Lars Hedin

Explicit local exchange-correlation potentials

The possibilities of the Hohenberg-Kohn-Sham local density theory are explored in view of recent advances in the theory of the interacting electron gas. The authors discuss and provide numerical data for the effective exchange-correlation potentials mu xc for ground state problems and Vxc for excitation spectra. The potential mu xc(r) is written as a factor beta ( rho (r)), which depends on the local density rho (r), times the Kohn-Sham-Gaspar potential mu x=-e2kF/ pi . The factor beta , which is represented by a simple analytical formula, varies between 1 for very high densities and about 1.5 for very low densities, where mu xc thus approaches the Slater approximation. The potential Vxc is given in the form of a table. The explicit predictions of the approximate theories are mapped in their linearized versions. The theory is also developed for the case when the ion cores are treated separately, and the local density approximation is applied only to the valence electrons.

On correlation effects in electron spectroscopies and the GW approximation

The GW approximation (GWA) extends the well-known Hartree-Fock approximation (HFA) for the self-energy (exchange potential), by replacing the bare Coulomb potential v by the dynamically screened potential W, e.g. Vex = iGv is replaced by GW = iGW. Here G is the one-electron Greens function. The GWA like the HFA is self-consistent, which allows for solutions beyond perturbation theory, like say spin-density waves. In a first approximation, iGW is a sum of a statically screened exchange potential plus a Coulomb hole (equal to the electrostatic energy associated with the charge pushed away around a given electron). The Coulomb hole part is larger in magnitude, but the two parts give comparable contributions to the dispersion of the quasi-particle energy. The GWA can be said to describe an electronic polaron (an electron surrounded by an electronic polarization cloud), which has great similarities to the ordinary polaron (an electron surrounded by a cloud of phonons). The dynamical screening adds new crucial features beyond the HFA. With the GWA not only bandstructures but also spectral functions can be calculated, as well as charge densities, momentum distributions, and total energies. We will discuss the ideas behind the GWA, and generalizations which are necessary to improve on the rather poor GWA satellite structures in the spectral functions. We will further extend the GWA approach to fully describe spectroscopies like photoemission, x-ray absorption, and electron scattering. Finally we will comment on the relation between the GWA and theories for strongly correlated electronic systems. In collecting the material for this review, a number of new results and perspectives became apparent, which have not been published elsewhere.

A New Approach to the Theory of Photoemission from Solids

By neglecting certain terms in the Hamiltonian (of importance only in the immediate neighbourhood of the threshold energy) we are able to write an exact expression for the photoemission intensity which involves the standard time inverted LEED state and broadened hole-states. If inelastic extrinsic losses are neglected our expression is similar to the one used by e.g. Feibelman and Eastman [1], Pendry [2] and Spanjaard et al. [3]. Our theory also allows inelastic losses (including interference between intrinsic and extrinsic losses) to be evaluated. The expressions are similar to those obtained by Inglesfield [4], but the damping effect no longer has to be put in by hand. Our theory further can handle not only core electron but also valence electron photoemission and it is not restricted to metals but applies to all types of solids. We have also traced why and when Inglesfields one step theory agrees with a semiclassical calculation.

New structure in the single-particle spectrum of an electron gas

Calculations of the one-electron Greens function give a single-particle spectrum where, besides the usual quasi-particles, a new peak of appreciable strength appears which corresponds to an electron coupled to real plasmons.

Effects of recoil on shake-up spectra in metals

An infinite summation method is used to obtain the intrinsic photoemission spectrum of a conduction electron in the sudden limit. It is predicted that an electron at the bottom of the conduction band should have an asymmetry index comparable to that of a core electron and that the strengths of its plasmon satellites should be similar to those of a core electron. The width of their plasmon satellites, however, should become smaller under the influence of recoil. In essence, our results show that the exchange-correlation hole left after a photoemitted conduction electron has a very similar effect as the core hole left after a photoemitted core electron. Use of synchrotron radiation gives high enough a resolution to make possible the verification of these effects.

MAGNETIC PHASES NEAR THE VAN HOVE SINGULARITY IN S- AND D-BAND HUBBARD MODELS

We investigate the magnetic instabilities of the nondegenerate (s-band) and a degenerate (d-band) Hubbard model in two dimensions using many-body effects due to particle-particle diagrams and Hund’s rule local correlations. The density of states and the position of the Van Hove singularity change depending on the value of next-nearest-neighbor hopping t′. The Stoner parameter is strongly reduced in the s-band case, and ferromagnetism survives only if the electron density is small and the band has flat regions. Due to next-nearest-neighbor hopping there are flat regions in Γ−X and Γ−Y directions. In contrast, for the d-band case the reduction of the Stoner parameter which follows from particle-particle correlations is much smaller and ferromagnetism survives to a large extent. Inclusion of local spin-spin correlations has a limited destabilizing effect on the magnetic states. (Less)

Extrinsic and intrinsic processes in EXAFS

The author extends the ideas of Bardyszewski and Hedin (1987) to treat EXAFS. He summarises the theory, adds new viewpoints and extends the theory.

Sudden approximation in photoemission and beyond

The conditions behind sudden approximation are critically examined. The fuzzy band expression is derived in detail from first principles. We go beyond the sudden approximation to account for both extrinsic losses and interference effects. In an extension of earlier work we discuss both core and valence satellites including both intrinsic and extrinsic amplitudes, and high energy excitations as well as low energy electron-hole pairs. We show how the extrinsic losses in photoemission can be connected with the electron energy loss function. This is achieved by three approximations, to connect the dynamically screened potential in the bulk solid to the loss function, to account for the surface, and lastly to extrapolate zero momentum loss data to include dispersion. The extrinsic losses are found to be weak for small loss energies. For larger loss energies the extrinsic losses can be strong and have strong interference with the intrinsic losses depending on the nature of the solid. The transition from the adiabatic to the sudden regime is discussed for atoms and localized systems and compared with the situation for solids. We argue that in solids for photoelectron energies above some 10 eV the external losses are mainly connected with spacially extended excitations. We discuss strongly correlated quasi-two-dimensional solids with Bi2212 as example, and find an asymmetric broadening of the main peak from shake up of acoustic three-dimensional plasmons. In the superconducting state the loss function is assumed to have a gap, which then leads to a peak-dip-hump structure in the photoemission spectrum. This structure is compared with a corresponding structure in tunneling

Theory of Atomic Optical Potential in Solid Application to Electron-Helium Scattering

We develop an approximation for the optical potential in a solid valid at intermediate energies, i.e., above about 50 eV. The present approximation for the optical potential is based on GW-expression. We separate the RPA polarization propagator into a core-electron and a valence-electron part, and can then achieve a corresponding separation of the optical potential. We apply this method to electron-He elastic scattering, and we find satisfactory agreement with the observed results. We also study the importance of self-consistency, and the sensitivity to a parameter, average excitation energy .

New Approach to the Theory of Atomic Optical Potential in Solids

We develop an approximation for the optical potential in a solid valid at intermediate energies, say energies from some 50 eV and larger. The importance of good optical potentials at these energies is clear from experimental and theoretical work on elastic electron-atom scattering. We cannot however directly take over free-atom potentials for use in a solid. For one thing the valence electrons are largely reorganized when the atom is placed in a solid. One also has to consider the screening effects in solids. Our approximation for the optical potential builds on the GW-expression. We separate the RPA polarization propagator in a core electron and a valence electron part, and can then achieve a corresponding separation of the optical potential.