A Note on a Recent Attempt to Improve the Pin-Frankl Bound

We provide a counterexample to a lemma used in a recent tentative improvement of the the Pin-Frankl bound for synchronizing automata. This example naturally leads us to formulate an open question, whose answer could fix the line of proof, and improve the bound.Comment: Short note presenting a counterexample and the resulting open questio

The long-wavelength behaviour of the exchange-correlation kernel in the Kohn-Sham theory of periodic systems

The polarization-dependence of the exchange-correlation (XC) energy functional of periodic insulators within Kohn-Sham (KS) density-functional theory requires a ${\cal O} (1/q^2)$ divergence in the XC kernel for small vectors q. This behaviour, exemplified for a one-dimensional model semiconductor, is also observed when an insulator happens to be described as a KS metal, or vice-versa. Although it can occur in the exchange-only kernel, it is not found in the usual local, semi-local or even non-local approximations to KS theory. We also show that the test-charge and electronic definitions of the macroscopic dielectric constant differ from one another in exact KS theory, but are equivalent in the above-mentioned approximations

Effect of the spin-orbit interaction on the thermodynamic properties of crystals: The specific heat of bismuth

In recent years, there has been increasing interest in the specific heat $C$ of insulators and semiconductors because of the availability of samples with different isotopic masses and the possibility of performing \textit{ab initio} calculations of its temperature dependence $C(T)$ using as a starting point the electronic band structure. Most of the crystals investigated are elemental (e.g., germanium) or binary (e.g., gallium nitride) semiconductors. The initial electronic calculations were performed in the local density approximation and did not include spin-orbit interaction. Agreement between experimental and calculated results was usually found to be good, except for crystals containing heavy atoms (e.g., PbS) for which discrepancies of the order of 20% existed at the low temperature maximum found for $C/T^3$. It has been conjectured that this discrepancies result from the neglect of spin-orbit interaction which is large for heavy atoms ($\Delta_0\sim$1.3eV for the $p$ valence electrons of atomic lead). Here we discuss measurements and \textit{ab initio} calculations of $C(T)$ for crystalline bismuth ($\Delta_0\sim$1.7 eV), strictly speaking a semimetal but in the temperature region accessible to us ($T >$ 2K) acting as a semiconductor. We extend experimental data available in the literature and notice that the \textit{ab initio} calculations without spin-orbit interaction exhibit a maximum at $\sim$8K, about 20% lower than the measured one. Inclusion of spin-orbit interaction decreases the discrepancy markedly: The maximum of $C(T)$ is now only 7% larger than the measured one. Exact agreement is obtained if the spin-orbit hamiltonian is reduced by a factor of $\sim$0.8.Comment: 4 pages, 3 figure

Non-linear optical susceptibilities, Raman efficiencies and electrooptic tensors from first-principles density functional perturbation theory

The non-linear response of infinite periodic solids to homogenous electric fields and collective atomic displacements is discussed in the framework of density functional perturbation theory. The approach is based on the 2n + 1 theorem applied to an electric-field-dependent energy functional. We report the expressions for the calculation of the non-linear optical susceptibilities, Raman scattering efficiencies and electrooptic coefficients. Different formulations of third-order energy derivatives are examined and their convergence with respect to the k-point sampling is discussed. We apply our method to a few simple cases and compare our results to those obtained with distinct techniques. Finally, we discuss the effect of a scissors correction on the EO coefficients and non-linear optical susceptibilities

Band Offsets at the Si/SiO2_2 Interface from Many-Body Perturbation Theory

We use many-body perturbation theory, the state-of-the-art method for band gap calculations, to compute the band offsets at the Si/SiO$_2$ interface. We examine the adequacy of the usual approximations in this context. We show that (i) the separate treatment of band-structure and potential lineup contributions, the latter being evaluated within density-functional theory, is justified, (ii) most plasmon-pole models lead to inaccuracies in the absolute quasiparticle corrections, (iii) vertex corrections can be neglected, (iv) eigenenergy self-consistency is adequate. Our theoretical offsets agree with the experimental ones within 0.3 eV

