Several improvements of the tetrahedron method for Brillouin-zone integrations are presented. (1) A translational grid of k points and tetrahedra is suggested that renders the results for insulators identical to those obtained with special-point methods with the same number of k points. (2) A simple correction formula goes beyond the linear approximation of matrix elements within the tetrahedra and also improves the results for metals significantly.For a required accuracy this reduces the number of k points by orders of magnitude. (3) Irreducible k points and tetrahedra are selected by a fully automated procedure, requiring as input only the space-group operations. (4) The integration is formulated as a weighted sum over irreducible k points with integration weights calculated using the tetrahedron method once for a given band structure. This allows an e%cient use of the tetrahedron method also in plane-wave-based electronic-structure methods.

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We describe the LDA bandstructure of YBa2Cu3O7 in the F 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, H + 8 and H 8 ; for respectively the even and odd bands of the bi-layer. Of the 8 orbitals, Cu x 2 y 2 ; O2x; O3y; and Cus have character and Cuxz; Cuyz; O2z; and O3z have character. The roles of the Cus orbital, which has some Cu 3z 2 1 character, and the four orbitals are as follows: Cus provides 2nd-and 3rd-nearest-neighbor (t 0 and t 00 ) intra-plane hopping, as well as hopping between planes (t?): The -orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4--band Hamiltonian is generic for at CuO2 planes and we use it for analytical studies. The k k -dependence is expressed as one on u (cos bky + cos akx) =2 and one on v (cos bky cos akx) =2: The latter arises solely through the in uence of Cus: The reduction of the -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 k 0:25 eV v 2 (1 2ut 0 =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 k -dependence. We show that the inclusion of t 0 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 mean-eld theory using di erent 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.

By calculation and analysis of the bare conduction bands in a large number of hole-doped high-temperature superconductors, we have identified the energy of the so-called axial-orbital as the essential, material-dependent parameter. It is uniquely related to the range of the intra-layer hopping. It controls the Cu 4s-character, influences the perpendicular hopping, and correlates with the observed Tc at optimal doping. We explain its dependence on chemical composition and structure, and present a generic tight-binding model. PACS numbers: 74.25.Jb, 74.62.Bf, 74.62.Fj, The mechanism of high-temperature superconductivity (HTSC) in the hole-doped cuprates remains a puzzle [1]. Many families with CuO 2 -layers have been synthesized and all exhibit a phase diagram with T c going through a maximum as a function of doping. The prevailing explanation is that at low doping, superconductivity is destroyed with rising temperature by the loss of phase coherence, and at high doping by pair-breaking [2]. For the materials-dependence of T c at optimal doping, T c max , the only known, but not understood, systematics is that for materials with multiple CuO 2 -layers, such as HgBa 2 Ca n−1 Cu n O 2n+2 , T c max increases with the number of layers, n, until n ∼3. There is little clue as to why for n fixed, T c max depends strongly on the family, e.g. why for n=1, T c max is 40 K for La 2 CuO 4 and 85 K for Tl 2 Ba 2 CuO 6 , although the Neel temperatures are fairly similar. A wealth of structural data has been obtained, and correlations between structure and T c have often been looked for as functions of doping, pressure, uniaxial strain, and family. However, the large number of structural and compositional parameters makes it difficult to find what besides doping controls the superconductivity. Insight was recently provided by Seo et al. [3] who grew ultrathin epitaxial La 1.9 Sr 0.1 CuO 4 films with varying degrees of strain and measured all relevant structural parameters and physical properties. For this single-layer material it was concluded that the distance between the charge reservoir and the CuO 2 -plane is the key structural parameter determining the normal state and superconducting properties.Most theories of HTSC are based on a Hubbard model with one Cu d x 2 −y 2 -like orbital per CuO 2 unit. The oneelectron part of this model is, in the k-representation:with t, t ′ , t ′′ , ... denoting the hopping integrals (≥ 0) on the square lattice (Fig. 1) Relation between the one-orbital model (t, t ′ , t ′′ , ...) and the nearest-neighbor four-orbital model [4] (ε d − εp ∼ 1 eV, t pd ∼ 1.5 eV, εs − εp ∼ 16 − 4 eV, tsp ∼ 2 eV) .The LDA band structure of the best known, and only stoichiometric optimally doped HTSC, YBa 2 Cu 3 O 7 , is more complicated than what can be described with the t-t ′ model. Nevertheless, careful analysis has shown [4] that the low-energy, layer-related features, which are the only generic ones, can be described by a nearest-neighbor, tight-binding model with four orbitals per layer (Fig. 1), Cu d x 2 −...