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1
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The Numerical Solution of the Imaginary-Axis Eliashberg Equations

100%
Szczęśniak R.
Acta Physica Polonica A
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2006
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vol. 109
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issue 2
179-186
EN
In the paper, we solve the imaginary-axis Eliashberg equations. We calculate numerically self-consistently the superconducting order function, the wave function renormalization factor, and the energy shift function as a function of the Matsubara frequency. We consider different values of the average number of the electrons per lattice site. Additionally, we study the temperature dependence of the order function and the wave function renormalization factor. The possible extension of the Eliashberg theory to the case of the high-T_C superconductors was also briefly discussed.
2
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On the Ratio of the Energy Gap Amplitude to the Critical Temperature for Cupratesi (Acta Physica Polonica A 126, A-92 (2014), ERRATUM)

64%
Szczęśniak R., Durajski A.
Acta Physica Polonica A
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2016
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vol. 130
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issue 6
1443
EN
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).
3
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Thermodynamic Properties of the Superconducting State in the K_{3}C_{60} Fulleride

64%
Szczęśniak R., Barasiński A.
Acta Physica Polonica A
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2009
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vol. 116
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issue 6
1053-1058
EN
In the framework of the Eliashberg formalism, we have calculated the thermodynamic properties of the superconducting state in K_{3}C_{60} (the critical temperature T_C = 19.50 K). We have obtained the following results: (i) The critical value of the Coulomb pseudopotential is equal to 0.387. (ii) The values of the ratios R_1 ≡ 2Δp(0)/k_{B}T_C and R_2 ≡ ΔC(T_C)/C^{N}(T_C) are bigger than in the BCS model; R_1 = 4.01 and R_2 = 1.58. (iii) The electron effective mass m*_{e} reaches the highest value for T = T_C; [m*_{e}]_max = 2.86 m_{e}, where m_{e} is the bare electron mass. Additionally, we have given the analytical expressions for T_C, Δ(T), R_1 and R_2.
4
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On the Thermodynamic Critical Field for the K_3C_{60} and Rb_3C_{60} Fullerides

64%
Durajski A., Szczęśniak R.
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vol. 126
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issue 1
342-343
EN
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}.
5
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Thermodynamic Critical Magnetic Field for Chlorine Halide Superconductor at High Pressure

64%
Szczęśniak D., Szczęśniak R.
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vol. 126
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issue 1
344-345
EN
At present, hydrides are considered as a one of the most interesting high-temperature superconductors with the classical electron-phonon pairing mechanism. In the present paper, we have analyzed the dependence of the thermodynamic critical magnetic field (H_c) on the temperature for the chlorine halide superconductor. The calculations have been made in the framework of the Eliashberg formalism for the following pressure values: p_{1}=320 GPa and p_{2}=360 GPa. We have shown that H_c increases strongly with the increase of the pressure: [H_c(0)]_{p_{2}}/[H_c(0)]_{p_{1}}= 1.43. Furthermore, the dimensionless ratio: R_{H} ≡ T_cC^{N}(T_c)/H_c^{2}(0), where T_c and C^{N} denote the critical temperature and the specific heat of the normal state, differs from the value predicted by the Bardeen-Cooper-Schrieffer theory. In particular: [R_{H}]_{p_{1}}=0.166 and [R_{H}]_{p_{2}}=0.158.
6
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The Properties of the Superconducting State in YNi_2B_2C: The One-Band Eliashberg Approach

64%
Jarosik M., Szczęśniak R.
Acta Physica Polonica A
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2011
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vol. 119
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issue 6
863-867
EN
The basic thermodynamic parameters of the superconducting state in YNi_2 B_2 C were calculated in the framework of the one-band Eliashberg model. The effective Eliashberg function, determined on the basis of the transport function, was used during calculations. It was shown that the dimensionless ratios are equal to: R_1 ≡ 2Δp(0)/k_{B} T_{C} = 3.87, R_2 ≡ ΔC(T_{C})/C^{N}(T_{C}) = 1.79 and R_3 ≡ T_{C} C^{N}(T_{C}) / H_{C}^2(0) = 0.159. The value R_1 fairly agrees with the experimental data whereas R_2 and R_3 agree very well.
7
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Strong-Coupling Description of the High-Temperature Superconductivity in the Molecular Hydrogen

