A brief review is given of recent positron studies of metal and semiconductor nanocrystals. The prospects offered by positron annihilation as a sensitive method to access nanocrystal (NC) properties are described and compared with other experimental methods. The tunability of the electronic structure of nanocrystals underlies their great potential for application in many areas. Owing to their large surface-to-volume ratio, the surfaces and interfaces of NCs play a crucial role in determining their properties. Here we focus on positron 2D angular correlation of annihilation radiation (2D-ACAR) and (two-detector) Doppler studies for investigating surfaces and electronic properties of CdSe NCs.

S. W. H. Eijt B. Barbiellini A. J. Houtepen D. Vanmaekelbergh P. E. Mijnarends A. Bansil

The effect of temperature controlled annealing on the confined valence electron states in CdSe nanocrystal arrays, deposited as thin films, was studied using two-dimensional angular correlation of annihilation radiation (2D-ACAR). A reduction in the intensity by ~35% was observed in a feature of the positron annihilation spectrum upon removal of the pyridine capping molecules above 200 degrees Celsius in a vacuum. This reduction is explained by an increased electronic interaction of the valence orbitals of neighboring nanocrystals, induced by the formation of inorganic interfaces. Partial evaporation of the nanoporous CdSe layer and additional sintering into a polycrystalline thin film was observed at a relatively low temperature of ~486 degrees Celsius.

S. W. H. Eijt P. E. Mijnarends L. C. van Schaarenburg A. J. Houtepen D. Vanmaekelbergh B. Barbiellini A. Bansil

Positron annihilation lifetime spectroscopy (PALS) and positron-electron momentum density (PEMD) studies on multilayers of PbSe nanocrystals (NCs), supported by transmission electron microscopy (TEM), show that positrons are strongly trapped at NC surfaces, where they provide insight into the surface composition and electronic structure of PbSe NCs. 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.

L. Chai W. Al-Sawai Y. Gao A. J. Houtepen P. E. Mijnarends B. Barbiellini H. Schut L. C. van Schaarenburg M. A. van Huis L. Ravelli W. Egger S. Kaprzyk A. Bansil S. W. H. Eijt

Laplacian Abelian Projection is discussed. This term refers to the use of a new (``Laplacian'') gauge fixing prescription for implementing the Abelian Projection of QCD. The gauge condition is based on the lowest-lying eigenvector of the covariant Laplacian operator in the adjoint representation. This Laplacian gauge fixing procedure is free of the ambiguities which plague lattice simulations which work with the popular Maximally Abelian Gauge. Furthermore, Laplacian gauge fixed configurations enjoy a natural kind of smoothness. These two properties are crucial for a reliable determination of physical quantities using the Abelian Projection. We also examine a new, Higgs-field-like observable which emerges as a by-product of the method. This quantity can be used to identify magnetic monopoles in a way independent of the traditional prescription. It is argued that physically relevant magnetic monopoles are accomodated well by the Laplacian method, while they are suppressed (too) strongly in Maximally Abelian Gauge. Finally, first evidence of abelian dominance in the Laplacian Abelian Projection is presented.

A. J. van der Sijs

In this work we show the advantages of using the Coulomb-hole plus screened-exchange (COHSEX) approach in the calculation of potential energy surfaces. In particular, we demonstrate that, unlike perturbative $GW$ and partial self-consistent $GW$ approaches, such as eigenvalue-self-consistent $GW$ and quasi-particle self-consistent $GW$, the COHSEX approach yields smooth potential energy surfaces without irregularities and discontinuities. Moreover, we show that the ground-state potential energy surfaces (PES) obtained from the Bethe-Salpeter equation, within the adiabatic connection fluctuation dissipation theorem, built with quasi-particle energies obtained from perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate results for diatomic molecules close to their equilibrium distance. When self-consistent COHSEX quasi-particle energies and orbitals are used to build the BSE equation the results become independent of the starting point. We show that self-consistency worsens the total energies but improves the equilibrium distances with respect to BSE@COHSEX@HF. This is mainly due to changes in the screening inside the BSE.

