We present first-principles calculations of optimally localized Wannier functions for Cu and use these for an abinitio determination of Hubbard (Coulomb) matrix elements. We use a standard linearized muffin-tin orbital calculation in the atomic-sphere approximation (LMTO-ASA) to calculate Bloch functions, and from these determine maximally localized Wannier functions using a method proposed by Marzari and Vanderbilt. The resulting functions were highly localized, with greater than 89% of the norm of the function within the central site for the occupied Wannier states. Two methods for calculating Coulomb matrix elements from Wannier functions are presented and applied to fcc Cu. For the unscreened onsite Hubbard U for the Cu 3d-bands we have obtained about 25eV. These results are also compared with results obtained from a constrained local-density approximation (LDA) calculation.

Unscreened Hartree-Fock approximation (HFA) calculations for metallic Fe, Co, Ni, and Cu are presented, by using a quantum-chemical approach. We believe that these are the first HFA results to have been done for crystalline 3d transition metals. Our approach uses a linearized muffin-tin orbital calculation to determine Bloch functions for the Hartree one-particle Hamiltonian, and from these obtains maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and two-particle Coulomb matrix elements are calculated. The resulting second-quantized multi-band Hamiltonian with ab-initio parameters is studied within the simplest many-body approximation, namely the unscreened, self-consistent HFA, which takes into account exact exchange and is free of self-interactions. Although the d-bands sit considerably lower within HFA than within the local (spin) density approximation L(S)DA, the exchange splitting and magnetic moments for ferromagnetic Fe, Co, and Ni are only slightly larger in HFA than what is obtained either experimentally or within LSDA. The HFA total energies are lower than the corresponding LSDA calculations. We believe that this same approach can be easily extended to include more sophisticated ab-initio many-body treatments of the electronic structure of solids.

In this paper, the full-potential linearized augmented plane-wave (LAPW) method within the generalized gradient approximation (GGA) was used to calculate the effect of hydrostatic pressure at zero temperature on the 4d transition metal zirconium. For the hexagonal close-packed (hcp), omega (ω), and body-centred cubic (bcc) structures the enthalpy, H = E + pV , was calculated as a function of pressure p. We obtained an ω to bcc transition pressure of 28.2 GPa. Temperature-dependent contributions were obtained from tight-binding calculations of the phonons in the quasiharmonic approximation and were used to calculate the Gibbs free energy as a function of both temperature T and pressure for these three structures. From the comparison of these free energies the phase boundaries were calculated in the Tp phase diagram, and compared to the experimentally determined boundaries. We discuss the importance of anharmonicity for understanding the material properties of zirconium, and limitations of quasiharmonic phonon theories for predicting phase transformations.

The possibility of non-s-wave superconductivity induced by phonons is investigated using a simple model that is inspired by Sr$_2$RuO$_4$. The model assumes a two-dimensional electronic structure, a two-dimensional spin-fluctuation spectrum, and three-dimensional electron-phonon coupling. Taken separately, each interaction favors formation of spin-singlet pairs (of s symmetry for the phonon interaction and d$_{x^2-y^2}$ symmetry for the spin interaction), but in combination, a variety of more unusual singlet and triplet states are found, depending on the interaction parameters. This may have important implications for Sr$_2$RuO$_4$, providing a plausible explanation of how the observed spin fluctuations, which clearly favor d$_{x^2-y^2}$ pairing, may still be instrumental in creating a superconducting state with a different (e.g., p-wave) symmetry. It also suggests an interpretation of the large isotope effect observed in Sr$_2$RuO$_4$. These results indicate that phonons could play a key role in establishing the order-parameter symmetry in Sr$_2$RuO$_4$, and possibly in other unconventional superconductors.Comment: 6 pages, 5 figures, submitted to Phys. Rev.