Theory of structural response to macroscopic electric fields in ferroelectric systems

We have developed and implemented a formalism for computing the structural response of a periodic insulating system to a homogeneous static electric field within density-functional perturbation theory (DFPT). We consider the thermodynamic potentials E(R,eta,e) and F(R,eta,e) whose minimization with respect to the internal structural parameters R and unit cell strain eta yields the equilibrium structure at fixed electric field e and polarization P, respectively. First-order expansion of E(R,eta,e) in e leads to a useful approximation in which R(P) and eta(P) can be obtained by simply minimizing the zero-field internal energy with respect to structural coordinates subject to the constraint of a fixed spontaneous polarization P. To facilitate this minimization, we formulate a modified DFPT scheme such that the computed derivatives of the polarization are consistent with the discretized form of the Berry-phase expression. We then describe the application of this approach to several problems associated with bulk and short-period superlattice structures of ferroelectric materials such as BaTiO3 and PbTiO3. These include the effects of compositionally broken inversion symmetry, the equilibrium structure for high values of polarization, field-induced structural phase transitions, and the lattice contributions to the linear and the non-linear dielectric constants.Comment: 19 pages, with 15 postscript figures embedded. Uses REVTEX4 and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/sai_pol/index.htm

Lattice Properties of PbX (X = S, Se, Te): Experimental Studies and ab initio Calculations Including Spin-Orbit Effects

During the past five years the low temperature heat capacity of simple semiconductors and insulators has received renewed attention. Of particular interest has been its dependence on isotopic masses and the effect of spin- orbit coupling in ab initio calculations. Here we concentrate on the lead chalcogenides PbS, PbSe and PbTe. These materials, with rock salt structure, have different natural isotopes for both cations and anions, a fact that allows a systematic experimental and theoretical study of isotopic effects e.g. on the specific heat. Also, the large spin-orbit splitting of the 6p electrons of Pb and the 5p of Te allows, using a computer code which includes spin-orbit interaction, an investigation of the effect of this interaction on the phonon dispersion relations and the temperature dependence of the specific heat and on the lattice parameter. It is shown that agreement between measurements and calculations significantly improves when spin-orbit interaction is included.Comment: 25 pages, 12 Figures, 1 table, submitted to PR

High-order density-matrix perturbation theory

We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the Kohn-Sham wavefunctions. It has the following advantages: (i) it allows a simple derivation for the expression for the high order derivatives of the density matrix; (ii) in extended insulators, the treatment of uniform-electric-field perturbations and of the polarization derivatives is straightforward.Comment: 4 page

Ab initio phonon dispersion curves and interatomic force constants of barium titanate

The phonon dispersion curves of cubic BaTiO_3 have been computed within a first-principles approach and the results compared to the experimental data. The curves obtained are very similar to those reported for KNbO_3 by Yu and Krakauer [Phys. Rev. Lett. 74, 4067 (1995)]. They reveal that correlated atomic displacements along chains are at the origin of the ferroelectric instability. A simplified model illustrates that spontaneous collective displacements will occur when a dozen of aligned atoms are coupled. The longitudinal interatomic force constant between nearest neighbour Ti and O atoms is relatively weak in comparison to that between Ti atoms in adjacent cells. The small coupling between Ti and O displacements seems however necessary to reproduce a ferroelectric instability.Comment: 12 pages, 4 figure

First principles study of strain/electronic interplay in ZnO; Stress and temperature dependence of the piezoelectric constants

We present a first-principles study of the relationship between stress, temperature and electronic properties in piezoelectric ZnO. Our method is a plane wave pseudopotential implementation of density functional theory and density functional linear response within the local density approximation. We observe marked changes in the piezoelectric and dielectric constants when the material is distorted. This stress dependence is the result of strong, bond length dependent, hybridization between the O $2p$ and Zn $3d$ electrons. Our results indicate that fine tuning of the piezoelectric properties for specific device applications can be achieved by control of the ZnO lattice constant, for example by epitaxial growth on an appropriate substrate.Comment: accepted for publication in Phys. Rev.