O. K. Andersen

LDA energy bands, low-energy hamiltonians, t′, t″, t⊥ (k), and J⊥

Abstract We describe the LDA band structre of YBa2Cu3O7 in the ϵF ± 2 eV range using orbital projections and compare with YBa2Cu4O8. Then, the high-energy and chain-related degrees of freedom are integrated out and we arrive at two, nearest-neighbor, orthogonal, two-center, 8-band Hamiltonians, H8+ and H8−, for respectively the even and odd bands of the bi-layer. Of the 8 orbitals, Cux2 −y2, O2x, O3y, and Cus have σ character and Cuxz, Cuyz, O2z, and O3z have π character. The roles of the Cus orbital, which has some Cu3z2 − 1 character, and the four π orbitals are as follows: Cus provides 2nd- and 3rd-nearest-neighbor (t′ and t″) intra-plane hopping, as well as hopping between planes (t⊥). The π-orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4-σ-band Hamiltonian is generic for flat CuO2 planes and we use it for analytical studies. The k∥-dependence is expressed as one on u ≡ (cos bk y + cos ak x ) 2 and one on v ≡ (cos bk y − cos ak x ) 2 . The latter arises solely through the influence of Cus. The reduction of the σ-Hamiltonian to 3- and 1-band Hamiltonians is explicitly discussed and we point out that, in addition to the hoppings commonly included in many-body calculations, the 3-band Hamiltonian should include hopping between all 2nd-nearest-neighbor oxygens and that the 1-band Hamiltonian should include 3rd-nearest-neighbor hoppings. We calculate the single-particle hopping between the planes of a bi-layer and show that it is generically: t⊥ (k ∥ ) ≈ 0.25 eV · v 2 (1 − 2ut′ t ) −2 . The hopping through insulating spacers such as (BaO)Hg(BaO) is an order of magnitude smaller, but seems to have the same k∥-dependence. We show that the inclusion of t′ is crucial for understanding ARPES for the anti-ferromagnetic insulator Sr2CuO2Cl2. Finally, we estimate the value of the inter-plane exchange constant J⊥ for an un-doped bi-layer in meanfield theory using different single-particle Hamiltonians, the LDA for YBa2Cu3O6, the eight- and four-band Hamiltonians, as well as an analytical calculation for the latter. We conclude that J⊥ ~ − 20 meV.

Electron-phonon interaction in the normal and superconducting states of MgB 2

For the 40K-superconductor MgB2 we have calculated the electronic and phononic structures and the electron-phonon interaction throughout the Brillouin zone ab initio. In contrast to the isoelectronic graphite, MgB2 has holes in the bonding sigma-bands, which contribute 42 per cent to the density of states: N(0) =0.355 states/(MgB2 eV spin). The total interaction strength, lambda =0.87 and lambda,tr=0.60, is dominated by the coupling of the sigma-holes to the bond-stretching optical phonons with wavenumbers in a narrow range around 590 cm^{-1}. Like the holes, these phonons are quasi two-dimensional and have wave-vectors close to Gamma-A, where their symmetry is E. The pi-electrons contribute merely 0.25 to lambda and to lambda,tr. With Eliashberg theory we evaluate the normal-state resistivity, the density of states in the superconductor, and the B-isotope effect on Tc and Delta0, and find excellent agreement with experiments, when available. Tc=40 K is reproduced with mu*=0.10 and 2Delta0/kB Tc=3.9. MgB2 thus seems to be an intermediate-coupling e-ph pairing s-wave superconductor.

Band-structure trend in hole-doped cuprates and correlation with T(c max).

By calculation and analysis of the bare conduction bands in a large number of hole-doped high-temperature superconductors, we have identified the range of the intralayer hopping as the essential, material-dependent parameter. It is controlled by the energy of the axial orbital, a hybrid between Cu 4s, apical-oxygen 2p(z), and farther orbitals. Materials with higher T(c max) have larger hopping ranges and axial orbitals more localized in the CuO2 layers.

