Martti J. Puska

Electronic structure calculations with GPAW: A real-space implementation of the projector augmented-wave method

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.

Defect spectroscopy with positrons: A general calculational method

A new, versatile method of calculating positron states in solids is described. The main purpose is to develop a practical scheme accurate enough to reliably predict annihilation characteristics for positrons trapped at defect clusters of varying size, geometry and impurity environment, in order to help analyse experimental data. The positron potential is constructed from the full lattice electrostatic potential, and a local-density approximation for the correlation potential. The three-dimensional positron Schrodinger equation is solved by finite-element techniques. Enhancement effects in the annihilation rate are parametrised in a simple way, both for simple and transition metals. The applications discussed include vacancies, vacancy clusters and impurity-vacancy complexes in a number of metals. Good agreement with experiment in cases where comparison is possible suggests a good predictive power for the scheme.

Positron affinities for elemental metals

The relevant quantity in the comparison of the absolute positron energy levels in different materials is the sum of the internal electron and positron chemical potentials, i.e. the sum of the Fermi level and the bottom of the lowest positron band relative to a common, well-defined reference energy. This sum is defined as the positron affinity. The positron affinity reflects the preference of the positron for different components in heterostructures made of different materials and the preference between the host matrix and precipitates in alloys. Moreover, the affinity is closely related to the positron work function and positronium formation potential which are important parameters in the slow-positron-beam experiments. The authors have determined the positron affinity for the alkaline and alkaline-earth metals, 3d-, 4d-, and 5d-transition metal series, and for some metals on the right in the Periodic Table. The diamond structure semiconductors are also considered. The determination is based on the self-consistent electron structure calculations and the subsequent calculation of the positron band structure within the local-density approximation. The trends are studied and interpreted along the different columns and rows of the Periodic Table. The results are also compared with available experiments.

Time-dependent density-functional theory in the projector augmented-wave method.

We present the implementation of the time-dependent density-functional theory both in linear-response and in time-propagation formalisms using the projector augmented-wave method in real-space grids. The two technically very different methods are compared in the linear-response regime where we found perfect agreement in the calculated photoabsorption spectra. We discuss the strengths and weaknesses of the two methods as well as their convergence properties. We demonstrate different applications of the methods by calculating excitation energies and excited state Born-Oppenheimer potential surfaces for a set of atoms and molecules with the linear-response method and by calculating nonlinear emission spectra using the time-propagation method.

Impurity effects in quantum dots: Toward quantitative modeling

We have studied the single-electron transport spectrum of a quantum dot in

Three real-space discretization techniques in electronic structure calculations

\mathrm{GaAs}∕\mathrm{AlGaAs}

Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories

resonant tunneling device. The measured spectrum has irregularities indicating a broken circular symmetry. We model the system with an external potential consisting of a parabolic confinement and a negatively charged Coulombic impurity placed in the vicinity of the quantum dot. The model leads to good agreement between the calculated single-electron eigenenergies and the experimental spectrum. Furthermore, we use the spin-density-functional theory to study the energies and angular momenta when the system contains many interacting electrons. In the high magnetic field regime the increasing electron number is shown to reduce the distortion induced by the impurity.

Native defects and self-diffusion in GaSb

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

Hydrogen chemisorbed on nickel surfaces: A wave-mechanical treatment of proton motion

We study a model quantum dot system in an external magnetic field by using both spin-density-functional theory and current-spin density-functional theory. The theories are used with local approximations for the spin-density and vorticity. The reliabilities of different parametrizations for the exchange-correlation functionals are tested by comparing the ensuing energetics with quantum Monte Carlo results. The limit where the vorticity dependence should be used in the exchange-correlation functionals is discussed.

Conductance oscillations in metallic nanocontacts

The native defects in GaSb have been studied with first-principles total-energy calculations. We report the structures and the formation energies of the stable defects and estimate the defect concentrations under different growth conditions. The most important native defect is the GaSb antisite, which acts as an acceptor. The other important defects are the acceptor-type Ga vacancy and the donor-type Ga interstitial. The Sb vacancies and interstitials are found to have much higher formation energies. A metastable state is observed for the SbGa antisite. The significantly larger concentrations of the Ga vacancies and interstitials compared to the corresponding Sb defects is in accordance with the asymmetric self-diffusion behavior in GaSb. The data supports the next-nearest-neighbor model for the self-diffusion, in which the migration occurs independently in the different sublattices. Self-diffusion is dominated by moving Ga atoms.