Electron-positron Momentum Density Research Articles

Local electron correlation effects on the fermiology of the weak itinerant ferromagnet ZrZn2

The Fermi surface topology plays an important role in the macroscopic properties of metals. It can be particularly sensitive to electron correlation, which appears to be especially significant for the weak itinerant ferromagnet ZrZn2. Here, we look at the differences in the predicted Fermi surface sheets of this metallic compound in its paramagnetic phase for both density functional theory (DFT) and the combination of DFT with dynamical mean field theory (DFT + DMFT). The theoretical spectral functions evaluated at the Fermi level were used along with calculations of the electron–positron momentum density (also known as the two-photon momentum density) in k-space to provide insights into the origin of certain features of the Fermi surface topology. We compare this two photon momentum density to that extracted from the positron annihilation experimental data (2004 Phys. Rev. Lett. 92 107003). The DFT + DMFT densities are in better agreement with the experiment than the DFT, particularly with regard to the flat bands around the L and W high symmetry points. The experimental neck around L, which relates to a van Hove singularity, is present in DFT + DMFT but not in the DFT. We find that these flat bands, and as such the Fermi surface topology, are sensitive to the many body electron correlation description, and show that the positron annihilation technique is able to probe this. This description is significant for the observed behavior such as the Lifshiftz transition around the quantum critical point.

Study on anisotropies and momentum densities in AlN, GaN and InN by positron annihilation

The independent particle model (IPM) coupled with empirical pseudopotential method (EPM) was used to compute the thermalized positron charge densities in specific family of binary tetrahedrally coordinated crystals of formula ANB8-N. Initial results show a clear asymmetrical positron charge distribution relative to the bond center. It is observed that the positron density is maximum in the open interstices and is excluded not only, from the ion cores but also to a considerable degree from the valence bonds. Electron-positron momentum densities are calculated for the (001,110) planes. The results are used to analyze the positron effects in AlN, GaN and InN compounds. Our computational technique provides the theoretical means of interpreting the k-space densities obtained experimentally using the twodimensional angular correlation of annihilation radiation (2D-ACAR).

Understanding electron-positron momentum densities in solids: effect of the positron distribution

Abstract The influence of the positron distribution on the electron-positron (e-p) momentum densities (MDs) is studied in terms of the l (l = s, p, d, f) character of the initial electronic state. The effect of the positron is discussed for momenta in the extended and reduced zone scheme on the example of Al (simple metal), Cu (metal with almost filled d shell), and Cr (transition metal). Present result indicates a weak sensitivity of the e-p MD inside the central Fermi surface to the positron charge density for the delocalized s and p electrons. In the case of d states, the effect of the positron on the relevant contribution to the e-p MD directly reflects the degree of localization of d electrons in the electron density of states.

Compton Scattering and Various ACAR Experiments in~Mg

Electron positron (e p) momentum densities in Mg are studied using three di erent sets of angular correlation of annihilation radiation (ACAR) and Compton scattering experimental data. ACAR data, measured with almost identical resolution, give both a similar anisotropy of the Fermi surface and a similar e p enhancement factor inside this surface. However, as concerns a contribution of Umklapp components of valence-electron densities there are essential di erences depending on experimental data. Due to a strong dependence of such densities on di erent theoretical approaches describing e-p correlations, it is suggested to perform additional, high statistics and resolution ACAR measurements for Mg and analyze them as suggested in the paper.

Surfaces of colloidal PbSe nanocrystals probed by thin-film positron annihilation spectroscopy

Positron annihilation lifetime spectroscopy and positron-electron momentum density (PEMD) studies on multilayers of PbSenanocrystals (NCs),supported by transmission electron microscopy, show that positrons are strongly trapped at NC surfaces, where they provide insight into the surface composition and electronic structure of PbSeNCs. Our analysis indicates abundant annihilation of positrons with Se electrons at the NC surfaces and with O electrons of the oleic ligands bound to Pb ad-atoms at the NC surfaces, which demonstrates that positrons can be used as a sensitive probe to investigate the surface physics and chemistry of nanocrystals inside multilayers. Ab initio electronic structure calculations provide detailed insight in the valence and semi-core electron contributions to the positron-electron momentum density of PbSe. Both lifetime and PEMD are found to correlate with changes in the particle morphology characteristic of partial ligand removal.

Size estimation of embedded Cu nanoprecipitates in Fe by using affinitively trapped positrons

By utilizing a unique characteristic of the affinitively trapped positrons, here we demonstrate a powerful method to estimate the sizes of the embedded Cu nanoprecipitates (and subnanoprecipitates) (ECNPs) in Fe. The positron-electron momentum density distributions in the ECNPs with various sizes in a thermally aged Fe-Cu dilute alloy were measured by using the two-dimensional angular correlation of positron annihilation radiation technique and the momentum smearing around the Fermi cutoff was clearly observed. It is clarified that this smearing effect is proportional to the inverse of the average radii of the ECNPs and thus it can be employed to estimate the ECNPs' sizes. Moreover, the ECNPs' sizes obtained by the present method are compared with those obtained by the three-dimensional atom probe technique and good agreement is observed, justifying the size estimation using the smearing effect. It is noteworthy that the present technique can detect the smearing due to the ECNPs with their radii even below about 0.5 nm and thus gives an important trend in the smearing reflecting the average size of the ECNPs in this range.

