Nonuniqueness and derivative discontinuities in density-functional theories for current-carrying and superconducting systems

Current-carrying and superconducting systems can be treated within density-functional theory if suitable additional density variables (the current density and the superconducting order parameter, respectively) are included in the density-functional formalism. Here we show that the corresponding conjugate potentials (vector and pair potentials, respectively) are {\it not} uniquely determined by the densities. The Hohenberg-Kohn theorem of these generalized density-functional theories is thus weaker than the original one. We give explicit examples and explore some consequences.Comment: revised version (typos corrected, some discussion added) to appear in Phys. Rev.

Effective vanishing order of the Levi determinant

On a smooth domain in complex n space of finite D'Angelo q-type at a point, an effective upper bound for the vanishing order of the Levi determinant \text{coeff}\{\partial r \wedge \dbar r \wedge (\partial \dbar r)^{n-q}\} at that point is given in terms of the D'Angelo q-type, the dimension of the space n, and q itself. The argument uses Catlin's notion of a boundary system as well as techniques pioneered by John D'Angelo.Comment: 22 pages; typos in example from p.20 fixed in the second versio

Friedel oscillations in one-dimensional metals: from Luttinger's theorem to the Luttinger liquid

Charge density and magnetization density profiles of one-dimensional metals are investigated by two complementary many-body methods: numerically exact (Lanczos) diagonalization, and the Bethe-Ansatz local-density approximation with and without a simple self-interaction correction. Depending on the magnetization of the system, local approximations reproduce different Fourier components of the exact Friedel oscillations.Comment: 3 pages, 3 figures, Manuscript accepted by Journal of Magnetism and Magnetic Materials, special issue for LAWMMM 2007 conferenc

Stabilized jellium model and structural relaxation effects on the fragmentation energies of ionized silver clusters

Using the stabilized jellium model in two schemes of `relaxed' and `rigid', we have calculated the dissociation energies and the fission barrier heights for the binary fragmentations of singly-ionized and doubly-ionized Ag clusters. In the calculations, we have assumed spherical geometries for the clusters. Comparison of the fragmentation energies in the two schemes show differences which are significant in some cases. This result reveals the advantages of the relaxed SJM over the rigid SJM in dynamical processes such as fragmentation. Comparing the relaxed SJM results and axperimental data on fragmentation energies, it is possible to predict the sizes of the clusters just before their fragmentations.Comment: 9 pages, 12 JPG figure

Exact-exchange density-functional theory for quasi-two-dimensional electron gases

A simple exact-exchange density-functional method for a quasi-two-dimensional electron gas with variable density is presented. An analytical expression for the exact-exchange potential with only one occupied subband is provided, without approximations. When more subbands are occupied the exact-exchange potential is obtained numerically. The theory shows that, in contradiction with LDA, the exact-exchange potential exhibits discontinuities and the system suffers a zero-temperature first-order transition each time a subband is occupied. Results suggesting that the translational symmetry might be spontaneously broken at zero temperature are presented. An extension of the theory to finite temperatures allows to describe a drop in the intersubband spacing in good quantitative agreement with recent experiments.Comment: 14 pages, 3 figure

Spin Resolution of the Electron-Gas Correlation Energy: Positive same-spin contribution

The negative correlation energy per particle of a uniform electron gas of density parameter $r_s$ and spin polarization $\zeta$ is well known, but its spin resolution into up-down, up-up, and down-down contributions is not. Widely-used estimates are incorrect, and hamper the development of reliable density functionals and pair distribution functions. For the spin resolution, we present interpolations between high- and low-density limits that agree with available Quantum Monte Carlo data. In the low-density limit for $\zeta = 0$, we find that the same-spin correlation energy is unexpectedly positive, and we explain why. We also estimate the up and down contributions to the kinetic energy of correlation.Comment: new version, to appear in PRB Rapid Communicatio

Compressibility and Electronic Structure of MgB2 up to 8 GPa

The lattice parameters of MgB2 up to pressures of 8 GPa were determined using high-resolution x-ray powder diffraction in a diamond anvil cell. The bulk modulus, B0, was determined to be 151 +-5 GPa. Both experimental and first-principles calculations indicate nearly isotropic mechanical behavior under pressure. This small anisotropy is in contrast to the 2 dimensional nature of the boron pi states. The pressure dependence of the density of states at the Fermi level and a reasonable value for the average phonon frequency account within the context of BCS theory for the reduction of Tc under pressure.Comment: REVTeX file. 4 pages, 4 figure

Exchange and correlation as a functional of the local density of states

A functional $E_{xc}[\rho(\r,\epsilon)]$ is presented, in which the exchange and correlation energy of an electron gas depends on the local density of occupied states. A simple local parametrization scheme is proposed, entirely from first principles, based on the decomposition of the exchange-correlation hole in scattering states of different relative energies. In its practical Kohn-Sham-like form, the single-electron orbitals become the independent variables, and an explicit formula for the functional derivative is obtained.Comment: 5 pages. Expanded version. Will appear in Phys. Rev.

Exact-exchange density-functional calculations for noble-gas solids

The electronic structure of noble-gas solids is calculated within density functional theory's exact-exchange method (EXX) and compared with the results from the local-density approximation (LDA). It is shown that the EXX method does not reproduce the fundamental energy gaps as well as has been reported for semiconductors. However, the EXX-Kohn-Sham energy gaps for these materials reproduce about 80 % of the experimental optical gaps. The structural properties of noble-gas solids are described by the EXX method as poorly as by the LDA one. This is due to missing Van der Waals interactions in both, LDA and EXX functionals.Comment: 4 Fig

Correlation energies of inhomogeneous many-electron systems

We generalize the uniform-gas correlation energy formalism of Singwi, Tosi, Land and Sjolander to the case of an arbitrary inhomogeneous many-particle system. For jellium slabs of finite thickness with a self-consistent LDA groundstate Kohn-Sham potential as input, our numerical results for the correlation energy agree well with diffusion Monte Carlo results. For a helium atom we also obtain a good correlation energy.Comment: 4 pages,1 figur