Theory of inelastic lifetimes of low-energy electrons in metals

Abstract

Electron dynamics in the bulk and at the surface of solid materials are well known to play a key role in a variety of physical and chemical phenomena. In this article we describe the main aspects of the interaction of low-energy electrons with solids, and report extensive calculations of inelastic lifetimes of both low-energy electrons in bulk materials and image-potential states at metal surfaces. New calculations of inelastic lifetimes in a homogeneous electron gas are presented, by using various well-known representations of the electronic response of the medium. Band-structure calculations, which have been recently carried out by the authors and collaborators, are reviewed, and future work is addressed. q

Electronic excitations: density-functional versus many-body Green’s-function approaches

“…Further, an energy-dependent correlation decreases the Hartree-Fock band gap by raising the valence-band energy and lowering the conduction-band energy. There is some empirical evidence that supports the idea that even in the first iteration (that is, using just the noninteracting Green's function G 0 ) one obtains quite accurate results for oneelectron properties such as the excitation energy Louie, 1985, 1986;Godby et al, 1986Godby et al, , 1987Godby et al, , 1988Aryasetiawan and Gunnarsson, 1998) and the quasiparticle lifetime (Campillo et al, 1999;Schö ne et al, 1999;Echenique et al, 2000;Campillo, Silkin, et al, 2000;Keyling et al, 2000;Silkin et al, 2001;Spataru et al, 2001). This is important for practical applications of the GW approach since, despite its formal simplicity, the practical solution of the self-consistent GW equations is a formidable task, which has been carried out only recently: self-consistent calculations were performed for the homogeneous electron gas (Holm and von Barth, 1998;Holm and Aryasetiawan, 2000;García-Gonzá lez and Godby, 2001), simple semiconductors, and metals (Shirley, 1996; Schö ne and Eguiluz, 1998).…”

Decay of electronic excitations at metal surfaces

“…In the case of a homogeneous electron gas for the energies involved in surface and image-potential states and for the case of an electron density equal to that of Cu (4s 1 ) valence electrons the GW-TDLDA result for the lifetime is $20% less than that of GW-RPA [16]. For this particular case, this reduction is slightly more than compensated by the reduction in the interaction originated by taking into account exchange and correlation effects between the probe electron and the electron gas (GWG-TDLDA).…”

“…inverse lifetime, of an electron with energy E i > E F is obtained on the energy-shell approximation in terms of the imaginary part of the complex non-local self-energy operator [13,16]:…”

“…The theoretical calculations use different models depending on the interactions relevant for the scattering processes. The decay rate due to inelastic electron-electron scattering is calculated using the GW approximation for the self energy [13][14][15][16]. For the electron-phonon interaction the Eliashberg function is used [17][18][19].…”

Surface plasmons in metallic structures

“…74,75 We then calculate the eigenfunctions and eigenvalues of the corresponding hamiltonian, and we evaluate the dynamical density-response function χ 0 (z, z ′ ; q, ω). Finally, we solve an integral equation to obtain the RPA interacting density-response function χ(z, z ′ ; q, ω).…”