Calculated lifetimes of hot electrons in aluminum and copper using a plane-wave basis set

Schöne, Wolf-Dieter; Keyling, Robert; Bandić, Mario; Ekardt, W.

doi:10.1103/physrevb.60.8616

Cited by 66 publications

(99 citation statements)

References 41 publications

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“…A comparison between the theoretical and experimental data reveals good agreement for band energies above 2 eV but it shows a huge discrepancy for energies below 2 eV. 7,8 Alike results have been found by similar calculations. 9 This shows that the GW approximation does not contain enough physics to explain the lifetime of hot electrons in Cu.…”

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confidence: 70%

Transient excitonic states in noble metals and Al

Schöne

Ekardt

2002

Phys. Rev. B

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Bound states between electrons and holes, so-called excitons, are an ubiquitous feature in the spectra of excited states of molecules, clusters, and in a variety of solids such as semiconductors or ionic solids. It is common wisdom that excitons do not exist in metals because the attractive, long-range particle-hole interaction which is needed for the formation of an exciton does not exist in metals due to almost complete screening. We showed in a previous publication that excitons in metals can exist as transient states right after the creation of the electron-hole pair which explained in a natural way the up to then not understood transitions seen in Cu in the experimental spectra of time-resolved two-photon photoemission spectroscopy. In this paper we report about transient excitonic states in Ag and Au. We explain why these states have not yet been detected in Ag but we predict their existence. We show furthermore why transient excitonic states cannot be built up in Al. DOI: 10.1103/PhysRevB.65.113112 PACS number͑s͒: 78.47.ϩp, 72.15.Lh, 71.10.Ϫw, 71.20.Gj With the advent of modern femtosecond laser technology it has become possible to measure ultrafast relaxation processes of excited electrons in metals. [1][2][3] Whereas in most cases the experimentally observed states can be identified as single-particle band states there are other cases where the experimental results cannot be explained on the basis of a single-particle band structure. Most prominent are the measurements of the lifetime of excited electrons using timeresolved two-photon photoemission ͑TR-2PPE͒ spectroscopy performed on single crystals of Cu ͑Refs. 1,2,4͒ and Au. 5 They show data for states in the ͑100͒ and ͑111͒ direction in an energy range between 1 and 4 eV. We are not aware of any such data for Ag. These two directions are of special interest since the band structures for all three noble metals do not show single-particle states in these directions for the energy range under consideration ͑1-4 eV͒. 6 There is a second observation; Ogawa et al. 1 also measured the lifetime of excited electrons in the Cu͑110͒ direction. Since this direction shows a single-electron band the lifetime of electrons in this band has been calculated using a state-of-the-art ab initio many-body calculation within the GW approximation. A comparison between the theoretical and experimental data reveals good agreement for band energies above 2 eV but it shows a huge discrepancy for energies below 2 eV. 7,8 Alike results have been found by similar calculations. 9 This shows that the GW approximation does not contain enough physics to explain the lifetime of hot electrons in Cu. This is noteworthy because calculations utilizing the GW approximation typically lead to very good agreement with experimental data, a fact that laid the foundation for its big success. 10 It was speculated that the observed states are caused by an attractive interaction between the photoelectron and its localized hole in the d bands. 4 In a recent paper 11 we presented a model which sub...

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confidence: 70%

Transient excitonic states in noble metals and Al

Schöne

Ekardt

2002

Phys. Rev. B

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“…In this simple model and for energies very near the Fermi level (|E − E F | ≪ E F ), the inelastic lifetime is found to be, in the high-density limit (r s → 0) 33 , τ (E) = 263 r −5/2 s (E − E F ) −2 fs, where E and E F are expressed in eV 34 . Deviations from this simple formula, which have been shown to be mainly due to band-structure effects 16,17 , were clearly observed 3,6,7 . First-principles caculations of the hole dynamics in the noble metals copper and gold have been reported very recently 18 , too.…”

Section: Theoretical Model and Discussionmentioning

confidence: 92%

“…This technique allows to determine lifetimes only from a detailed analysis of linewidths 14,15 , and requires simultaneously low temperatures, excellent energy as well as angular resolution and in general tunable photon energy. This expense is more than compensated by the very detailed understanding of the one-photon excitation channel and the possibility to locate a photo-hole exactly with respect to both initial-state energy E i and wave vector k. Recent calculations have shown that any reliable theory of hot-electron and hole lifetimes in metals must go beyond a free-electron description of the solid 16,17,18 . In Sec.…”

Section: Introductionmentioning

confidence: 99%

Lifetime ofdholes at Cu surfaces: Theory and experiment

et al. 2001

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We have investigated the hole dynamics at copper surfaces by high-resolution angle-resolved photoemission experiments and many-body quasiparticle GW calculations. Large deviations from a free-electron-like picture are observed both in the magnitude and the energy dependence of the lifetimes, with a clear indication that holes exhibit longer lifetimes than electrons with the same excitation energy. Our calculations show that the small overlap of d-and sp-states below the Fermi level is responsible for the observed enhancement. Although there is qualitative good agreement of our theoretical predictions and the measured lifetimes, there still exist some discrepancies pointing to the need of a better description of the actual band structure of the solid.

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“…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).…”

Section: First Iteration Step: the Gw Approximationmentioning

confidence: 95%

“…When the full energy dependence of the dielectric matrix is retained, the integration in may be performed along the imaginary axis, where Ϫ1 is well behaved (Godby et al 1988;Schö ne and Eguiluz, 1998), by picking up all the poles along the real axis (Aryasetiawan, 1992;Fleszar and Hanke, 2000), or by using the transition-space spectral representation of Ϫ1 , which allows one to perform the frequency integration analytically (Shirley and Martin, 1993). 24 c. Application of the self-energy ⌺ For many applications, the simple prescriptions described above have yielded results within 10-15 % of the experimental ones, the typical example being the direct quasiparticle gap of diamond, as discussed in the introduction.…”

Section: A Evaluation Of the Green's Function Gmentioning

confidence: 99%

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

2002

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Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy ⌺ and the electron-hole interaction. A good approximation for ⌺ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of ⌺. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress. CONTENTS

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Calculated lifetimes of hot electrons in aluminum and copper using a plane-wave basis set

Cited by 66 publications

References 41 publications

Transient excitonic states in noble metals and Al

Transient excitonic states in noble metals and Al

Lifetime ofdholes at Cu surfaces: Theory and experiment

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

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