Thermodynamic properties of superconductors with paramagnetic impurity under pressure

A study is made of the influence of Van Hove singularities in the density of electron states on the critical temperature $T_c$, the order parameter $\Delta$, and the energy gap $\Omega_g$ of a superconductor with paramagnetic impurity. The behavior of these quantities is studied as a function of the pressure and the impurity. All these depend strongly on the difference between the valences of the impurity atoms and atoms of the metal. Depending on the topological nature of the change of the Fermi surface, the critical impurity concentrations $\Gamma_\mathrm{cr}$ and $\Gamma_{\Omega_g}=0$ can increase or decrease with increasing pressure. They are not inversal, but depend strongly on the difference between the valences of the impurity atoms and the metal. Expressions are obtained for the thermodynamic critical field at $T=0$ and $T=T_c$, and the discontinuity in the specific heat at the critical point $T=T_c$ is also calculated. These quantities depend on the pressure and also on the impurity when allowance is made for the Van Hove singularities in the electron density states.