Characterization of the high‐pressure superconductivity in the Pnma phase of calcium

Abstract

The thermodynamic parameters of the superconducting state in calcium under the pressure at 161 GPa have been calculated within the framework of the Eliashberg approach. It has been shown that the value of the Coulomb pseudopotential is high (µ * C = 0.24) and the critical temperature (TC = 25 K) should be determined from the modified Allen-Dynes formula. In addition, it has been found that the basic dimensionless ratios of the thermodynamic parameters significantly diverge from the BCS predictions, and take the following values: (i) The zero temperature energy gap to the critical temperature (R1 ≡ 2∆ (0) /kBTC) is equal to 4.01. (ii) The ratio R2 ≡ C S (TC ) − C N (TC) /C N (TC ) equals 2.17, where C S and C N denote the specific heats for the superconducting and normal state, respectively. (iii) The quantity R3 ≡ TCC N (TC ) /H 2 C (0) = 0.158, where HC indicates the thermodynamic critical field. Finally, it has been proven that the electron effective mass is large and takes the maximum of 2.32me at TC.

Isotropic and anisotropic description of superconducting state in CaC6 compound

“…The numerical methods tested in the works [27][28][29][30][31] have been used. The stable solutions have been obtained for T ≥ T 0 = 2 K.…”

Phonon-mediated superconductivity in compressed NbH4 compound

“…critical temperature in a strict way can be determined using the Eliashberg equations. Recently, it has been proved for various conventional phonon-mediated superconductors in which the critical temperatures have been also determined experimentally [26,29].…”

“…This approach has been described in paper [24] and successfully used in the study of other hydrogen-rich compounds [17,19,25], and also in the study of materials for which is a possibility of comparison of the theoretical and experimental results (e.g. simple elements: Ca, S, Li, and compounds: CaLi 2 , K 3 C 60 , Rb 3 C 60 , MgB 2 ) [26][27][28][29][30][31]. Let us note that our calculated results agree quantitatively with the available experimental data.…”

The thermodynamic properties of the high-pressure superconducting state in the hydrogen-rich compounds

“…Let us note that the thermodynamic properties of the superconducting state of lithium and calcium differ very significantly from the expectations of the BCS theory [35], [36], [37], [38], [39], [40]. It is also important to describe their properties, it is necessary to assume anomalously high values of the Coulomb pseudopotential (µ ⋆ ).…”

“…However, it is unclear whether the value of the critical temperature for CaH 6 will not to significantly decrease when too large values of µ ⋆ are assumed. This possibility cannot be excluded a priori taking into account the results obtained for the superconducting state in calcium [36], [40]. Due to extremely interesting results obtained in the publication [41], we have determined the values of all relevant thermodynamic parameters characterizing the superconducting state in CaH 6 .…”