Characteristics of the Eliashberg formalism on the example of high-pressure superconducting state in phosphor

The work describes the properties of the high-pressure superconducting state in phosphor: $p\in\{20, 30, 40, 70\}$ GPa. The calculations were performed in the framework of the Eliashberg formalism, which is the natural generalization of the BCS theory. The exceptional attention was paid to the accurate presentation of the used analysis scheme. With respect to the superconducting state in phosphor it was shown that: (i) the observed not-high values of the critical temperature ($\left[T_{C}\right]_{p=30{\rm GPa}}^{\rm max}=8.45$ K) result not only from the low values of the electron - phonon coupling constant, but also from the very strong depairing Coulomb interactions, (ii) the inconsiderable strong - coupling and retardation effects force the dimensionless ratios $R_{\Delta}$, $R_{C}$, and $R_{H}$ - related to the critical temperature, the order parameter, the specific heat and the thermodynamic critical field - to take the values close to the BCS predictions.Comment: 6 pages, 6 figure

Properties of the superconducting state in compressed Sulphur

The thermodynamic properties of the superconducting state in Sulphur under the pressure at 160 GPa were determined. It has been shown that: (i) the critical value of the Coulomb pseudopotential is equal to 0.127; (ii) the critical temperature (T_{C} =17 K) should be calculated by using the modified Allen-Dynes formula; (iii) the effective electron-electron interaction is attractive in the range of frequencies from zero to the frequency slightly lesser than the maximum phonon frequency (~ 0.85\Omega_{max}); (iv) the dimensionless ratios 2\Delta (0)/k_{B}T_{C}, $\Delta C(T_{C})/C^{N}(T_{C}) and T_{C}C^{N}(T_{C})/H^{2}_{C}(0) are equal to 3.7, 1.65 and 0.16 respectively; (v) the ratio of the effective to bare electron mass reaches maximum of 1.77 for T=T_{C}.Comment: 3 pages, 5 figure

Specifc Heat and Thermodynamic Critical Field for Calcium under the Pressure at 120 GPa

The free energy difference between the superconducting and normal state for Calcium under the pressure at 120 GPa has been determined. The numerical calculations have been made in the framework of the imaginary axis Eliashberg approach. On the basis of the obtained results the specific heat in the superconducting C^{S}(T) and normal C^{N}(T) state, as well as, the thermodynamic critical field H_{C}(T) have been obtained. It has been shown that the characteristic values of the considered thermodynamic quantities do not obey the BCS universal laws. In particular, {\Delta}C(T_{C})/C^N(T_{C})=2.48 and T_{C}C^{N}(T_{C})/H_{C}^{2}(0)=0.154.Comment: 3 pages, 4 figure