Dominant role of the 2D Van Hove singularity on the Fermi surface and generalized susceptibility of the quasi-2D superconductor La_2-xM_xCuO₄ (M = Sr, Ba, ...)

The dominant role of the 2D van Hove saddle point singularity on the Fermi surface (FS) and generalized susceptibility, χ(q), in the quasi-2D superconductor La_2-xM_xCuO₄ is shown for varying compositions x of divalent additions M=Sr, Ba .... Dramatic topological changes in the FS with x indicate that composition can play the role of pressure in the classic work of Lifshitz. Very close correlations of large peaks in χ(q) with Fermi surface nesting features are found, along the Γ-X and Γ-N directions in the Brillouin zone, for varying x. The peak at X and N for x=0 which apparently drives, via a soft phonon mode, the transition from the bct to the orthorhombic phase is shifted to smaller q values. These results are consistent with the semiconducting behavior of La₂CuO₄ and superconductivity when stabilized with x>0 additions. Finally, orbital frequencies (areas) and masses are given which show the range required for de Haas-van Alphen or other experiments.