Application of the weighted-density approximation to the accurate description of electron-positron correlation effects in materials

Vincent Callewaert, Rolando Saniz, Bernardo Barbiellini, Arun Bansil, and Bart Partoens

Phys. Rev. B 96, 085135 – Published 24 August 2017

Abstract

We discuss positron-annihilation lifetimes for a set of illustrative bulk materials within the framework of the weighted-density approximation (WDA). The WDA can correctly describe electron-positron correlations in strongly inhomogeneous systems, such as surfaces, where the applicability of (semi-)local approximations is limited. We analyze the WDA in detail and show that the electrons which cannot screen external charges efficiently, such as the core electrons, cannot be treated accurately via the pair correlation of the homogeneous electron gas. We discuss how this problem can be addressed by reducing the screening in the homogeneous electron gas by adding terms depending on the gradient of the electron density. Further improvements are obtained when core electrons are treated within the LDA and the valence electron using the WDA. Finally, we discuss a semiempirical WDA-based approach in which a sum rule is imposed to reproduce the experimental lifetimes.

Received 16 May 2017
Revised 28 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.085135

Physics Subject Headings (PhySH)

Elemental materials

Density functional approximations Positron annihilation spectroscopy

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Vincent Callewaert^1,*, Rolando Saniz¹, Bernardo Barbiellini², Arun Bansil², and Bart Partoens¹

¹Department of Physics, Universiteit Antwerpen, Antwerpen 2020, Belgium
²Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA

^*vincent.callewaert@uantwerpen.be

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Vol. 96, Iss. 8 — 15 August 2017

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Images

Figure 1
Comparison of the LDA potentials as parametrized by Boronski and Nieminen (BN) [19], and Drummond et al. (Dr) [31] with the corresponding WDA potentials of Eq. (20) for the homogeneous electron gas. For the enhancement factors, we took the parametrizations from the same references.
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Figure 2
Results of (a) positron annihilation lifetime calculations and (b) the relative change in the electron positron overlap with respect to the LDA for various elemental materials using Rubaszek's [28] approach. Horizontal black lines denote the LDA lifetimes for each system. Different colors are used to distinguish the results for various choices of the enhancement factor $γ$ : BR (Brandt-Reinheimer), BN (Boronski-Nieminen), and Dr (Drummond).
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Figure 3
Results of a simple model (discussed in the text) to illustrate the behavior of WDA screening in the vicinity of a local minimum (left column of panels) and maximum (right column of panels) of the electron density. The position of the positron $r_{p}$ is taken at $r = 0$ (red dots in topmost figures). The second row plots the radial dependence of the screening cloud for the LDA (green), the WDA using the local electron density (orange), and the WDA using an effective density that satisfies the sum rule (blue). The insets show the same quantities on a linear scale. Figures in the bottom row show the radially integrated differences between the WDA and LDA screening clouds; in order to satisfy the sum rule, this quantity should integrate to zero.
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Figure 4
Scaling of (a) the relative error of the lifetime and (b) the relative change in the electron-positron overlap with respect to the LDA with the gradient correction parameter $α$ applied to the WDA. (c) Lifetimes obtained via Eq. (30) where the local density is inserted in the enhancement factor instead of the effective density [unlike the results in (a)]. Only results obtained with the Drummond enhancement term are shown. Markers indicate calculated results and lines serve as guides to the eye.
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Figure 5
Results of (a) positron annihilation lifetime calculations and (b) the relative change in the electron positron overlap with respect to the LDA for various elemental materials using the WDA with shell partitioning. Horizontal black lines denote the LDA lifetimes for each system. Different colors are used to distinguish the results for various choices of the enhancement factor $γ$ : BR (Brandt-Reinheimer), BN (Boronski-Nieminen), and Dr (Drummond).
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Figure 6
Scaling of the calculated positron annihilation lifetimes with an imposed screening charge in the sum rule. The results have been obtained with shell partitioning and the Drummond enhancement factor.
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