First-principles study of lattice instabilities in Ba_xSr_(1-x)TiO_3

Using first-principles calculations based on a variational density functional perturbation theory, we investigate the lattice dynamics of solid solutions of barium and strontium titanates. Averaging the information available for the related pure compounds yields results equivalent to those obtained within the virtual crystal approximation, providing frequencies which are a good approximation to those computed for a (111) ordered supercell. Using the same averaging technique we report the evolution of the ferroelectric and antiferrodistortive instabilities with composition.Comment: 9 pages, 2 figures, Proceedings for Fundamental Physics of Ferroelectrics, Aspen (CO), Feb. 13-20, 200

Electron localization : band-by-band decomposition, and application to oxides

Using a plane wave pseudopotential approach to density functional theory we investigate the electron localization length in various oxides. For this purpose, we first set up a theory of the band-by-band decomposition of this quantity, more complex than the decomposition of the spontaneous polarization (a related concept), because of the interband coupling. We show its interpretation in terms of Wannier functions and clarify the effect of the pseudopotential approximation. We treat the case of different oxides: BaO, $\alpha$-PbO, BaTiO$_3$ and PbTiO$_3$. We also investigate the variation of the localization tensor during the ferroelectric phase transitions of BaTiO$_3$ as well as its relationship with the Born effective charges

Ab initio studies of phonon softening and high pressure phase transitions of alpha-quartz SiO2

Density functional perturbation theory calculations of alpha-quartz using extended norm conserving pseudopotentials have been used to study the elastic properties and phonon dispersion relations along various high symmetry directions as a function of bulk, uniaxial and non-hydrostatic pressure. The computed equation of state, elastic constants and phonon frequencies are found to be in good agreement with available experimental data. A zone boundary (1/3, 1/3, 0) K-point phonon mode becomes soft for pressures above P=32 GPa. Around the same pressure, studies of the Born stability criteria reveal that the structure is mechanically unstable. The phonon and elastic softening are related to the high pressure phase transitions and amorphization of quartz and these studies suggest that the mean transition pressure is lowered under non-hydrostatic conditions. Application of uniaxial pressure, results in a post-quartz crystalline monoclinic C2 structural transition in the vicinity of the K-point instability. This structure, intermediate between quartz and stishovite has two-thirds of the silicon atoms in octahedral coordination while the remaining silicon atoms remain tetrahedrally coordinated. This novel monoclinic C2 polymorph of silica, which is found to be metastable under ambient conditions, is possibly one of the several competing dense forms of silica containing octahedrally coordinated silicon. The possible role of high pressure ferroelastic phases in causing pressure induced amorphization in silica are discussed.Comment: 17 pages, 8 figs., 8 Table

Nonlocality of Kohn-Sham exchange-correlation fields in dielectrics

The theory of the macroscopic field appearing in the Kohn-Sham exchange-correlation potential for dielectric materials, as introduced by Gonze, Ghosez and Godby, is reexamined. It is shown that this Kohn-Sham field cannot be determined from a knowledge of the local state of the material (local crystal potential, electric field, and polarization) alone. Instead, it has an intrinsically nonlocal dependence on the global electrostatic configuration. For example, it vanishes in simple transverse configurations of a polarized dielectric, but not in longitudinal ones.Comment: 4 pages, two-column style with 2 postscript figures embedded. Uses REVTEX and epsf macros. Also available at http://www.physics.rutgers.edu/~dhv/preprints/index.html#dv_gg

The PseudoDojo: Training and grading a 85 element optimized norm-conserving pseudopotential table

First-principles calculations in crystalline structures are often performed with a planewave basis set. To make the number of basis functions tractable two approximations are usually introduced: core electrons are frozen and the diverging Coulomb potential near the nucleus is replaced by a smoother expression. The norm-conserving pseudopotential was the first successful method to apply these approximations in a fully ab initio way. Later on, more efficient and more exact approaches were developed based on the ultrasoft and the projector augmented wave formalisms. These formalisms are however more complex and developing new features in these frameworks is usually more difficult than in the norm-conserving framework. Most of the existing tables of norm- conserving pseudopotentials, generated long ago, do not include the latest developments, are not systematically tested or are not designed primarily for high accuracy. In this paper, we present our PseudoDojo framework for developing and testing full tables of pseudopotentials, and demonstrate it with a new table generated with the ONCVPSP approach. The PseudoDojo is an open source project, building on the AbiPy package, for developing and systematically testing pseudopotentials. At present it contains 7 different batteries of tests executed with ABINIT, which are performed as a function of the energy cutoff. The results of these tests are then used to provide hints for the energy cutoff for actual production calculations. Our final set contains 141 pseudopotentials split into a standard and a stringent accuracy table. In total around 70.000 calculations were performed to test the pseudopotentials. The process of developing the final table led to new insights into the effects of both the core-valence partitioning and the non-linear core corrections on the stability, convergence, and transferability of norm-conserving pseudopotentials. ...Comment: abstract truncated, 17 pages, 25 figures, 8 table

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

An efficient k.p method for calculation of total energy and electronic density of states

An efficient method for calculating the electronic structure in large systems with a fully converged BZ sampling is presented. The method is based on a k.p-like approximation developed in the framework of the density functional perturbation theory. The reliability and efficiency of the method are demostrated in test calculations on Ar and Si supercells

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

Density-functional theory of polar insulators

We examine the density-functional theory of macroscopic insulators, obtained in the large-cluster limit or under periodic boundary conditions. For polar crystals, we find that the two procedures are not equivalent. In a large-cluster case, the exact exchange-correlation potential acquires a homogeneous ``electric field'' which is absent from the usual local approximations, and the Kohn-Sham electronic system becomes metallic. With periodic boundary conditions, such a field is forbidden, and the polarization deduced from Kohn-Sham wavefunctions is incorrect even if the exact functional is used

Optical signature of symmetry variations and spin-valley coupling in atomically thin tungsten dichalcogenides

Motivated by the triumph and limitation of graphene for electronic applications, atomically thin layers of group VI transition metal dichalcogenides are attracting extensive interest as a class of graphene-like semiconductors with a desired band-gap in the visible frequency range. The monolayers feature a valence band spin splitting with opposite sign in the two valleys located at corners of 1st Brillouin zone. This spin-valley coupling, particularly pronounced in tungsten dichalcogenides, can benefit potential spintronics and valleytronics with the important consequences of spin-valley interplay and the suppression of spin and valley relaxations. Here we report the first optical studies of WS2 and WSe2 monolayers and multilayers. The efficiency of second harmonic generation shows a dramatic even-odd oscillation with the number of layers, consistent with the presence (absence) of inversion symmetry in even-layer (odd-layer). Photoluminescence (PL) measurements show the crossover from an indirect band gap semiconductor at mutilayers to a direct-gap one at monolayers. The PL spectra and first-principle calculations consistently reveal a spin-valley coupling of 0.4 eV which suppresses interlayer hopping and manifests as a thickness independent splitting pattern at valence band edge near K points. This giant spin-valley coupling, together with the valley dependent physical properties, may lead to rich possibilities for manipulating spin and valley degrees of freedom in these atomically thin 2D materials