Journal of Superconductivity, Vol. 9, No. 4, 1996 Phase Separation and Charge Density Waves: Possible Sources of Non-Fermi Liquid Behavior and Pairing in High-Temperature Superconductors C. Castellani, 1 C. Di Castro, 1 and M. Grilli ~ Received 15 July 1995 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 quasipartieles 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. KEY WORDS: Phase separation; charge density waves; non-Fermi liquid behavior; high-temperature superconductors. The understanding of the pairing mechanism in high-To superconductors is related to the understand- ing of the anomalous behavior of the normal phase. As far as the superconducting phase is concerned, together with the high value of the critical tempera- tures, one of the most debated problems is the symme- try of the order parameter. Even though the present experimental situation is not completely settled [4], evidences for the d-wave pairing come from several different experiments, i.e., angle-resolved photo- emission [1], penetration depth [2], and Josephson coupling [3] experiments. For the normal phase, vari- ous properties cannot be described in terms of the Fermi Liquid (FL) theory, e.g., the behavior of the resistivity, which is linear in T at optimal doping for some decades. One possible explanation for these ano- malous properties of the normal phase is that the low 1Dipartimento di Fisica, Universit/t "La Sapienza," P.le Aldo Moro 2, 00185 Roma, Italy. 413 dimensionality of such highly anisotropic systems and their correlated nature are at the origin of a break- down of the Fermi liquid (FL). FL theory indeed breaks down in a variety of physical situations as, for instance, in the quasi-one dimensional conductors. The one-dimensional metal- lic phase is described by the so-called Luttinger liquid theory with no quasi-particle weight at the Fermi sur- face [6]. In d = 1 the small momentum transfer scatter- ing processes (the only relevant processes in the Luttinger liquid theory) allow for charge and spin conservation for the states near the left and right Fermi points separately. The low-energy properties of the metallic phase in one dimension are uniquely determined by these four conservations which render the (left and right) density and current essentially equal, allowing for the integrability of the system. Technically this is achieved for instance by the use of the equation of motion and the Ward identities implementing the previous conservations [7,8]. The 0896-1107/96/0800-0413509.50/0 9 1996 PlenumPublishing Corporation