Electron–positron momentum density distribution of Gd from 2D ACAR data via Maximum Entropy and Cormack’s methods

A successful application of the Maximum Entropy Method (MEM) to the reconstruction of electron–positron momentum density distribution in gadolinium out of the experimental of 2D ACAR data is presented. Formally, the algorithm used was prepared for two-dimensional reconstructions from line integrals. For the first time the results of MEM, applied to such data, are compared in detail with the ones obtained by means of Cormack’s method. It is also shown how the experimental uncertainties may influence the results of the latter analysis. Preliminary calculations, using WIEN2k code, of band structure and Fermi surface have been done as well.

Three-dimensional electron-positron momentum distribution of O3+-irradiated 6H SiC using two positron spectroscopy techniques simultaneously

A three-dimensional (3D) positron annihilation spectroscopy system (3DPASS) capable of determining 3D electron-positron (e−-e+) momentum densities from measurements of deviations from co-linearity and energies of photons from e−-e+ annihilation events was employed to examine the effects of O-atom defects in 6H SiC. Three-dimensional momentum datasets were determined for 6H SiC irradiated with 24 MeV O3+ ions. Angular correlation of annihilation radiation (ACAR) and coincidence Doppler-broadening of annihilation radiation (CDBAR) analyses are presented. In addition, a novel technique is illustrated for analyzing 3D momentum datasets in which the parallel momentum component, p|| (obtained from the CDBAR measurement) is selected for annihilation events that possess a particular perpendicular momentum component, p- observed in the 2D ACAR spectrum.

Influence of Electron-Electron Correlations and Lattice Effects on Positron-Electron Enhancement Factors

We present an approach taking into account the effect of electron-electron (e-e) correlations on electron-positron (e-p) momentum density distributions. The approach bases on the modification of the Bethe-Goldstone (B-G) equation for the positron in the electron gas due to self-energy effects. The example calculations have been performed for selected parameters corresponding to simple metals. The calculated dependencies exhibit the increase of the e-p enhancement factors below Fermi momentum, like Kahana enhancements, and a decrease above the Fermi sphere, leading to a many-body “tail” in the e-p momentum density distributions. Moreover, the influence of lattice effects on enhancement factors (EF) is taken into account. This decreases by a few percent the absolute values of the e-p momentum distributions and the corresponding annihilation rates and for real metals such as Mg or Cu evidently improve the agreement with experiment.

Experimental determination of the state-dependent enhancement of the electron-positron momentum density in solids

The state-dependence of the enhancement of the electron-positron momentum density is investigated for some transition and simple metals (Cr, V, Ag and Al). Quantitative comparison with linearized muffin-tin orbital calculations of the corresponding quantity in the first Brillouin zone is shown to yield a measurement of the enhancement of the s, p and d states, independent of any parameterizations in terms of the electron density local to the positron. An empirical correction that can be applied to a first-principles state-dependent model is proposed that reproduces the measured state-dependence very well, yielding a general, predictive model for the enhancement of the momentum distribution of positron annihilation measurements, including those of angular correlation and coincidence Doppler broadening techniques.

Effect of mono vacancy on electron and positron properties of 3C SiC

AbstractFirst principle calculation of the electron and positron band structure in the perfect and defected 3C silicon carbide (SiC) is performed within the linear muffin‐tin orbital (LMTO) method in the atomic spheres approximation (ASA). For Si and C vacancy the insulator‐metal transition is observed. Effect of the electron–positron interaction on the resulting positron distribution is studied. Theoretical electron and electron–positron momentum densities for Si and C mono vacancies, obtained within various approximations to the electron–positron correlations, are discussed in comparison with the relevant characteristics in the perfect 3C SiC.

STUDY ON MOMENTUM DENSITY IN SEMICONDUCTOR ALLOYS GeC and SnC BY POSITRON ANNIHILATION

The independent particle model (IPM) coupled with empirical pseudopotential method (EPM) was used to compute the thermalized positron charge densities in specific family of binary tetrahedrally coordinated crystals of formula ANB8-N . Initial results show a clear asymmetrical positron charge distribution relative to the bond center. It is observed that the positron density is maximum in the open interstices and is excluded not only from the ion cores but also to a considerable degree from the valence bonds. Electron-positron momentum densities are calculated for the (001, 110) planes. The results are used to analyze the positron effects in GeC and SnC . Our computational technique provides the theoretical means of interpreting the k-space densities obtained experimentally using the two-dimensional angular correlation of annihilation radiation (2D-ACAR).

