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 `__ · :doc:`Catalogue ` · :doc:`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 :doc:`review register ` for the checks and decisions.