Phase separation and charge density waves: Possible sources of non-Fermi liquid behavior and pairing in high-temperature superconductors

In the absence of a sufficiently singular interaction between the particles, the Fermi-liquid state is stable above one dimension. To reconcile this finding with the observed anomalies in the cuprates one is therefore led to the search for mechanisms giving singular interactions. A recent proposal indicates the cuprates as being close to a charge instability, which would drive the system toward phase separation (in the absence of long-range Coulomb forces between the carriers) or toward the formation of incommensurate charge-density waves in the more physical case of charged carriers. Close to these instabilities strong singular and attractive scattering arises between the quasiparticles at the Fermi surface. This scattering would easily account for both the anomalous behavior of the normal metallic phase and for the strong pairing mechanism leading to high-temperature superconductivity. The strong momentum dependence of the singular attraction would also give rise to the (likely) observed unusual d-wave symmetry of the superconducting order parameter in these systems.