary

Single-site and multisite resonant photoemission theory studied by Keldysh Green’s functions

Single (on-site) and multisite (multiatom) resonant photoemission (MARPE) processes are systematically studied by use of nonrelativistic Keldysh Green's function theory. We apply skeleton expansion in terms of renormalized one-electron Green's functions. In this theoretical framework we discuss the importance of the radiation field screening and the dynamically polarized part ${W}_{p}$ in the screened Coulomb propagator. The radiation field screening plays a crucial role in observing the MARPE: We obtain expressions of the resonant processes (on site and multiatom) in terms of an x-ray absorption factor whose imaginary part is proportional to the x-ray absorption intensity. If we neglect ${W}_{p}$, the calculated MARPE intensity is much smaller than the observed one. We also point out the importance of the structure factor in the MARPE analyses. Typically highly symmetric atomic arrangement around a photoemitting atom provides us with no MARPE signal, but outermost oxygen atoms give rise to considerably strong MARPE because of symmetry lowering. On the other hand, low symmetric systems like rutile, perovskite, and $\ensuremath{\alpha}$-alumina $({\mathrm{Fe}}_{2}{\mathrm{O}}_{3})$ structures can give rise to finite MARPE even in the case of photoemission from inner layers of perfect crystals. The polarization dependence of the MARPE follows the same selection rule as the main photoemission processes, whereas the O $1s$ MARPE from ${\mathrm{Fe}}_{2}{\mathrm{O}}_{3}$ shows a rather complicated rule. These specific features of MARPE provide useful local structural information.

Singular dynamics of underscreened magnetic impurity models

We give a comprehensive analysis of the singular dynamics and of the low-energy fixed point of one-channel impurity $s\text{\ensuremath{-}}d$ models with ferromagnetic and underscreened antiferromagnetic couplings. We use the numerical renormalization group (NRG) to perform calculations at $T=0$. The spectral densities of the one-electron Green's functions and t-matrices are found to have very sharp cusps at the Fermi level $(\ensuremath{\omega}=0)$, but do not diverge. The approach of the Fermi level is governed by terms proportional to $1∕{\mathrm{ln}}^{2}(\ensuremath{\omega}∕{T}_{0})$ as $\ensuremath{\omega}\ensuremath{\rightarrow}0$. The scaled NRG energy levels show a slow convergence as $1∕(N+C)$ to their fixed point values, where $N$ is the iteration number and $C$ is a constant dependent on the coupling $J$ from which the low energy scale ${T}_{0}$ can be deduced, with a renormalized coupling $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}(\ensuremath{\omega})=1∕\mathrm{ln}(\ensuremath{\omega}∕{T}_{0})$. We calculate also the dynamical spin susceptibility, and the elastic and inelastic scattering cross sections as a function of $\ensuremath{\omega}$. The inelastic scattering goes to zero as $\ensuremath{\omega}\ensuremath{\rightarrow}0$, as expected for a Fermi liquid, but anomalously slowly compared to the fully screened case. We obtain the asymptotic forms for the phase shifts for elastic scattering of the quasiparticles in the high-spin and low-spin channels. The asymptotic forms found for the one-electron Green's functions and $t$-matrices do not simply correspond to a perturbation expansion in powers of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{J}(\ensuremath{\omega})$.

Static and dynamic conductivity for a model of Tl 2Mn 2O 7

The compound Tl 2Mn 2O 7 exhibits colossal magneto resistance, which is not adequately explained by the double exchange mechanism. We use Hubbard operators to reformulate a previous model of Ventura and Alascio (Phys. Rev. B 56 (1997) 14533), and we obtain approximate one-electron Green's functions (GF) for this model, using a method introduced by Foglio and Figueira (Phys. Rev. B 60 (1999) 11361). With these GF we calculate the static and dynamic conductivity, both with and without applied magnetic fields.

Calculation and interpretation ofK-shell x-ray absorption near-edge structure of transition metal oxides

Simultaneous calculations of both K-edge x-ray-absorption near-edge structure (XANES) and ground-state electronic structure of $3d$ transition-metal oxides are presented. The calculations are based on a self-consistent one-electron real-space Green's-function approach, with many-body effects incorporated in terms of final-state potentials and a complex energy-dependent self-energy. The results are found to be in semiquantitative agreement with experiment at the metal K edges, except at the edge itself where a leading edge peak is found to be systematically low in intensity. A scattering theoretic interpretation is presented, which correlates the structure in the XANES with projected electronic density of states. This interpretation illustrates the crossover from a molecular orbital to a continuum resonance description of excited states. The importance of the core-hole potential in these calculations is also discussed.

Calculation ofΔ(k,ω)for a two-dimensionalt−Jcluster

Using numerical techniques, the diagonal and off-diagonal superconducting one-electron Green's functions are calculated for a two-dimensional (2D) t-J model on a periodic 32-site cluster at low doping. From these Green's functions, the momentum and frequency dependence of the pairing gap $\Delta ({\bf k}, \omega)$ are extracted. It has $d_{x^2-y^2}$ symmetry and exhibits $\omega$-dependent structure which depend upon J/t. We find that the pairing gap persists down to small J/t values. The frequency- and momentum-dependent renormalized energy and renormalization factor are also calculated.