Multigap superconducting state in molecular metallic hydrogen

Abstract

The thermodynamic parameters of the superconducting state, that gets induced in the metallic molecular hydrogen under the influence of the pressure at 414 GPa ($T_C=84$ K), have been determined. The calculations have been conducted in the framework of the three-band Eliashberg equations. The order parameters (${\Delta }^{\alpha }$) and the wave function renormalization factors ($Z^{\alpha }$) have been derived; the symbol $\alpha$ denotes the band index: $\alpha \in a,b,c$. It has been stated that the dimensionless ratios $2{\Delta }^{\alpha }(0)/k_B{T}_C$ are equal to: 5.55, 3.96 and 3.53, respectively. Next, the total normalized function of the density of states, the free energy, the thermodynamic critical field and the specific heat have been determined. The obtained results differ significantly from the results achieved in the framework of the one-band Eliashberg model for the comparable value of the pressure ($p=428$ GPa). In the last step, the values of the wave function renormalization factors have been estimated for $T_C$. It allowed us to calculate the maximum value of the electron effective mass in a given band [($[m_e^{\star }{]}_{\alpha }$). The following results have been achieved: $[m_e^{\star }{]}_a=2.99[m_e{]}_a$, $[m_e^{\star }{]}_b=2.10[m_e{]}_b$ and $[m_e^{\star }{]}_c=1.94[m_e{]}_c$, where $[m_e{]}_{\alpha }$ stands for the electron band mass.

References in corpus (5)

• Quasi-molecular and atomic phases of dense solid hydrogen
• Anisotropic superconductivity in the two-dimensional electron-phonon system
• Strong electron-phonon interaction in multiband superconductors
• The superconducting phase of Calcium under the pressure at 200 GPa: the strong-coupling description
• Thermodynamics of the superconducting state in Calcium at 200 GPa

Cited by in corpus (5)

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• Description of the thermodynamic properties of $\mathrm{Bi}{\mathrm{H}}_5$ and $\mathrm{Bi}{\mathrm{H}}_6$ superconductors beyond the mean-field approximation
• Characteristics of the Eliashberg formalism on the example of high-pressure superconducting state in phosphor
• High-pressure superconducting state in hydrogen