Some parameters of superconductors with an extreme singularity in the density of state: (s+d) model

We study some parameters of superconductors with δ-function type singularities in the electronic density of states (DOS), exhibiting (s+d)-wave symmetry of the order parameter. Starting with a pure s-wave pairing potential V_s, the critical temperature T_c at first slightly increases with increasing the d-wave interaction potential V_d, being determined by this interaction only for stronger V_d values. The ratio R=2|Δ(0)|/k_BT_c of the mean value of the zero temperature energy gap |Δ(0)| to T_c increases with increasing V_d, reaching a maximum which depends on the mixing interaction term. The maximum values of R are comparable with very high values obtained in some gap measurements. The jump in the specific heat at critical temperature is by a factor 2.4 higher for the extreme singularity of pure s-wave symmetry, as compared with the BCS theory with constant DOS. Such higher values of the jump are in agreement with the experimentally observed values, as well as with the calculations determined by extended saddle points in the electronic bands. By switching the d-wave channel, the value of the jump decreases. The results show the usefulness of calculations with δ-type singularities as a limiting case of very strong singularities in the DOS.