SUPERCONDUCTIVITY IN 2-DIMENSIONAL SYSTEMS - VANHOVE SINGULARITY AND COULOMB REPULSION

Although BCS theory completely neglects Coulomb repulsion, Anderson and Morel showed very early that it plays a central role in superconductivity. The main result of their model is that the Coulomb potential is weakened by renormalization in broad bands, thus allowing the apparition of superconductivity. This suppresses the possibility to achieve a high T(c) by narrowing the band to obtain a high density of state. The aim of this article is to show that nevertheless a peak in the density of states in the middle of a broad band can lead to a high T(c) by combining the advantages of both a high density of state and the renormalization of Coulomb potential by a broad band. We focus on the case of two dimensional materials (such as the new high T(c) superconductors with their Cu-O planes) where a logarithmic singularity always exists as shown by Van Hove.