Nonadiabatic dynamics of electron scattering from adsorbates in surface bands

Gumhalter, B.; Šiber, Antonio; Buljan, Hrvoje; Fauster, Thomas

doi:10.1103/physrevb.78.155410

Cited by 22 publications

(28 citation statements)

References 77 publications

(77 reference statements)

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“…[61] where it is analyzed the decay of a surface spin excitation when it interacts with a spin chain. A similar dynamics was recently predicted for a quasiparticle excitation at adsorbates in a surface band [62]. The real part of both poles of the GF coincide with the site energy, which means that the effective frequency is zero.…”

Section: A Region I: Collapsed Resonances (Overdamped Decay)mentioning

confidence: 72%

Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

2008

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We discuss how the bath's memory affects the dynamics of a swap gate. We present an exactly solvable model that shows various dynamical transitions when treated beyond the Fermi Golden Rule. By moving continuously a single parameter, the unperturbed Rabi frequency, we sweep through different analytic properties of the density of states: (I) collapsed resonances that split at an exceptional point in (II) two resolved resonances ; (III) out-of-band resonances; (IV) virtual states; and (V) pure point spectrum. We associate them with distinctive dynamical regimes: overdamped, damped oscillations, environment controlled quantum diffusion, anomalous diffusion and localized dynamics respectively. The frequency of the swap gate depends differently on the unperturbed Rabi frequency. In region I there is no oscillation at all, while in the regions III and IV the oscillation frequency is particularly stable because it is determined by the environment's band width. The anomalous diffusion could be used as a signature for the presence of the elusive virtual states.

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Section: A Region I: Collapsed Resonances (Overdamped Decay)mentioning

confidence: 72%

Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

2008

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“…Once the stationary state of the electronic system described by the eigenstates of (4) has been attained, the electron decoherence and decay from stationary states may be described by the formalisms of Refs. [16,17,46]. www.pss-b.com of screening of quasiparticles at surfaces provides basic insight into the early evolution of energetics of intermediate electronic states probed in time and energy resolved pumpprobe investigations of the surface electronic structure and dynamics.…”

Section: Representation Of Exciton Screening By a N E F F E C T I V Ementioning

confidence: 98%

“…This gives way to the domination of individual interactions of quasiparticles with their developing screening charges as described by the last two terms on the RHS of (46). When the asymptotic limit of fully screened total interaction is reached (given by the sum of non-binding or very weakly binding e-h potential and fully developed electron and hole image potentials), the individual quasiparticle states will be well described by the final state one-particle Hamiltonian (4).…”

Section: Representation Of Exciton Screening By a N E F F E C T I V Ementioning

confidence: 99%

Excitonic precursor states in ultrafast pump–probe spectroscopies of surface bands

Gumhalter

Lazić

Došlić

2010

Physica Status Solidi (b)

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Phone: þ385 1 4698 805, Fax: þ385 1 4698 889We discuss the formation and evolution of transient coherent excitonic states induced by ultrashort laser irradiation of metal surfaces supporting the surface and image potential bands (typically the low index surfaces of Cu and Ag). These states, which evolve into the image potential states in the course of screening of primary optically excited electron-hole pair, may play the role of early intermediate states in pump-probe spectroscopies of surfaces (e.g. two-photon-photoemission or sum-frequency generation) if the formation of image charge density proceeds on the time scale of the order of or longer than the pump-probe pulse duration and delay. In this regime a pump-probe experiment may yield information on the characteristics of such states rather than the states in relaxed image potential bands. Time scales of the various stages of these processes are estimated using an exactly solvable model of surface screening.1 Early time interactions of quasiparticles excited at surfaces The interpretation of excitation and detection of quasiparticles at surfaces in pump-probe experiments utilizing ultrashort laser pulses requires the assessment of quasiparticle dynamics and system relaxation from a true early evolution standpoint. While the nonadiabatic dynamics has been discussed in connection with the studies of surfaces and surface reactions by pulsed laser beams (for review see Refs. [1, 2]), the non-Markovian relaxation effects [3,4] following optical excitation of surfaces have only recently become the subject of interest and theoretical modelling [5]. Here we shall discuss these effects on the example of two-photon-photoemission (2PPE) from paradigmatic systems whose initial ground state accommodates partly occupied quasi-two-dimensional surface state bands (Q2D SS-bands) on top of the bulk valence and conduction band structure [typically on (111) surfaces of Cu and Ag]. The discussion will be focused on electronic screening processes as the dominant relaxation mechanism and in this context on the dynamics of formation of the much discussed Q2D image potential band states (IS-states) that are observed in the surface projected band gaps between the vacuum level E V and the Fermi energy E F of the substrate [6]. These bands are not incorpotated in the initial equilibrium electronic structure because they arise as a result of the response of the system to introduction of electronic charge outside the surface.In the initial step of 2PPE from surface bands [7] an electron excited out of the SS-band state by absorption of a pump pulse photon of energy v pu E V À E F will first feel the initial state effective substrate potential and the interaction with unscreened SS-hole left behind. This leads to formation of a coherent primary exciton whose bound state discrete energy levels E l < E V may form a Rydberglike series characterized by the quantum numbers l that reflect the specificities of constrained electronic motion [8][9][10]. Subsequently, the two photocreated quasipart...

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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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Nonadiabatic dynamics of electron scattering from adsorbates in surface bands

Cited by 22 publications

References 77 publications

Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

Dynamical regimes of a quantum SWAP gate beyond the Fermi golden rule

Excitonic precursor states in ultrafast pump–probe spectroscopies of surface 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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