Characteristics of the <i>s</i>–Wave Symmetry Superconducting State in the BaGe₃ Compound

Abstract

Thermodynamic properties of the s−wave symmetry superconducting phase in three selected structures of the BaGe 3 compound ( P 6 3 / m m c , A m m 2 , and I 4 / m m m ) were discussed in the context of DFT results obtained for the Eliashberg function. This compound may enable the implementation of systems for quantum information processing. Calculations were carried out within the Eliashberg formalism due to the fact that the electron−phonon coupling constant falls within the range λ ∈ 0.73 , 0.86 . The value of the Coulomb pseudopotential was assumed to be 0.122 , in accordance with the experimental results. The value of the Coulomb pseudopotential was assumed to be 0.122 , in accordance with the experimental results. The existence of the superconducting state of three different critical temperature values, namely, 4.0 K, 4.5 K and 5.5 K, depending on the considered structure, was stated. We determined the differences in free energy ( Δ F ) and specific heat ( Δ C ) between the normal and the superconducting states, as well as the thermodynamic critical field ( H c ) as a function of temperature. A drop in the H c value to zero at the temperature of 4.0 K was observed for the P 6 3 / m m c structure, which is in good accordance with the experimental data. Further, the values of the dimensionless thermodynamic parameters of the superconducting state were estimated as: R Δ = 2 Δ ( 0 ) / k B T c ∈ { 3.68 , 3.8 , 3.8 } , R C = Δ C ( T c ) / C N ( T c ) ∈ { 1.55 , 1.71 , 1.75 } , and R H = T c C N ( T c ) / H c 2 ( 0 ) ∈ { 0.168 , 0.16 , 0.158 } , which are slightly different from the predictions of the Bardeen−Cooper−Schrieffer theory ( [ R Δ ] B C S = 3.53 , [ R C ] B C S = 1.43 , and [ R H ] B C S = 0.168 ). This is caused by the occurrence of small retardation and strong coupling effects.

Keywords

• <i>s</i>–wave symmetry Eliashberg formalism
• BaGe₃ superconductor
• thermodynamic properties