A model with a singular electronic density of states and some properties of high-temperature superconductors

The influence of singularities in the electronic density of states (DOS) on high-temperature superconductors is studied in the framework of the conven tional BCS theory. By using a DOS with singularities at two different point s we are able to explain the asymmetry in the isotope exponent alpha with r espect to the point where T-e is maximum. A DOS with a power law singularit y reproduces the vanishingly small values of alpha and large values of R-2 = Delta C(T-c)/C-n(T-c), the ratio of the jump in the electronic specific h eat to the normal specific heat at T = T-c, observed in certain high-T-c ma terials. However, the value of the ratio R-1 = 2 Delta(0)/k(B)T(e), does no t deviate much from its canonical BCS value of 3.53, in agreement with earl ier results.