van Hove scenario for a high Tc superconductor having a (s+d)-wave symmetry order parameter

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 Tc′ these equations are linear in Δs and Δd 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 Tc are solved analytically to yield an expression for the transition temperature Tc. The equations for T=0 K are solved numerically for different values of ωb (the cutoff frequency of the magnetic excitation responsible for superconductivity in the system). The dependence of the ratio 2Δ(0)/kBTc (with Δ(0)=Δs(0)(1+R2) and R being the ratio of the two components of the OP at T=0 K) on ωb is shown.