Van Hove Singularities in BCS Theory

Abstract

<p> The influence of a logarithmically dependent (van Hove singularity) electronic density of states is studied in the weak-coupling limit. Through analytic and numerical analysis it is found that the model can give rise to temperatures in the 100 K range, and that universal BCS ratios such as 2Δ/kBTC and ΔC/γTC do not change essentially from their constant BCS values. The consequences of this model on the calculation of the isotope effect and specific heat are discussed in detail and compared to recent experimental results.</p>