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.
Highlights
Ba–Ge type compounds are intensively studied with respect to the broad range of their possible technological applications, especially in thermoelectric devices [1,2], which are used for energy production and cooling
Symmetry 2019, 11, 977 compounds are used for the implementation of systems that perform quantum information processing [4]
We are going to determine all the interesting thermodynamical properties of the s–wave symmetry superconducting state induced in the BaGe3 compound for three crystalline structures: P63 /mmc, Amm2, and I4/mmm
Summary
Ba–Ge type compounds are intensively studied with respect to the broad range of their possible technological applications, especially in thermoelectric devices [1,2], which are used for energy production and cooling. Ba–Ge type compounds are well worth the attention with respect to their interesting low-temperature thermodynamic properties, including the s–wave symmetry superconducting ones [10,11]. It was pointed out, in particular, that the Ba24 Ge100 system undergoes a transition to the superconducting state at the temperature of 0.24 K [12,13,14], as the Ba24 Si100 one. We are going to determine all the interesting thermodynamical properties of the s–wave symmetry superconducting state induced in the BaGe3 compound for three crystalline structures: P63 /mmc, Amm, and I4/mmm
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