Superconductivity and the Van Hove Scenario

We give a review of the role of the Van Hove singularities in superconductivity. Van Hove singularities (VHs) are a general feature of low-dimensional systems. They appear as divergences of the electronic density of states (DOS). Jacques Friedel and Jacques Labbé were the first to propose this scenario for the A15 compounds. In NbTi, for example, Nb chains give a quasi-1D electronic structure for the d-band, leading to a VHs. They developed this model and explained the high T _C and the many structural transformations occurring in these compounds. This model was later applied by Jacques Labbé and Julien Bok to the cuprates and developed by Jacqueline Bouvier and Julien Bok. The high T _C superconductors cuprates are quasi-bidimensional (2D) and thus lead to the existence of Van Hove singularities in the band structure. The presence of VHs near the Fermi level in the cuprates is now well established. In this context we show that many physical properties of these materials can be explained, in particular the high critical temperature T _C, the anomalous isotope effect, the superconducting gap and its anisotropy, and the marginal Fermi liquid properties, they studied these properties in the optimum and overdoped regime. These compounds present a topological transition for a critical hole doping p≈0.21 hole per CuO₂ plane.