A model for high-temperature superconductors based on the idea of Cooper pairs comprised of electrons from different bands is studied. We propose that the two bands relevant for the cuprates are comprised of Cu $d_{x^2-y^2},$ $d_{z^2},$ planar O $p_{\sigma },$ and apical O $p_z$ orbitals. Along the diagonal, $k_x{=k}_y$ in the Brillouin zone, the two-band Fermi surfaces may cross. We associate the optimal doping for the highest $T_c$ with this point because only in the vicinity of this touching point are interband Cooper pairs energetically possible. Due to the lack of time-reversal invariance of an interband Cooper pair with itself, the standard interpretation of Josephson tunneling is altered such that the detailed nature of the single-particle tunneling matrix elements contributes to the supercurrent. The $d_{x^2-y^2}$ gap observations from Josephson tunneling are shown to arise from our model with pairing due to phonons. A Hubbard model is written down for the two bands at the Fermi energy with realistic parameters for ${\mathrm{La}}_{1.85}{\mathrm{Sr}}_{0.15}{\mathrm{CuO}}_4.$ The anomalous normal-state features in the NMR are calculated and qualitatively explained as due to the character of the two bands in the vicinity of the crossing point. The Hall effect is calculated using standard Bloch-Boltzmann transport theory. The observed strong temperature dependence of the Hall coefficient is reproduced and is due to the strong reshaping of the current-carrying band Fermi surface due to band repulsion with the other band for dopings very close to the Fermi-surface touching point. Reasonable quantitative agreement is also obtained for the NMR and Hall effect. A linear resistivity at optimal doping is expected due to the proximity of the second band in k space which can strongly relax the current and the “smallness” of the current-carrying Fermi surface.

• Received 8 September 1997

DOI:https://doi.org/10.1103/PhysRevB.58.12307