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

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 electronpositron 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 semi-empirical WDA-based approach in which a sum-rule is imposed to reproduce the experimental lifetimes.

A multi-stop time-of-flight spectrometer for the measurement of positron annihilation-induced electrons in coincidence with the Doppler-shifted annihilation gamma photon

“…The gamma-Auger electron coincidence spectroscopy technique described in Section 3.3.2 can extract the contribution of the momenta of specific core electronic levels to the total Doppler broadening of the annihilation gamma spectrum. This provides a method to experimentally benchmark the ability of existing ab-initio techniques that aims to accurately predict the characteristics of a surface-trapped positron [44]. The gamma spectra associated with Auger electron emission have zero contribution from Ps formation; whereas the gamma photons that are associated with the exponentially decaying tail of the secondary electron spectrum, as shown in Figure 12(a), are entirely due to Ps formation.…”

“…On the other hand, the no-coincidence singles spectrum contains Doppler-shifted annihilation gamma photons from both valence and core annihilations. The singles spectrum is, however, dominated by valence annihilations because of the reduced overlap of the positron wavefunction with electron wavefunction belonging to the core electronic states [5][6][7]44] and therefore should exhibit less broadening than the spectrum associated with the K-shell annihilations. Figure 14(b) shows that the Doppler-broadened spectrum from K-shell annihilations is significantly broader than the singles spectrum: the FWHM of the K-shell annihilation spectrum is 1.5 times the FWHM of the singles spectrum.…”

Nature of the Positron State in CdSe Quantum Dots

“…In this Letter, we demonstrate the existence of a positron surface state in CdSe QDs through quantitative and systematic comparison of PALS spectra with corresponding first-principles calculations. Two methods, namely, the LDA+CMM [22,23] and the recently developed implementation of the WDA [24,25], are used to model the electron-positron correlation potential. In contrast to the standard implementation of the LDA+CMM, our calculations within the WDA show that the positron wave function is characterized consistently by the presence of a clear peak located at the surface of CdSe QDs, with calculated lifetimes close to the experimental values.…”

“…Indeed, since the LDA enhancement factor implicitly assumes that the screening electron cloud is attached to the positron, its use is inconsistent with the use of the image potential since the screening cloud resides at the surface of the material [23]. In contrast, the WDA has the correct asymptotic behavior far away from the surface, and hence it does not require an empirical correction of the potential and the enhancement factor [21], but corrections are necessary in order to reproduce the experimental bulk lifetimes [24,45,46]. Here we apply the shell-partitioning method, treating the Cd(5s), Cd(4d), S(4s) and Se(4p) electrons as valence electrons, and a modified screening charge Q [24], assumed to be equal to the charge of a single electron in earlier work [45,46].…”

“…In contrast, the WDA has the correct asymptotic behavior far away from the surface, and hence it does not require an empirical correction of the potential and the enhancement factor [21], but corrections are necessary in order to reproduce the experimental bulk lifetimes [24,45,46]. Here we apply the shell-partitioning method, treating the Cd(5s), Cd(4d), S(4s) and Se(4p) electrons as valence electrons, and a modified screening charge Q [24], assumed to be equal to the charge of a single electron in earlier work [45,46]. In this way, an adequate description of the screening can be obtained, which in turn can be expected to yield a good description of the electron-positron interaction potential at the surface.…”