Simultaneous, coincident 2-D ACAR and DBAR using segmented HPGe detectors incorporating sub-pixel interpolation

A three-dimensional Positron Annihilation Spectrometry System (3D PASS) for determination of 3D electron-positron (e--e+) momentum densities by measuring coincident annihilation photons was designed, constructed and characterized. 3D PASS collects a single data set including correlated photon energies and coincident photon positions which are typically collected separately by two-dimensional angular correlation of annihilation radiation (2D ACAR) and two-detector coincident Doppler broadening of annihilation radiation (CDBAR) spectrometry. 3D PASS is composed of two position-sensitive, high-purity germanium (HPGe) double-sided strip detectors (DSSD(s)) linked together by a 32-channel, 50 MHz digital electronics suite. The DSSDs data were analyzed to determine location of photon detection events using an interpolation method to achieve a spatial resolution less than the 5-mm width of the DSSDs' charge collection strips. The interpolation method relies on measuring a figure-of-merit proportional to the area of the transient charges observed on both strips directly adjacent to the charge collection strip detecting the full charge deposited by the annihilation photon. This sub-pixel resolution, corresponding to the error associated with event location within a sub-pixel was measured for both DSSDs using the approach outlined in Williams et al [1] and was on the order of ± 0.20 mm (± one-standard deviation). As a result of the sub-pixel resolution, the distance between the DSSDs and material sample was reduced by a factor of five compared to what is typically required in 2D ACAR systems was necessary to achieve 0.5-mrad angular resolution. This reduction in the system's footprint decreases attenuation of the annihilation photons in the air between the material sample and the DSSDs and increases the solid angle between the sample and the DSSDs, ultimately resulting in higher system detection efficiency. 3D PASS was characterized in the same manner comparable to state-of-the-art 2D ACAR and CDBAR spectrometers. 3D PASS spectra were collected and analyzed for single-crystal copper (Cu) and silicon carbide (6H SiC) and compared with the results in the literature.

Study on momentum density in semiconductor compounds ZnS, ZnSe and ZnTe by positron annihilation

The independent particle model (IPM) coupled with empirical pseudopotential method (EPM) was used to compute the thermalised positron charge densities in specific family of binary tetrahedrally coordinated crystals of formula ANB8?N . Initial results show a clear asymmetrical positron charge distribution relative to the bond centre. It is observed that the positron density is maximum in the open interstices and is excluded not only, from the ion cores but also to a considerable degree from the valence bonds. Electron-positron momentum densities are calculated for the (001, 110) planes. The results are used to analyse the positron effects in ZnS, ZnSe and ZnTe. Our computational technique provides the theoretical means of interpreting the k-space densities obtained experimentally using the two-dimensional angular correlation of annihilation radiation (2D-ACAR).

Theoretical studies of positron annihilation in YN and ScN

Valence electron and positron charge densities in YN and ScN are obtained from wave functions derived in a model pseudopotential band structure calculation coupled with the independent particle model (IPM). It is observed that the positron density is maximum in the open interstices and is excluded not only, from the ion cores but also to a considerable degree from the valence bonds. Electron–positron momentum densities are calculated for the (0 0 1) and (1 1 0) planes. The results are used to analyze the positron effect in binary alloy semiconductors.

Comparison of Various Reconstruction Techniques for Line Projections

The most effective and popular algorithms to reconstruct the three-dimensional electron–positron momentum density from the measurements of the two-dimensional angular correlation of annihilation radiation are based on the Fourier transform or polynomial expansion. We compare the efficacy of different methods in reconstructing the momentum density of the rare-earth based compounds ErGa3, CeIn3 and model profiles, presenting also our new filtering algorithm.

Image of electron densities from line and plane projections

We compare Fourier transforms with orthogonal polynomials techniques applied in reconstructing three-dimensional electron–positron momentum densities from two-dimensional angular correlation of annihilation radiation (2D-ACAR) spectra and electron momentum densities from one-dimensional Compton profiles (1D-CP). In the case of Fourier transforms, we show results for two different algorithms: filtered back projection and Fourier–Bessel method. These techniques are presented for 2D-ACAR spectra in Y, ErGa3 and model profiles.

Influence of Atomic Sphere Radii on the Electron-Positron Momentum Density Calculated for SiC within the LMTO-ASA

Influence of Atomic Sphere Radii on the Electron-Positron Momentum Density Calculated for SiC within the LMTO-ASA

Many-body effects on the electron-positron momentum density in simple and transition metals: Comparison with positron annihilation spectroscopy data

This paper deals with the influence of many-body effects on the electron-positron ($e$-$p$) momentum density in simple and transition metals. Five theoretical approaches to calculating $e$-$p$ momentum densities are confronted with three-dimensional densities, reconstructed from two-dimensional angular correlation of annihilation radiation experimental spectra in Mg, Cd, Cu, and Y. It is shown that a proper description of $e$-$p$ correlations has to include the lattice-periodical crystal potential as is done, e.g., in the Bloch-modified ladder theory. Moreover, it is demonstrated that electron-electron correlations are visible not only in Compton scattering but also in positron annihilation experiments.

Positron annihilation in boron nitride

Electron and positron charge densities are calculated as a function of position in the unit cell for boron nitride. Wave functions are derived from pseudopotential band structure calculations and the independent particle approximation (IPM), respectively, for electrons and positrons. It is observed that the positron density is maximum in the open interstices and is excluded not only from ion cores but also to a considerable degree from valence bonds. Electron-positron momentum densities are calculated for (001,110) planes. The results are used in order to analyse the positron effects in BN.