Abstract
The effects of having a van Hove singularity in the density of states on a high temperature superconductors having an (s+d)-wave symmetry order parameter (OP) are studied. It is assumed that superconductivity is due to the exchange of spin fluctuations. It is found that the two (s-wave and d-wave) components of the OP are determined by a set of coupled equations. Close to T c′ these equations are linear in Δ s and Δ d while at T=0 K, they form a set of non-linear equations in the two components of the OP. The equations for T close to T c are solved analytically to yield an expression for the transition temperature T c. The equations for T=0 K are solved numerically for different values of ω b (the cutoff frequency of the magnetic excitation responsible for superconductivity in the system). The dependence of the ratio 2 Δ(0)/ k B T c (with Δ(0)=Δ s (0) (1+ R 2) and R being the ratio of the two components of the OP at T=0 K) on ω b is shown.
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