Quantum Percolation and Lattice Instabilities in High-T sub c Cuprate Superconductors.

Lattice instabilities are the mechanisms which place upper bounds on T sub c in theoretical models of superconductivity based on dynamical electron-phonon interactions. In percolative metals this upper bound can be much larger than in ballistic metals. For parameters appropriate to high-T sub c cuprates I show that the maximum value lambda tilde sub (max) of the percolative electron-phonon coupling constant is about four times larger than the value lambda sub (max) ~ 1 appropriate to ballistic metals. I also review values of lambda in ``anomalous'' ballistic metals, such as Nb sub 3 Ge homoepitaxial films, and show that these may be defect-enhanced.