Materials Theory

We use realistic pseudopotentials and a plane-wave basis to study the electronic structure of non-periodic, three-dimensional, 2000-atom (AlAs)_n/(GaAs)_m (001) superlattices, where the individual layer thicknesses n,m = {1,2,3} are randomly selected. We find that while the band gap of the equivalent (n = m = 2) ordered superlattice is indirect, random fluctuations in layer thicknesses lead to a direct gap in the planar Brillouin zone, strong wavefunction localization along the growth direction, short radiative lifetimes, and a significant band-gap reduction, in agreement with experiments on such intentionally grown disordered superlattices.

Ab initio molecular dynamics is used to study deformations of sodium clusters at temperatures 500⋯1100 K. Open-shell Na 14 cluster has two shape isomers, prolate and oblate, in the liquid state. The deformation is stabilized by opening a gap at the Fermi level. The closed-shell Na 8 remains magic also at the liquid state.

The evaluation of Coulomb forces is a difficult task. The summations that are involved converge only conditionally and care has to be taken in selecting the appropriate procedure to define the limits. The Ewald method is a standard method for obtaining Coulomb forces, but this method is rather slow, since it depends on the square of the number of atoms in a unit cell. In this paper we have adapted the plane-wise summation method for the evaluation of Coulomb forces. The use of this method allows for larger computational cells in molecular dynamics calculations.

The possible occurrence of either a charge-density-wave or a Kohn anomaly is governed by the presence of Fermi-surface nesting and the subtle interaction of electrons and phonons. Recent experimental and theoretical investigations suggest such an effect for the hydrogen covered Mo and W(110) surfaces. Using density-functional theory we examine the electronic structure and the electron-phonon coupling of these systems. Besides good agreement with the experimental phonon frequencies our study provides a characterization and quantitative analysis of an unusual scenario determining the electronic, vibrational, and structural properties of these surfaces.

An effective Hamiltonian for the ferroelectric transition in PbTi O 3 is constructed from first-principles density-functional-theory total-energy and linear-response calculations through the use of a localized, symmetrized basis set of ``lattice Wannier functions.'' Preliminary results of Monte Carlo simulations for this system show a first-order cubic-tetragonal transition at 660 K. The involvement of the Pb atom in the lattice instability and the coupling of local distortions to strain are found to be particularly important in producing the behavior characteristic of the PbTi O 3 transition. A tentative explanation for the presence of local distortions experimentally observed above T c is suggested. Further applications of this method to a variety of systems and structures are proposed for first-principles study of finite-temperature structural properties in individual materials.

Mercury has perhaps the strangest behavior of any of the metals. Although the other metals in column IIB have an hcp ground state, mercury's ground state is the body centered tetragonal β Hg phase. The most common phase of mercury is the rhombohedral α Hg phase, which is stable from 79K to the melting point and meta-stable below 79K. Another rhombohedral phase, γ Hg, is believed to exist at low temperatures. First-principles calculations are used to study the energetics of the various phases of mercury. Even when partial spin-orbit effects are included, the calculations indicate that the hexagonal close packed structure is the ground state. It is suggested that a better treatment of the spin-orbit interaction might alter this result.

A complete mapping in the Brillouin zone of the structural instability associated with the ferroelectric phase transitions of KNbO 3 has been obtained by first-principles calculations using an LAPW linear response approach. The wavevector dependence of the instability reveals pronounced two-dimensional character, which corresponds to chains oriented along ⟨100⟩ \ directions of displaced Nb atoms. The results are discussed in relation to models of the ferroelectric phase transitions.

We present a first-principles study of excitonic self-trapping in diamond. Our calculation provides evidence for self-trapping of the 1s core exciton and gives a coherent interpretation of recent experimental X-ray absorption and emission data. Self-trapping does not occur in the case of a single valence exciton. We predict, however, that self-trapping should occur in the case of a valence biexciton. This process is accompanied by a large local relaxation of the lattice which could be observed experimentally.

We present a first-principles study of 180-degree ferroelectric domain walls in tetragonal barium titanate. The theory is based on an effective Hamiltonian that has previously been determined from first-principles ultrasoft-pseudopotential calculations. Statistical properties are investigated using Monte Carlo simulations. We compute the domain-wall energy, free energy, and thickness, analyze the behavior of the ferroelectric order parameter in the interior of the domain wall, and study its spatial fluctuations. An abrupt reversal of the polarization is found, unlike the gradual rotation typical of the ferromagnetic case.

A first-principles study of the vibrational modes of PbTiO_3 in the ferroelectric tetragonal phase has been performed at all the main symmetry points of the Brillouin zone (BZ). The calculations use the local-density approximation and ultrasoft pseudopotentials with a plane-wave basis, and reproduce well the available experimental information on the modes at the Gamma point, including the LO-TO splittings. The work was motivated in part by a previously reported transition to an orthorhombic phase at low temperatures [(J. Kobayashi, Y. Uesu, and Y. Sakemi, Phys. Rev. B {\bf 28}, 3866 (1983)]. We show that a linear coupling of orthorhombic strain to one of the modes at Gamma plays a role in the discussion of the possibility of this phase transition. However, no mechanical instabilities (soft modes) are found, either at Gamma or at any of the other high-symmetry points of the BZ.