Plane dimpling and saddle-point bifurcation in the band structures of optimally doped high-temperature superconductors: A tight-binding model

We argue that extended saddle points observed at the Fermi level for optimally doped superconductors are essentially the bifurcated saddle points predicted by density-functional [local density approximation (LDA)] calculations. Such saddle points are caused by the dimple of the ${\mathrm{CuO}}_{2}$ planes and are enhanced by plane-plane hopping. Dimpling may provide a mechanism for pinning the Fermi level to the saddle points. Simple tight-binding Hamiltonians and an analytical expressions for the constant-energy contours are derived from the LDA bands of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7.}$ In addition to the ${\mathrm{O}}_{2}$ x O3 y, and Cu ${\mathit{x}}^{2}$-${\mathit{y}}^{2}$ orbitals, we find that O2 z and O3 z are crucial and Cu s, are crucial. The O z orbitals allow the pd\ensuremath{\sigma} antibond to tilt with the dimple.