On Inhomogeneous Damping of Electrons in Crystals

Bartoš, I.

doi:10.1002/pssb.2221220258

Cited by 10 publications

(2 citation statements)

References 3 publications

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“…The current conservation rule is violated by the presence of – iV i , and the incomplete reflection of electrons with energies falling in the forbidden gap of the k || ‐projected spectrum of the bulk substrate is interpreted as electron absorption. For nearly free electrons Im k ⊥ is of the order of V i / ħv ⊥ , so the mean free path (MFP), defined as $ \lambda = 1/2\;{\rm Im}\;k_ \bot,$ can be understood as the product of the electron lifetime $ \hbar /2V_{\rm i} $ and the group velocity $ v_ \bot.$ Microscopically, the phenomenological parameter $ V_{\rm i} $ is associated with the expectation value of the imaginary part of the self‐energy operator $ \langle \psi \vert\;{\rm Im}\;\Sigma \;\vert\psi \rangle $ 39–41, which can, in principle, be calculated from first principles within a quasi‐particle approach. A popular and computationally feasible scheme for self‐energy is the so‐called $ \Sigma = GW$ approximation 42, 43 proposed by Hedin in 1965.…”

Section: Fundamentals Of Very‐low Energy Electron Diffractionmentioning

confidence: 99%

A Simple Heterogeneous Catalyst for Phosphite Addition on Carbonyl Groups

et al. 2015

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Section: Fundamentals Of Very‐low Energy Electron Diffractionmentioning

confidence: 99%

A Simple Heterogeneous Catalyst for Phosphite Addition on Carbonyl Groups

et al. 2015

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“…The role of inhomogeneity of electron damping has been shown [14] to increase in the vicinity of the Brillouin zone boundary. It is manifested characteristically in partial electron densities of states D(k, E) (density of states with fixed wave vector k) depending on relative displacement of the real and imaginary components of the crystal potential, either a singularity below the gap gets sharpened and that above the gap gets broadened (out-of-phase case) or the asymmetry is reversed.…”

Section: Vleed Intensitiesmentioning

confidence: 99%

Electron Damping in Surface Studies

Bartoš

1992

Acta Phys. Pol. A

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Electron correlation is responsible for finite lifetimes of excited electrons in crystals. Lifetime energy dependence can be obtained for infinite jellium model and only very recently the first results for an infinite crystal have been evaluated (GW approximation). Here, a phenomenological approach, based on Green functions, is presented. Broadening of local densities of electron states as well as that of angular-resolved photoemission (ARUPS) peaks and very-low-energy-electron diffraction (VLEED) profiles, due to the imaginary component of the optical potential is reviewed and interpreted. Anisotropy of electron damping on crystal surfaces has been found in VLEED as a result of electron channeling along the densely packed (111) surface atomic planes in fcc crystals. Interpretation of peak widths in VLEED-and ARUPS-profiles provides a mean to learn about damping of electrons, excited on crystal surface. Quasi-particle lifetimesOne-particle approximation in the electron theory of crystals is surprisingly successful. This fact is explained by dressing the bare particles to form the quasi--particles with only a weak interaction (effective screening of correlation and exchange interactions).Quasi-particles, describing excited states of the system of electrons, have been studied in detail for a simplified model of jellium, where individual positive charges of ions are replaced by a uniform positive charge background.It has been found that the dispersion relation E(k) of electrons gets somewhat modifled (effective mass renormalization) and also that their lifetime (expressed as an imaginary part of electron self-energy) is in general finite. The electron lifetime is infinite at the Fermi level but shortens when electron is excited above the EF ; during its collisions with other electrons, electron-hole pairs can be created, and starting from the plasmon threshold energy also collective oscillations of the system can be induced. Numerical results for such an interacting electron gas have been obtained in the random phase approximation for electron densities typical for metals [1].(33)

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Cu(111) Electron Band Structure and Channeling by VLEED

Bartoš

Barbieri

Hove

et al. 1997

phys. stat. sol. (a)

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Very‐low‐energy electron diffraction (VLEED) intensities from clean Cu(111) surface have been measured in detail in the energy range 15 to 35 eV by low‐energy electron microscope. Corresponding theoretical I—V curves are obtained in good agreement with experimental data when the anisotropy of the electron attenuation is taken into account. The coincidence of the peaks in the I—V curves at normal incidence with two kinds of energy gaps of the electron band structure of the copper crystal (E boldk ∥=0) is interpreted. The small width of the resonance peak in the I—V curve at normal incidence is explained in terms of electron surface channeling. VLEED thus provides information about the unoccupied part of the electron band structure of copper which complements that obtained from angular resolved photoemission.

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On Inhomogeneous Damping of Electrons in Crystals

Cited by 10 publications

References 3 publications

A Simple Heterogeneous Catalyst for Phosphite Addition on Carbonyl Groups

A Simple Heterogeneous Catalyst for Phosphite Addition on Carbonyl Groups

Electron Damping in Surface Studies

Cu(111) Electron Band Structure and Channeling by VLEED

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