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 CuO₂ 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 YBa₂{Cu}₃O7. In addition to the O₂ x O3 y, and Cu x²-y² orbitals, we find that O2 z and O3 z are crucial and Cu s, are crucial. The O z orbitals allow the pd{σ} antibond to tilt with the dimple.