Pairing from repulsive interactions

Abstract

Long ago, Kohn and Luttinger [174] proposed that a superconducting instability should occur in Jellium. They focussed on pairs of parallel spin electrons of large relative angular momentum L. The large L and the triplet state keep the electrons apart, so the Coulomb repulsion is particularly mild in such pairs. At long distances, the screened interaction undergoes Friedel oscillations due to the singularity of the dielectric function at 2k_F (See Section 12.1.1). This means a slight over-screening of the repulsion in some distance ranges: one gets an effective attraction from the repulsion via a quantum mechanical correlation effect. Attraction in some distance ranges does not necessarily imply binding, but Kohn and Luttinger suggested that this effect could indeed produce pairing. While no such superconducting instability appears to be relevant to ordinary metals, the paradoxical theoretical idea that attraction could result from repulsion is fascinating and the discovery of high-T_c superconductivity [175] has stimulated a hot discussion on the possibility that something similar is realized in the Cuprates (although the pairs are singlets with L=2, so some important modification is needed). The fact that T_C can be above liquid N₂ (rather than liquid He) temperatures, and the evidence that this occurs in strongly correlated materials suggests to part of the community that the mechanism must be different from the conventional phonon-assisted BCS one[181].