We describe the LDA band structure of YBa2Cu3O7 in the epsilon F+or-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, Cu(x2-y2), O2x, O3y, and Cus have sigma character and Cuxz, Cuyz, O2z, and O3z have pi character. The roles of the Cus orbital, which has some Cu(3z2-1) character, and the four pi orbitals are as follows: Cu, provides 2nd- and 3rd-nearest-neighbor (t' and t") intra-plane hopping, as well as hopping between planes (tperpendicular to ). The pi -orbitals are responsible for bifurcation of the saddle-points for dimpled planes. The 4- sigma -band Hamiltonian is generic for flat CuO2 planes and we use it for analytical studies The k||-dependence is expressed as one on u identical to (cos bky+cos akx)/2 and one on nu identical to (cos bky-cos akx)/2. The latter arises solely through the influence of Cus. The reduction of the sigma -Hamiltonian to 3- and 1-band Hamiltonians is explicitly discussed and we point out that, in addition to the hopping 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 hopping. We calculate the single-particle hopping between the planes of a bi-layer and show that it is generically: tperpendicular to (k||) approximately=0.25 eV. nu 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 Jperpendicular to for an un-doped bi-layer in mean-field 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 Jperpendicular to -20 meV. 

Nearest e-print mirror site for mpi-stuttgart.mpg.de is http://xxx.uni-augsburg.de/abs/cond-mat/9509044.
 

Journal of the Physics and Chemistry of Solids, 56 1573-91, 1995.

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