Properties of the gap energy in the van Hove scenario of high-temperature superconductivity

Abstract

An exact transition-temperature (${\mathit{T}}_{\mathit{c}}$) formula is derived within the van Hove scenario of BCS phonon-mediated pairing theory consisting of a logarithmic singularity in the density of states (DOS) at the Fermi energy. Also evaluated are a near-exact zero-temperature gap-energy expression along with an exact (numerical) temperature-dependent gap energy. Though ${\mathit{T}}_{\mathit{c}}$ is greatly enhanced over the conventional BCS (constant DOS) value for given (weak) coupling, the zero-temperature gap-to-${\mathit{T}}_{\mathit{c}}$ ratio and the temperature-dependent gap energy both differ little from the BCS values.