Multigap superconducting state in molecular metallic hydrogen

• Main Authors: Szczȩśniak, R, Drzazga, E. A
• Format: Journal Article
• Language: English
• Published: 03-10-2012
• Subjects: Physics - Superconductivity
• DOI: 10.48550/arxiv.1209.5849

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 [($[m^{\star}_{e}]_{\alpha}$).
The following results have been achieved: $[m^{\star}_{e}]_{a}=2.99
[m_{e}]_{a}$, $[m^{\star}_{e}]_{b}=2.10 [m_{e}]_{b}$ and
$[m^{\star}_{e}]_{c}=1.94 [m_{e}]_{c}$, where $[m_{e}]_{\alpha}$ stands for the
electron band mass.