Competing Phases, Strong Electron-Phonon Interaction and Superconductivity in Elemental Calcium under High Pressure

The observed "simple cubic" (sc) phase of elemental Ca at room temperature in the 32-109 GPa range is, from linear response calculations, dynamically unstable. By comparing first principle calculations of the enthalpy for five sc-related (non-close-packed) structures, we find that all five structures compete energetically at room temperature in the 40-90 GPa range, and three do so in the 100-130 GPa range. Some competing structures below 90 GPa are dynamically stable, i.e., no imaginary frequency, suggesting that these sc-derived short-range-order local structures exist locally and can account for the observed (average) "sc" diffraction pattern. In the dynamically stable phases below 90 GPa, some low frequency phonon modes are present, contributing to strong electron-phonon (EP) coupling as well as arising from the strong coupling. Linear response calculations for two of the structures over 120 GPa lead to critical temperatures in the 20-25 K range as is observed, and do so without unusually soft modes.Comment: 8 pages, 6 figures, 1 table, accepted for publication in Phys. Rev.

SO(5) theory of insulating vortex cores in high-TcT_c materials

We study the fermionic states of the antiferromagnetically ordered vortex cores predicted to exist in the superconducting phase of the newly proposed SO(5) model of strongly correlated electrons. Our model calculation gives a natural explanation of the recent STM measurements on BSCCO, which in surprising contrast to YBCO revealed completely insulating vortex cores.Comment: 4 pages, 1 figur

Quasiparticle States at a d-Wave Vortex Core in High-Tc Superconductors: Induction of Local Spin Density Wave Order

The local density of states (LDOS) at one of the vortex lattice cores in a high Tc superconductor is studied by using a self-consistent mean field theory including interactions for both antiferromagnetism (AF) and d-wave superconductivity (DSC). The parameters are chosen in such a way that in an optimally doped sample the AF order is completely suppressed while DSC prevails. In the mixed state, we show that the local AF-like SDW order appears near the vortex core and acts as an effective local magnetic field on the quasiparticles. As a result, the LDOS at the core exhibits a double-peak structure near the Fermi level that is in good agreement with the STM observations on YBCO and BSCCO. The presence of local AF order near the votex core is also consistent with the recent neutron scattering experiment on LSCO.Comment: 4 pages, 2 ps 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

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.

Absence of Dipole Transitions in Vortices of Type II Superconductors

The response of a single vortex to a time dependent field is examined microscopically and an equation of motion for vortex motion at non-zero frequencies is derived. Of interest are frequencies near $\Delta^{2}/E_{F}$, where $\Delta$ is the bulk energy gap and $E_{F}$ is the fermi energy. The low temperature, clean, extreme type II limit and maintaining of equilibrium with the lattice are assumed. A simplification occurs for large planar mass anisotropy. Thus the results may be pertinent to materials such as $NbSe_2$ and high temperature superconductors. The expected dipole transition between core states is hidden because of the self consistent nature of the vortex potential. Instead the vortex itself moves and has a resonance at the frequency of the transition.Comment: 12 pages, no figure

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

Evaluation of Exchange-Correlation Energy, Potential, and Stress

We describe a method for calculating the exchange and correlation (XC) contributions to the total energy, effective potential, and stress tensor in the generalized gradient approximation. We avoid using the analytical expressions for the functional derivatives of E_xc*rho, which depend on discontinuous second-order derivatives of the electron density rho. Instead, we first approximate E_xc by its integral in a real space grid, and then we evaluate its partial derivatives with respect to the density at the grid points. This ensures the exact consistency between the calculated total energy, potential, and stress, and it avoids the need of second-order derivatives. We show a few applications of the method, which requires only the value of the (spin) electron density in a grid (possibly nonuniform) and returns a conventional (local) XC potential.Comment: 7 pages, 3 figure

A Real-Space Full Multigrid study of the fragmentation of Li11+ clusters

We have studied the fragmentation of Li11+ clusters into the two experimentally observed products (Li9+,Li2) and (Li10+,Li) The ground state structures for the two fragmentation channels are found by Molecular Dynamics Simulated Annealing in the framework of Local Density Functional theory. Energetics considerations suggest that the fragmentation process is dominated by non-equilibrium processes. We use a real-space approach to solve the Kohn-Sham problem, where the Laplacian operator is discretized according to the Mehrstellen scheme, and take advantage of a Full MultiGrid (FMG) strategy to accelerate convergence. When applied to isolated clusters we find our FMG method to be more efficient than state-of-the-art plane wave calculations.Comment: 9 pages + 6 Figures (in gzipped tar file