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

Abstract

The ab initio calculations suggest that the superconducting state in CaH6 under the pressure (p) at 150 GPa has the highest critical temperature among the examined hydrogen-rich compounds. For this reason, the relevant thermodynamic parameters of the superconducting state in CaH6 have been determined; a wide range of the Coulomb pseudopotential has been assumed: µ ⋆ ∈ 0.1, 0.3 . It has been found that: (i) The critical temperature (TC) changes in the range from 243 K to 180 K. (ii) The values of the ratio of the energy gap to the critical temperature (R∆ ≡ 2∆ (0) /kBTC ) can be found in the range from 5.42 to 5.02. (iii) The ratio of the specific heat jump (∆C (TC )) to the value of the specific heat in the normal state (C N (TC)), which has been represented by the symbol RC , takes the values from 3.30 to 3.18. (iv) The ratio RH ≡ TCC N (TC) /H 2 C (0), where HC (0) denotes the critical thermodynamic field, changes from 0.122 to 0.125. The above results mean that even for the strong electron depairing correlations the superconducting state in CaH6 is characterized by a very high value of TC, and the remaining thermodynamic parameters significantly deviate from the predictions of the BCS theory. The study has brought out the expressions that correctly predict the values of the thermodynamic parameters for the superconducting state in CaH6 and for the compounds: SiH4 (H2) 2 , Si2H6, B2H6, SiH4, GeH4, and PtH. Next, in the whole family of the hydrogen-rich compounds, the possible ranges of the values have been determined for TC, R∆, RC , and RH. It has been found that the maximum value of the critical temperature can be equal to 764 K, which very well correlates with TC for metallic hydrogen (p = 2 TPa). Other parameters (R∆, RC , and RH ) should not deviate from the predictions of the BCS theory more than the analogous parameters for CaH6.