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

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