Tight-binding modelling of the electronic band structure of layered superconducting perovskites

A detailed tight-binding analysis of the electron band structure of the CuO₂plane of layered cuprates is performed within a σ -band Hamiltonian including four orbitals - Cu 3d_{x² -y²} and Cu 4s, O 2p_x and O 2p_y . Both the experimental and theoretical indications in favour of a Fermi level located in a Cu or O band, respectively, are considered. For these two alternatives, analytical expressions are obtained for the linear combination of atomic orbitals (LCAO) electron wave functions suitable for the treatment of electron superexchange. Simple formulae for the Fermi surface and electron dispersions are derived by applying the Löwdin downfolding procedure to set up the effective copper and oxygen Hamiltonians. They are used to fit the experimental angle-resolved ultraviolet photoelectron spectroscopy (ARUPS) Fermi surface of Pb_0.42 Bi_1.73 Sr_1.94 Ca_1.3 Cu_1.92 O_8+x and both the ARPES and local density approximation (LDA) Fermi surface of . The value of presenting the hopping amplitudes as surface integrals of ab initioatomic wave functions is demonstrated as well. The same approach is applied to the RuO₂plane of the ruthenate Sr₂ RuO₄ . The LCAO Hamiltonians including the three in-plane π -orbitals Ru 4d_xy , O_a2p_y , O_b2p_x and the four transverse π -orbitals Ru 4d_zx , Ru 4d_yz , O_a2p_z , O_b2p_z are considered separately. It is shown that the equation for the constant-energy curves and the Fermi contours has the same canonical form as the one for the layered cuprates.