Electron scattering by random adsorbates: A tunable decoherence mechanism in surface bands

Marion, Sanjin; Gumhalter, B.

doi:10.1002/pssb.201100543

Cited by 6 publications

(3 citation statements)

References 35 publications

(59 reference statements)

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“…In contrast, surface structures with curvature radii from nanometers to sub-microns may have a strong effect on SEE. It is also reasonable to mention that the SEE yield from the surface with distributed structures of low concentration is proportional to the concentration of the structures [29,30] and greater than the SEE yield from the smooth surface as long as 0.01 a/L 1, here L is a distance between structural elements [19].…”

Section: Discussionmentioning

confidence: 99%

Secondary electron emission from surfaces with small structure

et al. 2015

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It is found that for objects possessing small surface structures with differing radii of curvature the secondary electron emission (SEE) yield may be significantly higher than for objects with smooth surfaces of the same material. The effect is highly pronounced for surface structures of nanometer scale, often providing a more than 100% increase of the SEE yield. The results also show that the SEE yield from surfaces with structure does not show an universal dependence on the energy of the primary, incident electrons as it is found for flat surfaces in experiments. We derive conditions for the applicability of the conventional formulation of SEE using the simplifying assumption of universal dependence. Our analysis provides a basis for studying low-energy electron emission from nano structured surfaces under a penetrating electron beam important in many technological applications.

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Section: Discussionmentioning

confidence: 99%

Secondary electron emission from surfaces with small structure

et al. 2015

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“…In this regime the low order self-energy corrections may represent a better approximation to the quasiparticle propagator, particularly in relation to its asymptotic time behavior characterized by the so-called quasiparticle collapse [36,[71][72][73][74]. Moreover, near the Fermi level the single particle approximation which separates electron from hole motion and leads to (34) and (35) becomes unrealistic and the processes like those shown in Fig.…”

Section: Range Of Validity and Limitations Of The Second Order Cummentioning

confidence: 99%

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

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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...

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“…Second order cumulant expansion becomes increasingly worse as the quasiparticle energy moves closer to the band edges where correlations between subsequent scattering events induced by λV may become large. In this regime the low order self-energy corrections may represent a better approximation to the quasiparticle propagator, particularly in relation to its asymptotic time behavior characterized by the so-called quasiparticle collapse [36,[71][72][73][74]. Moreover, near the Fermi level the single particle approximation which separates electron from hole motion and leads to (34) and ( 35) becomes unrealistic and the processes like those shown in Fig.…”

Section: Range Of Validity and Limitations Of The Second Order Cumula...mentioning

confidence: 99%

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

Gumhalter,

Kovač,

Caruso

et al. 2016

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Since the earliest implementations of the various GW approximations and cumulant expansion in the calculations of quasiparticle propagators and spectra, several attempts have been made to combine the advantageous properties and results of these two theoretical approaches. While the GW plus cumulant approach has proven successful in interpreting photoemission spectroscopy data in solids, the formal connection between the two methods has not been investigated in detail. By introducing a general bijective integral representation of the cumulants, we can rigorously identify at which point these two approximations can be connected for the paradigmatic model of quasiparticle interaction with the dielectric response of the system that has been extensively exploited in recent interpretations of the satellite structures in photoelectron spectra. We establish a protocol for consistent practical implementation of the thus established GW+cumulant scheme, and illustrate it by comprehensive state-of-the-art first-principles calculations of intrinsic angle-resolved photoemission spectra from Si valence bands.

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Electron scattering by random adsorbates: A tunable decoherence mechanism in surface bands

Cited by 6 publications

References 35 publications

Secondary electron emission from surfaces with small structure

Secondary electron emission from surfaces with small structure

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

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

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