franta_2014

D. Franta, D. Nečas, L. Zajíčková and I. Ohlídal, “Broadening of dielectric response and sum rule conservation”, Thin Solid Films 571, 496 (2014)

Source record · Catalogue · Review register

DOI: 10.1016/j.tsf.2013.11.148

Source kind: theory

Recorded technique: Theory: which quantity to convolve with a broadening function (the transition probability J = E^2 eps_i, the transition strength F = E eps_i, or eps_i itself) so that the Thomas-Reiche-Kuhn sum rule of franta_2013 is conserved, and how to combine the broadening with the Kramers-Kronig transform.

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 0 formulas.

Curation notes

Journal pages 496-501 = PDF pages 1-6. Identity checked against the first page. No material values: this record holds the definitions the UDM uses for broadening (franta_2014b, franta_2015b and franta_2017 cite it for the ‘Gauss-Dawson’ epsilon-broadening).

EQUATION MAP (journal pages). - Definitions, Eq. (1), p. 496: eps_i ~ J/E^2 = F/E; Eq. (2): int_0^inf F dE = N; Eq. (3): sigma_r ~ (eps0/hbar) F. - Gaussian broadening function, Eq. (13), p. 497: beta(x) = exp(-x^2/(2 B^2))/(sqrt(2 pi) B), B > 0 the rms width (energy). Lorentzian, Eq. (26), p. 498: beta(x) = (B/pi)/(x^2 + B^2). - The three broadenings, Eqs. (14)-(15), p. 497: J-broadening eps~_i = (beta * J)/E^2; F-broadening eps~_i = (beta * F)/E; eps-broadening eps~_i = beta * eps_i (* = convolution in E; beta must be even). General form Eq. (18): F~_m(E) = (E^m/2) int [beta(E - t) + (-1)^m beta(E + t)] F(t) t^-m dt, m = -1, 0, 1 for J-, F-, eps-broadening. - Sum-rule result (Section 4, pp. 497-498): F- and eps-broadening conserve int F dE (Eqs. (22), (23)); J-broadening does not (Eq. (24); Gaussian: Eq. (25), I = (sqrt(2) t/B) D(t/(sqrt(2) B)) with D the Dawson integral, equal to 1 at t ~ 1.307 B; Lorentzian: Eq. (27), I = 1/(1 + (B/t)^2) < 1). - Recommendations (pp. 498-499, 501): eps-broadening for interband transitions (F- and J-broadening create a spurious Drude-like singularity at E -> 0); F-broadening for intraband transitions (eps-broadening empties the region around E = 0); eps-broadening for multi-phonon bands (Section 5.3). FT-broadening (F-broadening times the Fermi-Dirac factor, Eqs. (32)-(33)) for direct intraband transitions at finite temperature (p. 500); Eq. (34) gives the strength moved to free carriers. - Real part (Section 6, p. 500): eps-broadened eps~_r = H[beta] * eps_i (Eq. (36)); for the Gaussian, Eq. (37): H[beta](x) = -(sqrt(2)/(pi B)) D(x/(sqrt(2) B)); F-broadened eps~_r = (1/E)(H[beta] * F) (Eq. (39)); complex kernel beta^ = H[beta] + i beta (Eq. (40)) - the ‘Gauss-Dawson’ function of franta_2014b Eq. (27). The Gaussian peak of the UDM (franta_2015b Eqs. (41)-(42)) is exactly the eps-broadening of a delta line with this kernel.

TEXT CORRECTION (not a coefficient): below Eq. (34), p. 500, the text reads ‘F~(E) is obtained using F-broadening in the case of intraband transitions and eps-broadening in the case of intraband transitions’; the second ‘intraband’ must be ‘interband’, by Sections 5.1-5.2 and the conclusion (p. 501).

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

No datasets are recorded.

Formulas

No formulas are recorded.

Corrections

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.