Ultrafast electronic response of Ag(111) and Cu(111) surfaces: From early excitonic transients to saturated image potential

Silkin, Viatcheslav M.; Lazić, Predrag; Došlić, Nađa; Petek, Hrvoje; Gumhalter, B.

doi:10.1103/physrevb.92.155405

Cited by 43 publications

(32 citation statements)

References 129 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This property has been widely assumed as a general feature in all later modellings of single quasiparticle interactions with bosonic type of excitations based on cumulant expansion [16,21,29,30,33,[35][36][37][41][42][43]. This approach has also proved extremely useful in the descriptions of ultrafast phenomena that can be revealed by time resolved electron spectroscopies [33,34,36,44,66].…”

Section: Single Quasiparticle Propagators From Cumulant Expansionmentioning

confidence: 98%

“…The justification for applying this model in the present studies of quasiparticles coupled to electronic excitations via the screened interaction W is the bosonic character of its dynamic component [34,44]. Since our attention will be focused on excitations with energies ranging over the entire bandwidths we shall assume zero temperature of the system.…”

Section: Propagators Of Quasiparticles and Bosonized Response Of mentioning

confidence: 99%

“…where χ q (ω ′ ) is the electronic density-density response function calculated in the standard RPA or one of its generalized versions [44]. Now, it is easy to verify that the function χ q (ω ′ ) calculated within the linear response formalism has the properties of a boson propagator (10) with the spectrum of excitations given by…”

Section: Quasiparticle Self-energy In the G0w0 Approximationmentioning

confidence: 99%

“…The major rationale for this approach lies in the fact that cumulant expansion provides exact solutions in the limiting cases of (1) [18], or a rapidly converging closed form solution in the general case [23,27,32,36]. Advantageous features of both approaches have been combined by a number of authors who have employed the GWA selfenergies as an input for cumulant representation of quasiparticle propagators so as to achieve a better description of satellite structure in the spectra [27,29,30,[33][34][35][36][37][41][42][43][44]. However, an explicit identification of the approximations underlying the combined use of GWA and cumulant expansion is still missing.…”

Section: Propagators Of Quasiparticles and Bosonized Response Of mentioning

confidence: 99%

“…Refs. [17,23,24,27,29,32,36], given the renewed interest in this technique and its use in conjunction with the GWA [29,30,35,37,[41][42][43][44] it seems appropriate and timely to systematically develop and discuss the key aspects of the GW + cumulant (GW+C) theory for interpretations of the results of both the stationary and time-resolved spectroscopies. This program is carried out in Secs.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the combined use of GW approximation and cumulant expansion in the calculations of quasiparticle spectra: The paradigm of Si valence bands

et al. 2016

View full text Add to dashboard Cite

PACS numbers: 71.15.Qe, 71.45.Gm Appendix A: Integral representation of cumulant seriesThe purpose of this appendix is to provide a rigorous mathematical foundation for the transformation (37) and its inverse (39) of the main text. We omit subscripts and superscripts and write simply ρ and C. Our goal is to define the mapping ρ(ν) → C(t), specify its domain and range, prove that it is one-to-one and onto, and describe its inverse map C(t) → ρ(ν). Moreover, at the end of the section we restrict our attention to a rather generic particular case that is sufficient for the application explained in the main part of this paper.Let M + (R) and M(R) respectively denote the space of finite positive measures and the space of finite signed measures on the real line (cf. Sections 1.2 and 4.1 in [1]). Indeed, an element of M(R) is simply a difference of two elements from M + (R). This space contains all absolutely integrable real-valued functions, but it also contains the "true" measures, such as absolutely summable linear combinations of Dirac delta-functions at certain points of R. For any finite signed measure ρ ∈ M(R) we interpret (37)of the main text asThis transformation is well-defined since the function (e −iνt − 1 + iνt)/ν 2 can be extended at ν = 0 in a way that it becomes a bounded continuous function on the whole real line and thus it can be integrated against the measure ρ. The basics of integration theory with respect to abstract measures can be found in the classical textbooks on measure theory, such as [1] and [2]. Let us remark that integration with respect to a general measure ρ is usually written with ρ(ν)dν replaced by dρ(ν) or ρ(dν) in mathematical literature in order to emphasize that ρ need not have a density (i.e. it could be a true measure). We will stick to the former notation, since it is also common to understand signed (or even complex) measures as particular cases of distributions (cf. Section 6.11 in [3]). * Corresponding author. Email: branko@ifs.hr Differentiation of (A1) is justified using the dominated convergence theorem (cf. Theorem 2.27(b) from [2]) and it yieldsĊ In the literature on probability theory (such as Chapter 3 of [7]), ρ is usually called the characteristic function of ρ, even though the normalization is slightly different there. Substituting t = 0 into (A1) and (A2) givesFrom (A3)-(A6) we see that an equivalent way of expressing C in terms of ρ iswith the usual convention thatIt is easy to see that C(t) is always two times continuously differentiable, but it is not true that every such function can be obtained from some ρ ∈ M(R), as we shall soon see.Now we claim that the transform defined by (A1) is a one-to-one map from M(R) to some collection of twice continuously differentiable functions, i.e. that different measures ρ map to different functions C. In order to verify that we assume ρ 1 → C and ρ 2 → C. From (A3) we get2 so the well-known fact that the Fourier-Stieltjes transform ρ → ρ is one-to-one (see Subsection VI. for any choice of points t 1 , . . . , t n ∈ R an...

show abstract