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 analytical expressions for the constant-energy contours are derived from the LDA bands of YBa2Cu3O7. In addition to the usual O2 x, O3 y, and Cu x2-y2 orbitals, we find that O2 z and O3 z are crucial and Cu s, xz, and yz important. The O z orbitals allow the pd sigma antibond to tilt with the dimple.
 

Physical Review B, 49 4145-57, 1994.