One-electron Green Research Articles

Difference between the small one-electron gap and the large optical gap in one-, two-, and three-dimensional half-filled Hubbard models

We calculate one-electron Green's functions and light absorption-type two-electron Green's functions for one-, two-, and three-dimensional half-filled Hubbard systems by a quantum Monte-Carlo simulation. It is shown that the one-electron density of state (DOS) has only a small gap while the light absorption spectrum has a relatively wide gap. The one-electron gap in the DOS is at most half as large as the two-electron gap in the light absorption spectrum, though it slightly increases with dimension. Such an apparent difference between two kinds of gaps is characteristic of the exotic insulating state with large quantum fluctuations.

Orbital magnetic susceptibility of the attractive Hubbard model

Our analysis of the orbital magnetic susceptibility χ of the attractive Hubbard model, above the superconducting transition temperature T c, is based on the usual T-matrix approximation to the electronic self-energy. In this framework the one-electron Green's function is coupled to virtual pair fluctuations. The linear response of the electronic current to an external vector potential A , which yields χ, obeys a linear integral equation. The attraction between electrons has three effects: (a) a renormalized group velocity appears in the coupling of the electrons to A ; (b) the electrons interact with each other by exchanging bosonic pair excitations; (c) there is a direct coupling of the virtual pairs to A . The pair contribution to χ has the same structure as the one obtained in a Landau–Ginzburg approach in Gaussian approximation, but differs in some details from the latter.

Models of the pseudogap state of two-dimensional systems

We analyze a number of ``nearly exactly'' solvable models of electronic spectrum of two-dimensional systems with well-developed fluctuations of short range order of ``dielectric'' (e.g. antiferromagnetic) or ``superconducting'' type, which lead to the formation of anisotropic pseudogap state on certain parts of the Fermi surface. We formulate a recurrence procedure to calculate one-electron Green's function which takes into account all Feynman diagrams in perturbation series and is based upon the approximate Ansatz for higher-order terms in this series. Detailed results for spectral densities and density of states are presented. We also discuss some important points concerning the justification of our Ansatz for higher-order contributions.

Pseudogap in the one-electron spectral functions of the attractive Hubbard model

We calculate the one-electron Green's function of the two-dimensional (2D) attractive Hubbard model by coupling the electrons to pair fluctuations. The latter are approximated by homogeneous amplitude fluctuations and phase correlations corresponding to the XY-model. The electronic density of states shows a pseudogap at temperatures well above the transition temperature T c. For a quasi-3D system, a superconducting gap emerges out of the pseudogap below T c.

Landauer Type Approach to Electron Conduction in One-Dimensional Systems and Interaction Effects

Electron conduction in one-dimensional system is investigated explicitly taking into account the reservoirs to which 1D channel is connected at its ends. We calculate the current driven by the chemical potential difference of two reservoirs, using the linear response theory by Kubo. At 0K, the conductance of 1D channel is expressed in terms of one-electron Green's functions even in the presence of the interaction, in contrast to the theory based on Kubo formula, in which two-electron Green's functions are essentially involved. The formalism in this paper provides a new interpretation of Landauer formula. As regards the interaction effects, the conductance of Fermi liquid without potential scattering is 2 e 2 / h , while that of Tomonaga-Luttinger liquid deceases with power low as the length of 1D channel increases.

Spectral properties of quasiparticles in a semiconductor

The one-electron excitation spectrum of the prototype semiconductor Si has been obtained from a first-principles calculation of the spectral-weight function $A(q\ensuremath{\rightarrow},\ensuremath{\omega})$ of the interacting one-electron Green's function. The Dyson equation has been solved with the self-energy operator obtained in the $\mathrm{GW}$ approximation, where the bare propagator $G$ and the \ensuremath{\omega}-dependent screening matrix $W,$ without (random-phase approximation) and with (time-dependent local density approximation) vertex corrections, have been computed within Kohn-Sham--local-density-approximation theory. Positions of quasiparticle peaks (i.e., the ``band structure''), their lifetimes, and satellite (plasmaron) spectral structures are extracted in a broad energy range.

