PROPERTIES OF THE GAP ENERGY IN THE VANHOVE SCENARIO OF HIGH-TEMPERATURE SUPERCONDUCTIVITY

An exact transition-temperature (T(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 T(c) is greatly enhanced over the conventional BCS (constant DOS) value for given (weak) coupling, the zero-temperature gap-to-T(c) ratio and the temperature-dependent gap energy both differ little from the BCS values.