Multiband model for tunneling in MgB2 junctions

A theoretical model for quasiparticle and Josephson tunneling in multiband superconductors is developed and applied to MgB2-based junctions. The gap functions in different bands in MgB2 are obtained from an extended Eliashberg formalism, using the results of band structure calculations. The temperature and angle dependencies of MgB2 tunneling spectra and the Josephson critical current are calculated. The conditions for observing one or two gaps are given. We argue that the model may help to settle the current debate concerning two-band superconductivity in MgB2.

Specific heat of MgB2 in a one- and a two-band model from first-principles calculations

The heat capacity anomaly at the transition to superconductivity of the layered superconductor MgB2 is compared to first-principles calculations with the Coulomb repulsion, µ*, as the only parameter which is fixed to give the measured Tc. We solve the Eliashberg equations for both an isotropic one-band model and a two-band model with different superconducting gaps on the π-band and σ-band Fermi surfaces. The agreement with experiments is considerably better for the two-band model than for the one-band model.

Three-Dimensional MgB2-Type Superconductivity in Hole-Doped Diamond

We substantiate by numerical and analytical calculations that the recently discovered superconductivity below 4 K in 3% boron-doped diamond is caused by electron-phonon coupling of the same type as in MgB2, albeit in three dimensions. Holes at the top of the zone-centered, degenerate sigma-bonding valence-band couple strongly to the optical bond-stretching modes. The increase from two to three dimensions reduces the mode softening crucial for T(c) reaching 40 K in MgB2. Even if diamond had the same bare coupling constant as MgB2, which could be achieved with 10% doping, T(c) would be only 25 K. Superconductivity above 1 K in Si (Ge) requires hole doping beyond 5% (10%).

Mott transition and suppression of orbital fluctuations in orthorhombic 3d(1) perovskites

Using t(2g) Wannier functions, a low-energy Hamiltonian is derived for orthorhombic 3d(1) transition-metal oxides. Electronic correlations are treated with a new implementation of dynamical mean-field theory for noncubic systems. Good agreement with photoemission data is obtained. The interplay of correlation effects and cation covalency (GdFeO3-type distortions) is found to suppress orbital fluctuations in LaTiO3 and even more in YTiO3, and to favor the transition to the insulating state.

Muffin-tin orbitals of arbitrary order

We have derived orbital basis sets from scattering theory. They are expressed as polynomial approximations to the energy dependence of a set of partial waves, in quantized form. The corresponding matrices, as well as the Hamiltonian and overlap matrices, are specified by the values on the energy mesh of the screened resolvent and its first energy derivative. These orbitals are a generalization of the third-generation linear muffin-tin orbitals and should be useful for electronic-structure calculations in general.

Orbital reflectometry of oxide heterostructures

The occupation of d orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition-metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations of the orbital occupation at surfaces and interfaces are believed to be responsible for massive variations of the magnetic and transport properties, but could not thus far be probed in a quantitative manner. Here we show that it is possible to derive quantitative, spatially resolved orbital polarization profiles from soft-X-ray reflectivity data, without resorting to model calculations. We demonstrate that the method is sensitive enough to resolve differences of ~3% in the occupation of Ni e(g) orbitals in adjacent atomic layers of a LaNiO(3)-LaAlO(3) superlattice, in good agreement with ab initio electronic-structure calculations. The possibility to quantitatively correlate theory and experiment on the atomic scale opens up many new perspectives for orbital physics in transition-metal oxides.

Calculated energy-band structures and chemical bonding in titanium and vanadium carbides, nitrides and oxides

Abstract The energy-band structures of TiCx, TiNx, TiOx, VCx, VNx and VOx, for x = 1.0 and 0.75, have been calculated self-consistently by the LMTO-ASA method. The equilibrium lattice constants, the bulk moduli, the cohesive energies, and the energies of vacancy formation have been determined. The available experimental data for the bulk moduli, cohesive energies and some electromagnetic data (Hall effect, magnetic susceptibility, thermopower) have been analyzed on the basis of the calculated results.