Direct orbital-free calculations using DFT and one-electron Green's functions: applications to atoms

A method based on density functional theory which utilizes the numerical calculation of one-electron Green's function instead of the diagonalization of the Kohn-Sham Hamiltonian is presented. The method is applied to atoms employing the approximation of spherically averaged electron density. The use of rectangular non-uniformly spaced basis functions for the representation of the radial part of the Hamiltonian provides a favourable dependence of the results on numerical parameters and a simple implementation scheme with the computational cost scaling linearly with the number of electrons. The all-electron SCF calculation within the generalized gradient approximation leads to encouraging results for the total and first ionization energies.

One-electron Green's function and electron tunneling in a two-dimensional electron system in a strong magnetic field

We investigate the properties of the one-electron Green's function in an interacting two-dimensional electron system in a strong magnetic field, which describes an electron tunneling into such a system. From finite-size diagonalization, we find that its spectral weight is suppressed near zero energy, reaches a maximum at an energy of about 0.2e 2 ϵl c , and decays exponentially at higher energies. We propose a theoretical model to account for the low-energy behavior. For the case of Coulomb interactions between the electrons, at even-denominator filling factors such as ν = 1 2 , we predict that the spectral weight varies as e ω u |ω| , for ω → 0.

Spectral sum rules for the Tomonaga-Luttinger model.

In connection with recent publications we discuss spectral sum rules for the Tomonaga-Luttinger model without using the explicit result for the one-electron Green's function. They are usefull in the interpretation of recent high resolution photoemission spectra of quasi-one-dimensional conductors. It is shown that the limit of infinite frequency and band cut\-off do not commute. Our result for arbitrary shape of the interaction potential generalizes an earlier discussion by Suzumura. A general analytical expression for the spectral function for wave vectors far from the Fermi wave vector $k_{F}$ is presented. Numerical spectra are shown to illustrate the sum rules.

Tunneling into a two-dimensional electron system in a strong magnetic field.

We investigate the properties of the one-electron Green's function in an interacting two-dimensional electron system in a strong magnetic field, which describes an electron tunneling into such a system. From finite-size diagonalization, we find that its spectral weight is suppressed near zero energy, reaches a maximum at an energy of about 0.2${\mathit{e}}^{2}$/\ensuremath{\epsilon}${\mathit{l}}_{\mathit{c}}$, and decays exponentially at higher energies. We propose a theoretical model to account for the low-energy behavior. For the case of Coulomb interactions between the electrons, at even-denominator filling factors such as \ensuremath{\nu}=1/2, we predict that the spectral weight varies as ${\mathit{e}}_{0}^{\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\omega}}}$/\ensuremath{\Vert}\ensuremath{\omega}\ensuremath{\Vert}, for \ensuremath{\omega}\ensuremath{\rightarrow}0.

Nonlinear resonant tunneling through an Anderson impurity at low temperature.

The problem of nonlinear resonant tunneling through an Anderson impurity is investigated in this letter using a combined -approach of Keldysh formalism and 1/N expansion at zero temperature. We find that to order 1/N, the Kondo resonance is not destroyed by any finite potential difference between external probes. The resulting one-electron Green's functions and differential conductance are presented. The effect of finite temperature is discussed

Doping dependence of the chemical potential in Bi2Sr2Ca1-xYxCu2O8+ delta.

A detailed study of the doping dependence of valence- and core-level spectra of ${\mathrm{Bi}}_{2}$${\mathrm{Sr}}_{2}$${\mathrm{Ca}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Y}}_{\mathit{x}}$${\mathrm{Cu}}_{2}$${\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ leads to the conclusion that the chemical potential shifts in a manner consistent with that of a simple doped semiconductor. The spectroscopically observed filling in of the gap upon doping of the correlated insulator is therefore not due to midgap states pinning the Fermi level, but most likely due to spectral weight resulting from the incoherent part of the one-electron Green's function.

Solution of Poisson's equation for arbitrarily shaped overlapping or nonoverlapping charge densities in terms of multipole moments.

The solution of Poisson's equation in terms of a Green's function expanded in spherical harmonics is presented. No restrictions are imposed on the charge density. An angular-momentum representation for the potential is obtained ready for application in self-consistent full-potential band-structure methods, which are based on a multicenter expansion of the one-electron Green's function into spherical harmonics.

