Analysis of the Vignale-Kohn current functional in the calculation of the optical spectra of semiconductors

Abstract

Analysis of the Vignale-Kohn current functional in the calculation of the optical spectra of semiconductors Berger, J. A.; de Boeij, P. L.; van Leeuwen, R. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. In this work, we investigate the Vignale-Kohn current functional when applied to the calculation of optical spectra of semiconductors. We discuss our results for silicon. We found qualitatively similar results for other semiconductors. These results show that there are serious limitations to the general applicability of the VignaleKohn functional. We show that the constraints on the degree of nonuniformity of the ground-state density and on the degree of the spatial variation of the external potential under which the Vignale-Kohn functional was derived are almost all violated. We argue that the Vignale-Kohn functional is not suited to use in the calculation of optical spectra of semiconductors since the functional was derived for a weakly inhomogeneous electron gas in the region above the particle-hole continuum, whereas the systems we study are strongly inhomogeneous and the absorption spectrum is closely related to the particle-hole continuum. DOI: 10.1103/PhysRevB.75.035116 PACS number͑s͒: 71.45.Gm, 31.15.Ew, 78.20.Ϫe, 78.66.Db I. INTRODUCTIONTime-dependent density functional theory ͑TDDFT͒ developed by Runge and Gross 1 makes it possible to describe the dynamic properties of interacting many-particle systems in an exact manner. 1-4 Dhara and Ghosh 5 and Ghosh and Dhara 6 showed that the Runge-Gross theorem could be extended to systems that are subjected to general timedependent electromagnetic fields ͑see also Ref. 7͒. The method has proven to be an accurate tool in the study of electronic response properties. 3,8,9 In this paper, we study infinite systems for which we use time-dependent currentdensity-functional theory ͑TDCDFT͒. 7,[10][11][12] In this approach, the electron density of TDDFT is substituted by the electron current density as the fundamental quantity. There are mainly three reasons to use TDCDFT instead of ordinary TDDFT. The first reason is related to the use of periodic boundary conditions, which provide an efficient way to describe infinite systems but that artificially remove the effects of density changes at the surface. 13 For example, when a system is perturbed by an electric field there will be a macroscopic response of the system and a current will be flowing through the interior with a n...

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