J. Arjan Berger Pierre-François Loos Pina Romaniello

We propose a simple and efficient real-space approach for the calculation of the ground-state energies of Wigner crystals in 1, 2, and 3 dimensions. To be precise, we calculate the first two terms in the asymptotic expansion of the total energy per electron which correspond to the classical energy and the harmonic correction due to the zero-point motion of the Wigner crystals, respectively. Our approach employs Clifford periodic boundary conditions to simulate the infinite electron gas and a renormalized distance to evaluate the Coulomb potential. This allows us to calculate the energies unambiguously and with a higher precision than those reported in the literature. Our results are in agreement with the literature values with the exception of harmonic correction of the 2-dimensional Wigner crystal for which we find a significant difference. Although we focus on the ground state, i.e., the triangular lattice and the body-centered cubic lattice, in two and three dimensions, respectively, we also report the classical energies of several other common lattice structures.

Estefania Alves Gian Luigi Bendazzoli Stefano Evangelisti J. Arjan Berger

The localization spread gives a criterion to decide between metallic versus insulating behaviour of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different operators are used for systems treated with Open or Periodic Boundary Conditions. In particular, in the case of periodic systems, we use the complex-position definition, that was already used in similar contexts for the treatment of both classical and quantum situations. In this study, we show that the localization spread evaluated on a finite ring system of radius $R$ with Open Boundary Conditions leads, in the large $R$ limit, to the same formula derived by Resta et al. for 1D systems with periodic Born-von K\'arm\'an boundary conditions. A second formula, alternative to the Resta's one, is also given, based on the sum-over-state formalism, allowing for an interesting generalization to polarizability and other similar quantities.

Celestino Angeli Gian Luigi Bendazzoli Stefano Evangelisti J. Arjan Berger

In this work we investigate the Wigner localization of two interacting electrons at very low density in two and three dimensions using the exact diagonalization of the many-body Hamiltonian. We use our recently developed method based on Clifford periodic boundary conditions with a renormalized distance in the Coulomb potential. To accurately represent the electronic wave function we use a regular distribution in space of gaussian-type orbitals and we take advantage of the translational symmetry of the system to efficiently calculate the electronic wave function. We are thus able to accurately describe the wave function up to very low density. We validate our approach by comparing our results to a semi-classical model that becomes exact in the low-density limit. With our approach we are able to observe the Wigner localization without ambiguity.

Miguel Escobar Azor Estefania Alves Stefano Evangelisti J. Arjan Berger

At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density profiles of fragments of Wigner crystals from first principles. To simulate Wigner fragments we use Clifford periodic boundary conditions and a renormalized distance in the Coulomb potential. Moreover, we show that high-spin restricted open-shell Hartree-Fock theory becomes exact in the low-density limit. We are thus able to accurately capture the localisation in two-dimensional Wigner fragments with many electrons. No assumptions about the positions where the electrons will localise are made. The density profiles we obtain emerge naturally when we minimise the total energy of the system. We clearly observe the emergence of the hexagonal crystal structure which has been predicted to be ground-state structure of the two-dimensional Wigner crystal.

Miguel Escobar Azor Amer Alrakik Louan de Bentzmann Xabier Telleria-Allika Alfredo Sánchez de Merás Stefano Evangelisti J. Arjan Berger

approaches. We demonstrate that the Wigner regime can be reached using small values of the confinement parameter. To obtain physical insight in our results we analyze them with a semi-analytical model for two electrons. Thanks to electronic-structure properties such as the one-body density and the particle-hole entropy, we are able to define a path that connects the Wigner regime to the Fermi-gas regime by varying the confinement parameter. In particular, we show that the particle-hole entropy as a function of the confinement parameter smoothly connects the two regimes. Moreover, it exhibits a maximum that could be interpreted as the transition point between the localized and delocalized regimes.

Xabier Telleria-Allika Miguel Escobar Azor Grégoire François Gian Luigi Bendazzoli Jon M. Matxain Xabier Lopez Stefano Evangelisti J. Arjan Berger