Properties of electron self-energies and their role in electron spectroscopies

The “ GW approximation” for the self-energy connected with the one-electron Green's function has been very successful in predicting band structures for a large class of semiconductors and insulators. The physical basis for this approximation and general features of its nonlocality will be discussed, as well as possible improvements. Besides quasiparticle energies the self-energy also gives the “intrinsic part” of the photoelectron spectrum. In general, however, a full description of experimental spectra measured with synchrotron radiation, such as photoemission, Auger spectra and EXAFS, cannot be given by the one-electron Green's function. A new theoretical approach to synchrotron radiation spectroscopies is given in terms of the coupling functions involved in the GW approximation and on-the-energy-shell one-electron Green's functions.

Theory of photoemission and inverse-photoemission spectra of highly correlated electron systems: A weak-coupling 1/N expansion.

An N-fold-degenerate Hubbard model is examined in the weak-coupling regime. The one-electron Green's function is calculated from a systematic expansion of the irreducible self-energy in powers of 1/N. To lowest order in the expansion, one obtains a trivial mean-field theory. In the next leading order in 1/N, one finds that the dynamics are dominated by bosonlike collective excitations. The resulting expansion has the characteristics of the standard weak-coupling field theory, except the inclusion of the 1/N factors extends the regime of applicability to include Stoner-like enhancement factors which can be N times larger. The joint valence-band photoemission and inverse-photoemission spectrum is given by the trace of the imaginary part of the one-electron Green's function. The electronic spectrum has been calculated by truncating the series expansion for the self-energy in the lowest nontrivial order of 1/N. For small values of the Coulomb interaction between the electrons, the spectrum reduces to the form obtained by calculating the self-energy to second order in the Coulomb interaction. The spectra shows a narrowing of the band in the vicinity of the Fermi level and long high-energy band tails. When the boson spectrum softens, indicating the vicinity of a phase transition, the electronic spectrum shows the appearance of satellites. The results are compared with experimental observations of anomalies in the electronic spectra of uranium-based systems. The relation between the electronic spectrum and the thermodynamic mass enhancements is also discussed.

Correlation effects in photoemission from adsorbates: Hydrogen on narrow-band metals.

This paper deals with photoemission from a one-level atom adsorbed on a metal surface within the context of Anderson's Hamiltonian. The occupied part of the adsorbate density of states (DOS) is calculated by means of a many-electron approach that incorporates the following ingredients: (1) A neat separation between final-state interactions and initial (ground-state) effects. (2) The method (a Lehmann-type representation) leans heavily on the resolvent operator, R(z)=(z-H${)}^{\mathrm{\ensuremath{-}}1}$, which is obtained by expressing Dyson's equation in terms of the (N-1)-electron states (configurations) that diagonalize the hopping-free part of Anderson's Hamiltonian, thereby including the atomic correlation (U) in a nonperturbative way while expanding in powers of the hopping parameter (V). (3) By using blocking methods, the matrix elements of R are grouped into equivalent 4\ifmmode\times\else\texttimes\fi{}4 matrix blocks, with residual interactions, which are then put in correspondence with the sites of a rectangular lattice, thereby making the problem isomorphic to that of finding a noninteracting one-electron Green's function in the Wannier representation. (4) Renormalized perturbation theory, along with a series of convolution theorems due to Hugenholtz and Van Hove, allows one to develop a self-consistency equation that automatically takes into account an infinite number of configurations. The resulting DOS is compared with photoemission spectra from hydrogen adsorbed on tungsten (half-filled metal band) and nickel (almost full). Correlation effects turn out to produce peaks at the appropriate energies, so that an unusually good agreement is found despite the featureless, semielliptical DOS adopted for the metal. Only gross features of this quantity, such as width, center, and occupation of the band, seem to matter in a photoemission calculation.

Completeness in configuration-interaction calculations.

