The model for the cuprates based on the modified electron-phonon pairing mechanism has been tested. For this purpose, the superconductors with high value of the critical temperature have been taken into consideration. In particular: YBa₂Cu₃O_{7-y}, HgBa₂CuO_{4+y}, HgBa₂Cu_{1-x}Zn_{x}O_{4+y}, and HgBa₂Ca₂Cu₃O_{8+y}. It has been shown that the dependence of the ratio R₁ ≡ 2Δ_{tot}^{(0)}/k_{B}T_{C} on the doping (p) can be properly predicted in the framework of the presented theory; the symbol Δ_{tot}^{(0)} denotes the energy gap amplitude at the temperature of zero kelvin, and T_{C} is the critical temperature. The numerical results have been supplemented by the formula which describes the function R₁(p).
In the paper the temperature dependence of the thermodynamic critical field (H_c) for the alkali-metal-doped fullerides K_3C_{60} and Rb_3C_{60} has been considered. The numerical calculations have been conducted in the framework of the Migdal-Eliashberg formalism. It has been shown that the obtained numerical values of H_c agree with the experimental data. Finally, the dimensionless ratio: R_{H} ≡ T_cC^{N} (T_c)/H^{2}_c(0) has been calculated, where T_c is the critical temperature and C^{N} denotes the specific heat in the normal state. The theoretical analysis has proved that for the considered fullerides the parameter R_{H} is beyond the BCS prediction. In particular: R_{H}=0.143 for K_3C_{60}, and R_{H}=0.145 for Rb_3C_{60}.
In the present paper, we report a theoretical study of the magnetic London penetration depth in ultrathin Pb films consisting of five to ten monolayers. Our calculations were performed within the framework of the strong-coupling approach. We observed that for thin films, the thermodynamic parameter exhibits an oscillatory behaviour connected with a quantum size effect. Moreover, we proved that the London penetration depth of Pb films cannot be correctly described using the Bardeen-Cooper-Schrieffer theory of superconductivity due to the strong-coupling and retardation effects. The Eliashberg theory, used in this paper, goes beyond the BCS theory to include these effects which allows to describe the superconducting state on the quantitative level.
The model for the cuprates based on the modified electron-phonon pairing mechanism has been tested. For this purpose, the superconductors with high value of the critical temperature have been taken into consideration. In particular: YBa_{2}Cu_{3}O_{7-y}, HgBa_{2}CuO_{4+y}, HgBa_{2}Cu_{1-x}Zn_{x}O_{4+y}, and HgBa_{2}Ca_{2}Cu_{3}O_{8+y}. It has been shown that the dependence of the ratio R_{1} ≡ 2Δ_{tot}^{(0)}/k_{B}T_{C} on the doping (p) can be properly predicted in the framework of the presented theory; the symbol Δ_{tot}^{(0)} denotes the energy gap amplitude at the temperature of zero kelvin, and T_{C} is the critical temperature. The numerical results have been supplemented by the formula which describes the function R_{1}(p).
In the paper, the values of the thermodynamic critical field (H_{C}) for francium have been calculated. It has been assumed the wide range of the pressure: p∈ ⟨7.2; 14⟩ GPa. The analysis has been performed in the framework of the strong-coupling formalism. It has been predicted that the value of the ratio H_{C}(0)/√ρ(0) increases with the increasing pressure from 3.08 meV to 5.84 meV, where ρ(0) denotes the electron density of states at the Fermi level. The dimensionless parameter T_{C}C^{N}(T_{C})/H²_{C}(0) is smaller than in the BCS theory and decreases with pressure from 0.150 to 0.141. The symbol T_{C} represents the critical temperature and C^{N} is the specific heat for the normal state.
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