Superconductivity of calcium under the pressure at 120 GPa

The properties of the superconducting state in calcium under the pressure at 120 GPa were analyzed. By using the imaginary axis Eliashberg equations it has been shown, that the Coulomb pseudopotential reaches the high value equal to 0.215. In the considered case, the critical temperature is not properly described by the Allen-Dynes formula and it should be calculated with an use of the modified expression. In the paper the exact solutions of the Eliashberg equations on the real axis were also obtained. On this basis it was stated, that the effective potential of the electron-electron interaction is attractive for the frequencies lower or equal to the maximum phonon frequency. Then, the dimensionless parameter 2\Delta(0)/k_{B}T_{C}=4.10 was calculated. In the last step it has been proven, that the ratio of the electron effective mass to the bare electron mass is high and reaches its maximum equal to 2.36 for the critical temperature

The superconducting phase of Calcium under the pressure at 200 GPa: the strong-coupling description

The thermodynamic parameters of the superconducting state in Calcium under the pressure at 200 GPa have been determined. The numerical analysis by using the Eliashberg equations in the mixed representation has been conducted. It has been stated, that the critical temperature ($T_{C}$) decreases from 36.15 K to 20.79 K dependently on the assumed value of the Coulomb pseudopotential ($\mu^{*}\in$). Next, the order parameter near the temperature of zero Kelvin ($\Delta(0)$) has been obtained. It has been proven, that the dimensionless ratio $2\Delta(0)/k_{B}T_{C}$ decreases from 4.25 to 3.90 together with the growth of $\mu^{*}$. Finally, the ratio of the electron effective mass to the electron bare mass ($m^{*}_{e}/m_{e}$) has been calculated. It has been shown, that $m^{*}_{e}/m_{e}$ takes the high value in the whole range of the superconducting phase's existence, and its maximum is equal to 2.23 for T=T_{C}.Comment: 5 pages, 5 figure

Scalability of non-adiabatic effects in lithium-decorated graphene superconductor

The analysis is conducted to unveil how the non-adiabatic effects scale within the superconducting phase of lithium-decorated graphene $(\text{LiC}_{6})$ . Based on the Eliashberg formalism it is shown that the non-adiabatic effects notably reduce essential superconducting parameters in $\text{LiC}_{6}$ and arise as a significant oppressor of the discussed phase. Moreover, non-adiabaticity is found to scale with the strength of superconductivity, proportionally to the phonon energy scale and inversely with respect to the electron-phonon coupling. These findings are partially in contrast to other theoretical studies and show that superconductivity in $\text{LiC}_{6}$ is more peculiar than previously anticipated. In this context, the guidelines for enhancing superconducting phase in $\text{LiC}_{6}$ and sibling materials are also proposed