d-wave superconductivity near charge instabilities

We investigate the symmetry of the superconducting order parameter in the proximity of a phase separation or of an incommensurate charge-density-wave instability. The attractive effective interaction at small or intermediate transferred momenta is singular near the instability. This strongly q-dependent interaction, together with a residual local repulsion between the quasiparticles and an enhanced density of states for band structures appropriate for the high-temperature superconducting oxides, strongly favors the formation of d-wave superconductivity. The relative stability with respect to superconductivity in the s-wave channel is discussed in detail, finding this latter hardly realized in the above conditions. The superconducting temperature is mostly determined by the closeness to the quantum critical point associated with the charge instability and displays a stronger dependence on doping with respect to a simple proximity to a van Hove singularity. The relevance of this scenario and the generic agreement of the resulting phase diagram with the properties displayed by high-temperature superconducting oxides is discussed.