Abstract
The influence of singularities in the electronic density of states (DOS) on high-temperature superconductors is studied in the framework of the conventional BCS theory. By using a DOS with singularities at two different points we are able to explain the asymmetry in the isotope exponent α with respect to the point where Tc is maximum. A DOS with a power law singularity reproduces the vanishingly small values of α and large values of R2 = ΔC(Tc)/Cn(Tc), the ratio of the jump in the electronic specific heat to the normal specific heat at T = Tc, observed in certain high-Tc materials. However, the value of the ratio R1 = 2Δ0/kBTc does not deviate much from its canonical BCS value of 3.53, in agreement with earlier results.
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