Strong configuration-interaction effects between autoionizing configurations of the form (ns${)}^{1}$(np${)}^{m+1}$ and bound configurations of the form (ns${)}^{2}$(np${)}^{m\mathrm{\ensuremath{-}}1}$(n'l') have been treated with truncated-discrete-basis calculations, either neglecting or approximating the continuum. It is shown that Fano's treatment of a level interacting with the continuum can be extended to the threshold region by including the Rydberg series of discrete levels. Inclusion of the infinite Rydberg series leads to a logarithmic singularity of matrix elements and the eigenvalue equation near the threshold region, which cancels the singularity arising from the integral over the continuum.The cancellation leads to a relatively simple eigenvalue equation for the strongly perturbed eigenvalues. Numerical evaluation of the eigenvalue equation leads to eigenvalues comparable to those found with multiconfiguration Hartree-Fock calculations. Concentration on the threshold regions leads to a unique prescription for passive continua normalization independent of the number of continua used. Numerical evaluation of the eigenvalue equation predicts a (4s${)}^{1}$(4p${)}^{5}$ $^{3}P$ level in Se 10 000 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ below the first ionization threshold, though no evidence for such a level is observed spectroscopically. By including the discrete levels in the Fano formalism, it is shown that the infinite discrete level sum plus integral over the continuum can be rewritten as an integral of the interaction potential and a modified one-electron Green's function, leading to a ``dressed'' one-electron orbital, which is readily computed and which contains the interesting effects of the strong interaction. Such dressed orbitals are used to calculate oscillator strengths to the ground state for the neutral halogens, ${\mathrm{Ar}}^{1+}$, and the neutral elements of column VI in the periodic table. For Cl, I, and Se, the calculated oscillator strengths from the ground state to the (ns${)}^{1}$(np${)}^{m+1}$ configuration are less than ${10}^{\mathrm{\ensuremath{-}}4}$, offering a plausible explanation for the nonidentification (Se) or misidentification (I) of these levels.

Green's-function formalism of electronic states in heavily doped semiconductors and its application to a problem of inter-valence-band absorption.

A semiempirical method is presented for calculating the electronic states in heavily doped semiconductors in terms of the one-electron Green's function. It has been shown previously that the theory developed on the basis of the semiempirical pseudopotential approach gives a satisfactory description of the impurity-band tail relevant to the heavy-mass band. On the other hand, it is shown in this paper that the theory gives a poor description of the impurity- and phonon-scattering effect on the intraband states even if the theory also takes into account the phonon scattering. Therefore the theory is improved in such a way as to take special account of the intraband states. The new theory is tested by calculating the inter-valence-band absorption constant with the use of this theory and by comparing the theoretical results with experiments. It is shown that the new theory gives a satisfactory description of the electronic states at all energies.

Interpretation of intensities in electron-momentum and photoelectron spectroscopiesag

Relative intensities for the photoelectron reaction on atoms and molecules are not related to structure calculations in the same way as those for the noncoplanar symmetric (e, 2e) reaction. The photoelectron dipole matrix element is dependent on recoil momentum only through the unique relationship of recoil momentum to the photon energy and is much harder to calculate for chemically-interesting momenta. Relative intensities for binary (e, 2e) reactions are independent of total energy at high enough energies and strongly dependent on symmetry and recoil momentum, for which an intensity profile can be measured for values starting at zero. In comparing with structure calculations, binary (e, 2e) intensities for low recoil momentum may be compared directly with pole strengths in calculations of the one-electron Green's function. In the case of states within a single symmetry manifold the relative intensities will be independent of recoil momentum up to some maximum, usually at least a few atomic units.

Traveling-cluster approximation for uncorrelated amorphous systems

We have developed a formalism for including cluster effects in the one-electron Green's function for a positionally disordered (liquid or amorphous) system without any correlation among the scattering sites. This method is an extension of the technique known as the traveling-cluster approximation (TCA) originally obtained and applied to a substitutional alloy by Mills and Ratanavararaksa. We have also proved the appropriate fixed-point theorem, which guarantees, for a bounded local potential, that the self-consistent equations always converge upon iteration to a unique, Herglotz solution. To our knowledge, this is the only analytic theory for considering cluster effects. Furthermore, we have performed some computer calculations in the pair TCA, for the model case of $\ensuremath{\delta}$-function potentials on a one-dimensional random chain. These results have been compared with "exact calculations" (which, in principle, take into account all cluster effects) and with the coherent-potential approximation (CPA), which is the single-site TCA. The density of states for the pair TCA clearly shows some improvement over the CPA and yet, apparently, the pair approximation distorts some of the features of the exact results.