Real-space local polynomial basis for solid-state electronic-structure calculations: A finite-element approach

We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the method is completely general and its convergence can be controlled systematically. Because the basis functions are strictly local in real space, the method allows for variable resolution in real space; produces sparse, structured matrices, enabling the effective use of iterative solution methods; and is well suited to parallel implementation. The method thus combines the significant advantages of both real-space-grid and basis-oriented approaches and so promises to be particularly well suited for large, accurate ab initio calculations. We develop the theory of our approach in detail, discuss advantages and disadvantages, and report initial results, including the first fully three-dimensional electronic band structures calculated by the method.Comment: replacement: single spaced, included figures, added journal referenc

Model for nucleation in GaAs homoepitaxy derived from first principles

The initial steps of MBE growth of GaAs on beta 2-reconstructed GaAs(001) are investigated by performing total energy and electronic structure calculations using density functional theory and a repeated slab model of the surface. We study the interaction and clustering of adsorbed Ga atoms and the adsorption of As_2 molecules onto Ga atom clusters adsorbed on the surface. The stable nuclei consist of bound pairs of Ga adatoms, which originate either from dimerization or from an indirect interaction mediated through the substrate reconstruction. As_2 adsorption is found to be strongly exothermic on sites with a square array of four Ga dangling bonds. Comparing two scenarios where the first As_2 gets incorporated in the incomplete surface layer, or alternatively in a new added layer, we find the first scenario to be preferable. In summary, the calculations suggest that nucleation of a new atomic layer is most likely on top of those surface regions where a partial filling of trenches in the surface has occurred before.Comment: 8 pages, 14 figures, Submitted to Phys. Rev. B (December 15, 1998). Other related publications can be found at http://www.fhi-berlin.mpg.de/th/paper.htm

Basis Functions for Linear-Scaling First-Principles Calculations

In the framework of a recently reported linear-scaling method for density-functional-pseudopotential calculations, we investigate the use of localized basis functions for such work. We propose a basis set in which each local orbital is represented in terms of an array of `blip functions'' on the points of a grid. We analyze the relation between blip-function basis sets and the plane-wave basis used in standard pseudopotential methods, derive criteria for the approximate equivalence of the two, and describe practical tests of these criteria. Techniques are presented for using blip-function basis sets in linear-scaling calculations, and numerical tests of these techniques are reported for Si crystal using both local and non-local pseudopotentials. We find rapid convergence of the total energy to the values given by standard plane-wave calculations as the radius of the linear-scaling localized orbitals is increased.Comment: revtex file, with two encapsulated postscript figures, uses epsf.sty, submitted to Phys. Rev.

Role of multiple subband renormalization in the electronic transport of correlated oxide superlattices

Metallic behavior of band-insulator/ Mott-insulator interfaces was observed in artificial perovskite superlattices such as in nanoscale SrTiO3/LaTiO3 multilayers. Applying a semiclassical perspective to the parallel electronic transport we identify two major ingredients relevant for such systems: i) the quantum confinement of the conduction electrons (superlattice modulation) leads to a complex, quasi-two dimensional subband structure with both hole- and electron-like Fermi surfaces. ii) strong electron-electron interaction requires a substantial renormalization of the quasi-particle dispersion. We characterize this renormalization by two sets of parameters, namely, the quasi-particle weight and the induced particle-hole asymmetry of each partially filled subband. In our study, the quasi-particle dispersion is calculated self-consistently as function of microscopic parameters using the slave-boson mean-field approximation introduced by Kotliar and Ruckenstein. We discuss the consequences of strong local correlations on the normal-state free-carrier response in the optical conductivity and on the thermoelectric effects.Comment: 11 pages, 4 figure

Towards a Linear-Scaling DFT Technique: The Density Matrix Approach

A recently proposed linear-scaling scheme for density-functional pseudopotential calculations is described in detail. The method is based on a formulation of density functional theory in which the ground state energy is determined by minimization with respect to the density matrix, subject to the condition that the eigenvalues of the latter lie in the range [0,1]. Linear-scaling behavior is achieved by requiring that the density matrix should vanish when the separation of its arguments exceeds a chosen cutoff. The limitation on the eigenvalue range is imposed by the method of Li, Nunes and Vanderbilt. The scheme is implemented by calculating all terms in the energy on a uniform real-space grid, and minimization is performed using the conjugate-gradient method. Tests on a 512-atom Si system show that the total energy converges rapidly as the range of the density matrix is increased. A discussion of the relation between the present method and other linear-scaling methods is given, and some problems that still require solution are indicated.Comment: REVTeX file, 27 pages with 4 uuencoded postscript figure

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.Comment: 28 pages, REVTEX, 5 ps figure

Holstein model in infinite dimensions at half-filling

The normal state of the Holstein model is studied at half-filling in infinite dimensions and in the adiabatic regime. The dynamical mean-field equations are solved using perturbation expansions around the extremal paths of the effective action for the atoms. We find that the Migdal-Eliashberg expansion breaks down in the metallic state if the electron-phonon coupling $\lambda$ exceeds a value of about 1.3 in spite of the fact that the formal expansion parameter $\lambda \omega_0/E_F$ ($\omega_0$ is the phonon frequency, $E_F$ the Fermi energy) is much smaller than 1. The breakdown is due to the appearance of more than one extremal path of the action. We present numerical results which illustrate in detail the evolution of the local Green's function, the self-energy and the effective atomic potential as a function of $\lambda$.Comment: Revtex + 17 postscript figures include

Influence of uniaxial tensile stress on the mechanical and piezoelectric properties of short-period ferroelectric superlattice

Tetragonal ferroelectric/ferroelectric BaTiO3/PbTiO3 superlattice under uniaxial tensile stress along the c axis is investigated from first principles. We show that the calculated ideal tensile strength is 6.85 GPa and that the superlattice under the loading of uniaxial tensile stress becomes soft along the nonpolar axes. We also find that the appropriately applied uniaxial tensile stress can significantly enhance the piezoelectricity for the superlattice, with piezoelectric coefficient d33 increasing from the ground state value by a factor of about 8, reaching 678.42 pC/N. The underlying mechanism for the enhancement of piezoelectricity is discussed

First-Principles Studies of Hydrogenated Si(111)--7×\times7

The relaxed geometries and electronic properties of the hydrogenated phases of the Si(111)-7$\times$7 surface are studied using first-principles molecular dynamics. A monohydride phase, with one H per dangling bond adsorbed on the bare surface is found to be energetically favorable. Another phase where 43 hydrogens saturate the dangling bonds created by the removal of the adatoms from the clean surface is found to be nearly equivalent energetically. Experimental STM and differential reflectance characteristics of the hydrogenated surfaces agree well with the calculated features.Comment: REVTEX manuscript with 3 postscript figures, all included in uu file. Also available at http://www.phy.ohiou.edu/~ulloa/ulloa.htm