Effect of a magnetic field on the specific heat jump of a superconducting alloy containing paramagnetic impurities with local states within the gap

The effect of a uniform magnetic field on the specific heat jump \({\Delta C}\) of a superconductor containing paramagnetic impurities has been investigated. The impurities are described by the Shiba-Rusinov model. Taking the normalized position of the bound state within the BCS gap ε₀=0.8 and 0.0 and the parameter α(=〈S _z ² 〉/S²)=1.0 and 1/3 as typical values, we find the detailed dependence of \({\Delta C}\) on the impurity concentration \(\bar c\) and the transition temperature T_c. In some cases \({\Delta C}\) diverges at certain values of \(\bar c\) or T_c, signaling a change of the normal-superconductor phase transition from second order to first order.