64%
Szczęśniak R., Jarosik M.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
841-844
EN
The detailed study of the selected thermodynamic properties of the superconducting phase in the molecular hydrogen under the pressure at 428 GPa has been presented. For the increasing value of the Coulomb pseudopotential μ^{*}∈〈0.08,0.15〉, the following results have been obtained: (i) the critical temperature decreases from 179 K to 141 K, (ii) the ratio R_{1}≡ 2Δ(0)/k_{B}T_{C} differs noticeably from the BCS value: R_{1}∈〈4.71,3.60〉; (iii) the electron effective mass is large and grows slightly together with the temperature ([m^{*}_{e}/m_{e}]_{max}=2.2 for T = T_{C}).
8
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The van Hove Singularity and Two-Dimensional Superconductivity. Exact Analytical Results

64%
Szczęśniak R., Grabiński S.
Acta Physica Polonica A
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2002
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vol. 102
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issue 3
401-407
EN
We investigate a weak-coupling approach to superconductivity in the density of states that develops in the two-dimensional lattice with the van Hove singularity located at the Fermi level. Exact analytical expressions for the superconducting order parameter at zero temperature (Δ(0)) and for discontinuity in the specific heat at critical temperature (Δ C) were derived. We show that the presence of the logarithmic singularity hardly affects the ratio 2Δ(0)/kT_c, whereas the temperature dependence of Δ C can pronouncedly deviate from the standard BCS result.
9
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Characterization of Novel High-Pressure Close-Packed Superconducting Phase of Boron

64%
Szczęśniak D., Szczęśniak R.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
254-256
EN
We report study on the thermodynamic properties of the novel high-pressure superconducting phase of boron with hexagonal P6₃/mcm structure. Our analysis is conducted at the pressure of p=400 GPa, which is motivated by the highest value of the superconducting transition temperature (T_{C}) observed previously under such conditions for the P6₃/mcm boron. Our investigations of the thermodynamic properties are performed within the Eliashberg formalism, due to the strong-coupling character of the considered material. In particular, we calculate the thermodynamic properties of the superconducting state which allows us to determine the values of the characteristic dimensionless parameters; the zero-temperature energy gap to the critical temperature, the ratio of the specific heats, as well as the ratio connected with the zero-temperature thermodynamic critical field.
10
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On the Magnetic Penetration Depth in Superconducting Ultrathin Lead Films

64%
Durajski A., Szczęśniak R.
Acta Physica Polonica A
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2017
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vol. 131
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issue 4
1051-1053
EN
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.
11
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Characteristics of the Eliashberg Formalism on the Example of High-Pressure Superconducting State in Phosphor

51%
Duda A., Szczęśniak R., Sowińska M., Domagalska I.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
649-654
EN
The work describes the properties of the high-pressure superconducting state in phosphor: p∈ {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 the observed not-high values of the critical temperature ([T_{C}]_{p=30GPa}^{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. Additionally the inconsiderable strong-coupling and retardation effects force the dimensionless ratios R_{Δ}, 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.
12
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The Thermodynamic Critical Field οf YNi_2B_2C Superconductor

51%
Jarosik M., Szczęśniak R., Szczęśniak D.
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issue 5
1031-1033
EN
In the presented work the dependence of the thermodynamic critical field (H_{C}) on the temperature for the YNi_2B_2C superconductor was determined in the framework of the Eliashberg formalism. The numerical calculations were conducted with the use of the modified transport Eliashberg function. It has been stated that the normalized field function H_{C}(T)/H_{C}(0) correctly reproduces the experimental data.
13
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Pressure Dependence of the Thermodynamic Critical Field in Francium

51%
Pach P., Szczęśniak R., Durajski A.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
231-233
EN
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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