# Characteristics of Superconducting State in Vanadium: the Eliashberg Equations and Semi-analytical Formulas

## Abstract

The superconducting state in vanadium characterizes with the critical temperature (T{sub c}) equal to 5.3 K. The Coulomb pseudopotential, calculated with the help of the Eliashberg equations, possesses anomalously high value μ{sup ⋆}(3Ω{sub max}) = 0.259 or μ{sup ⋆}(10Ω{sub max}) = 0.368 (Ω{sub max} denotes the maximum phonon frequency). Despite the relatively large electron-phonon coupling constant (λ = 0.91), the quantities such as the order parameter (Δ), the specific heat (C), and the thermodynamic critical field (H{sub c}) determine the values of the dimensionless ratios not deviating much from the predictions of the BCS theory: R{sub Δ} = 2Δ(0)/k{sub B}T{sub c} = 3.68, R{sub C} = ΔC(T{sub c}) /C{sup N}(T{sub c}) = 1.69, and R{sub H}=T{sub c}C{sup N}(T{sub c})/H{sub c}{sup 2}(0)=0.171. This result is associated with the reduction of the strong-coupling and the retardation effects by the high value of the Coulomb pseudopotential. It has been shown that the results of the Eliashberg formalism can be relatively precisely reproduced with the help of the semi-analytical formulas, if the value of μ{sup ⋆} is determined on the basis of the T{sub c}-Allen-Dynes expression (μAD⋆ = 0.198). The attention should be paid to the fact that in the numerical and in themore »

- Authors:

- Czȩstochowa University of Technology, Institute of Physics (Poland)
- University of Zielona Góra, Quantum Optics and Engineering Division, Faculty of Physics and Astronomy (Poland)

- Publication Date:

- OSTI Identifier:
- 22782486

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Superconductivity and Novel Magnetism

- Additional Journal Information:
- Journal Volume: 31; Journal Issue: 4; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; Article Copyright (c) 2017 The Author(s); http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1557-1939

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; BCS THEORY; COUPLING CONSTANTS; CRITICAL FIELD; CRITICAL TEMPERATURE; ELECTRON-PHONON COUPLING; FORECASTING; GORKOV-ELIASHBERG THEORY; ORDER PARAMETERS; SPECIFIC HEAT; STRONG-COUPLING MODEL; SUPERCONDUCTIVITY; TEMPERATURE RANGE 0000-0013 K; THERMODYNAMICS; VANADIUM

### Citation Formats

```
Drzazga, E. A., E-mail: edrzazga@wip.pcz.pl, Domagalska, I. A., Jarosik, M. W., Szczȩśniak, R., and Kalaga, J. K..
```*Characteristics of Superconducting State in Vanadium: the Eliashberg Equations and Semi-analytical Formulas*. United States: N. p., 2018.
Web. doi:10.1007/S10948-017-4295-Y.

```
Drzazga, E. A., E-mail: edrzazga@wip.pcz.pl, Domagalska, I. A., Jarosik, M. W., Szczȩśniak, R., & Kalaga, J. K..
```*Characteristics of Superconducting State in Vanadium: the Eliashberg Equations and Semi-analytical Formulas*. United States. doi:10.1007/S10948-017-4295-Y.

```
Drzazga, E. A., E-mail: edrzazga@wip.pcz.pl, Domagalska, I. A., Jarosik, M. W., Szczȩśniak, R., and Kalaga, J. K.. Sun .
"Characteristics of Superconducting State in Vanadium: the Eliashberg Equations and Semi-analytical Formulas". United States. doi:10.1007/S10948-017-4295-Y.
```

```
@article{osti_22782486,
```

title = {Characteristics of Superconducting State in Vanadium: the Eliashberg Equations and Semi-analytical Formulas},

author = {Drzazga, E. A., E-mail: edrzazga@wip.pcz.pl and Domagalska, I. A. and Jarosik, M. W. and Szczȩśniak, R. and Kalaga, J. K.},

abstractNote = {The superconducting state in vanadium characterizes with the critical temperature (T{sub c}) equal to 5.3 K. The Coulomb pseudopotential, calculated with the help of the Eliashberg equations, possesses anomalously high value μ{sup ⋆}(3Ω{sub max}) = 0.259 or μ{sup ⋆}(10Ω{sub max}) = 0.368 (Ω{sub max} denotes the maximum phonon frequency). Despite the relatively large electron-phonon coupling constant (λ = 0.91), the quantities such as the order parameter (Δ), the specific heat (C), and the thermodynamic critical field (H{sub c}) determine the values of the dimensionless ratios not deviating much from the predictions of the BCS theory: R{sub Δ} = 2Δ(0)/k{sub B}T{sub c} = 3.68, R{sub C} = ΔC(T{sub c}) /C{sup N}(T{sub c}) = 1.69, and R{sub H}=T{sub c}C{sup N}(T{sub c})/H{sub c}{sup 2}(0)=0.171. This result is associated with the reduction of the strong-coupling and the retardation effects by the high value of the Coulomb pseudopotential. It has been shown that the results of the Eliashberg formalism can be relatively precisely reproduced with the help of the semi-analytical formulas, if the value of μ{sup ⋆} is determined on the basis of the T{sub c}-Allen-Dynes expression (μAD⋆ = 0.198). The attention should be paid to the fact that in the numerical and in the semi-analytical approach the comparable values of the thermodynamic parameters for the same μ{sup ⋆} have been obtained only in the vicinity of the point μ{sup ⋆} = 0.1.},

doi = {10.1007/S10948-017-4295-Y},

journal = {Journal of Superconductivity and Novel Magnetism},

issn = {1557-1939},

number = 4,

volume = 31,

place = {United States},

year = {2018},

month = {4}

}