Transient excitonic states in noble metals and Al

Abstract

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...

Expeditious computation of nonlinear optical properties of arbitrary order with native electronic interactions in the time domain

“…It therefore defines the strength of the electron-hole interaction but not the Kohn-Sham bandstructure renormalization which, by construction, should be already included in ĥ, and is where dynamical screening is crucial 18,50 . Furthermore, an instantaneous selfenergy is in line with the current understanding, at the level of the BSE, that it correctly captures the excitonic spectrum of semiconductors because of the excitons' relatively long time-scales in comparison with the dynamical charge oscillations involved in screening [59][60][61] .…”

Expeditious computation of nonlinear optical properties of arbitrary order with native electronic interactions in the time domain

“…(While dynamical screening is crucial to obtain the correct quasiparticle renormalization [18,53], in our formulation, that effect is already encoded inĥ, by construction.) Furthermore, an instantaneous self-energy is in line with the current understanding, at the level of the BSE, that it correctly captures the excitonic spectrum of semiconductors-because of the excitons' relatively long timescales in comparison with the dynamical charge oscillations involved in screening [61][62][63].…”

Hot electron lifetimes in metals probed by time-resolved two-photon photoemission

“…Notably, direct experimental evidence for the transient generation of excitons at a metal surface was reported in a very recent study of Ag(1 1 1) [183]. In a work by Schöne et al [184,185] a model for the calculation of binding energies of transient bulk excitonic states in metals was introduced. Binding energies reported for copper indeed agreed with TR-2PPE data in Ref.…”