Multidimensional Watson lemma and its applications

Rytova, A. I.; Yarovaya, Elena

doi:10.1134/s0001434616030093

Cited by 13 publications

(11 citation statements)

References 7 publications

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“…For the Coulomb interaction W q we derive a modified form of the potential in ref. 's [26,27] for charges in a thin film of thickness d surrounded by a dielectric environment. In this work we explicitly take into account anisotropic dielectric tensors.…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, the optical response is given by a sum of Lorentzian peaks, whose position and oscillator strength is determined by the eigen energy E ν and wavefunctions Φ ν of exciton states ν. The latter are obtained by solving the Wannier equation [21,22,25] within an effective mass approximation and a thin-film approximation of the Coulomb potential to account for a non-uniform dielectric environment [26,27]. Details about the solution of the Wannier equation and the used ab initio parameters [28,29] are given in the SI.…”

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confidence: 99%

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Intrinsic lifetime of higher excitonic states in tungsten diselenide monolayers

et al. 2019

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The reduced dielectric screening in atomically thin transition metal dichalcogenides allows to study the hydrogen-like series of higher exciton states in optical spectra even at room temperature. The width of excitonic peaks provides information about the radiative decay and phonon-assisted scattering channels limiting the lifetime of these quasi-particles. While linewidth studies so far have been limited to the exciton ground state, encapsulation with hBN has recently enabled quantitative measurements of the broadening of excited exciton resonances. Here, we present a joint experimenttheory study combining microscopic calculations with spectroscopic measurements on the intrinsic linewidth and lifetime of higher exciton states in hBN-encapsulated WSe2 monolayers. Surprisingly, despite the increased number of scattering channels, we find both in theory and experiment that the linewidth of higher excitonic states is similar or even smaller compared to the ground state. Our microscopic calculations ascribe this behavior to a reduced exciton-phonon scattering efficiency for higher excitons due to spatially extended orbital functions. Monolayer transition metal dichalcogenides (TMDs)show pronounced Coulomb phenomena [1][2][3][4][5][6][7], which in bulk materials become observable predominantly at very low temperatures. Electron-hole pairs in TMDs exhibit binding energies of up to 0.5 eV giving rise to a Rydberg-like series of exciton states below the free particle bandgap [8][9][10][11]. While the relative position of excitonic resonances in optical spectra presents a fingerprint of Coulomb correlations [12][13][14], their linewidth contains information about their coherence lifetime and the underlying many-particle scattering processes. Previous studies on exciton linewidths in TMDs [15][16][17][18] have revealed efficient scattering into dark intervalley excitons [19] and have demonstrated strain-induced modifications of exciton-phonon scattering channels [20]. However, these studies have been restricted to the 1s exciton ground state, since the higher order resonances were dominated by inhomogeneous broadening and were challenging to resolve and analyze at elevated temperatures. Furthermore, exciton-phonon scattering within the rich phase space of excited exciton states has not been theoretically investigated in TMDs yet. Recently, the encapsulation of TMD materials in the layered wide-bandgap insulator hexagonal boron nitride (hBN) has been shown to drastically reduce the inhomogeneous broadening of excitonic resonances [10,11] and thereby enables to access temperature-dependent broadening of higher excitonic states.In this work, we present a joint experiment-theory study on the homogeneous broadening of higher excitonic resonances and the underlying microscopic scattering mechanism for the exemplary case of hBN-encapsulated * samuel.brem@chalmers.se Figure 1. Schematic illustration of the exciton bandstructure and possible scattering mechanisms. Optically generated excitons at zero center-of-mass momentum can dec...

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Intrinsic lifetime of higher excitonic states in tungsten diselenide monolayers

et al. 2019

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“…Twophoton absorption measurements have also been used to investigate excitonic states with p-symmetry, where a slight degeneracy break with respect to s-states is expected. 11 These features suggest that the electron-hole interaction potential in this system is not Coulombic: indeed, due to the lack of screening by the environment above the material layer, the interaction is expected to acquire a different form, as discussed decades ago 12,13 in the context of thin semiconductor films.…”

Section: Introductionmentioning

confidence: 95%

“…It is important to point out that despite the limitations of classical effective potential approaches 12,13 for describing atomically thin materials, they are a physical and efficient way of obtaining the electron-hole potential in the limit of a large number of layers. It is thus worthwile to investigate how this approach compares to the QEH model as the number of layers increases, in order to obtain a deeper understanding of the limitations of this simple approach.…”

Section: Introductionmentioning

confidence: 99%

Electrostatics of electron-hole interactions in van der Waals heterostructures

et al. 2018

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The role of dielectric screening of electron-hole interaction in van der Waals heterostructures is theoretically investigated. A comparison between models available in the literature for describing these interactions is made and the limitations of these approaches are discussed. A simple numerical solution of Poisson's equation for a stack of dielectric slabs based on a transfer matrix method is developed, enabling the calculation of the electron-hole interaction potential at very low computational cost and with reasonable accuracy. Using different potential models, direct and indirect exciton binding energies in these systems are calculated within Wannier-Mott theory, and a comparison of theoretical results with recent experiments on excitons in two-dimensional materials is discussed.PACS numbers:

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“…Under assumption (2) a BRW is called a heavy-tailed BRW. In this case we get the following recurrence criteria for BRWs with infinite variance of jumps: G 0 = ∞ for d = 1, α ∈ [1, 2), and G 0 is finite if d = 1, α ∈ (0, 1), or d ≥ 2, α ∈ (0, 2), followed from the behavior of p(t, x, y) ∼ h d,α t − d α as t → ∞, where h d,α is a positive constant depending on dimension of Z d (see, details in (Rytova and Yarovaya, 2016;Yarovaya, 2013)).…”

Section: Model and Previous Resultsmentioning

confidence: 99%

Survival analysis of particle populations in branching random walks

Rytova

Yarovaya

2019

Communications in Statistics - Simulation and Computation

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It is a common practice to describe branching random walks in terms of birth, death and walk of particles, which makes it easier to use them in different applications. The main results obtained for the models of symmetric continuoustime heavy-tailed branching random walks on a multidimensional lattice. We will be mainly interested in studying the problems related to the limiting behavior of branching random walks such as the existence of phase transitions under change of various parameters, the properties of the limiting distribution and the survival probability of a particle population. Emphasis is made on the survival analysis. The answers to these and other questions essentially depend on numerous factors which affect the properties of a branching random walk. Therefore, we will try to describe how the properties of a branching random walk depend on such characteristics of the underlying random walk as finiteness or infiniteness of the variance of jumps. The presented results are based on the Green's function representations of the transition probabilities of a branching random walk.

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Multidimensional Watson lemma and its applications

Cited by 13 publications

References 7 publications

Intrinsic lifetime of higher excitonic states in tungsten diselenide monolayers

Intrinsic lifetime of higher excitonic states in tungsten diselenide monolayers

Electrostatics of electron-hole interactions in van der Waals heterostructures

Survival analysis of particle populations in branching random walks

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