Skip to main content
SpringerLink
Log in

Analytical assessment of some characteristic ratios for s-wave superconductors

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

We evaluate some thermodynamic quantities and characteristic ratios that describe low- and high-temperature s-wave superconducting systems. Based on a set of fundamental equations derived within the conformal transformation method, a simple model is proposed and studied analytically. After including a one-parameter class of fluctuations in the density of states, the mathematical structure of the s-wave superconducting gap, the free energy difference, and the specific heat difference is found and discussed in an analytic manner. Both the zero-temperature limit T = 0 and the subcritical temperature range T ≲ Tc are discussed using the method of successive approximations. The equation for the ratio R1, relating the zero-temperature energy gap and the critical temperature, is formulated and solved numerically for various values of the model parameter. Other thermodynamic quantities are analyzed, including a characteristic ratio R2, quantifying the dynamics of the specific heat jump at the critical temperature. It is shown that the obtained model results coincide with experimental data for low-Tc superconductors. The prospect of application of the presented model in studies of high-Tc superconductors and other superconducting systems of the new generation is also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, Iron-based layered superconductor La[O1-xFx]FeAs (x = 0:05–0:12) with Tc = 26 K, J. Am. Chem. Soc. 130(11), 3296 (2008)

    Article  Google Scholar 

  2. H. Hosono and K. Kuroki, Iron-based superconductors: Current status of materials and pairing mechanism, Physica C 514, 399 (2015)

    Article  ADS  Google Scholar 

  3. M. Krzyzosiak, R. Gonczarek, A. Gonczarek, and L. Jacak, Conformal Transformation Method in Studies of High-Tc Superconductors–Beyond the Van Hove Scenario in: Superconductivity and Superconducting Wires, Eds. D. Matteri and L. Futino, Nova Science Publishers, Hauppage, New York, 2010, Ch. 5

    Google Scholar 

  4. R. Gonczarek and M. Krzyzosiak, Model of Superconductivity in the Singular Fermi Liquid in: Progress in Superconductivity Research, Ed. O. A. Chang, Nova Science Publishers, Hauppage, New York, 2008, Ch. 6

    Google Scholar 

  5. R. Gonczarek and M. Krzyzosiak, Conformal transformation method and symmetry aspects of the group C4v in a model of high-Tc superconductors with anisotropic gap, Physica C 426(431), 278 (2005)

    Article  ADS  Google Scholar 

  6. R. Gonczarek, L. Jacak, M. Krzyzosiak, and A. Gonczarek, Competition mechanism between singlet and triplet superconductivity in the tight-binding model with anisotropic attractive potential, Eur. Phys. J. B 49(2), 171 (2006)

    Article  ADS  Google Scholar 

  7. R. Gonczarek, M. Krzyzosiak, L. Jacak, and A. Gonczarek, Coexistence of spin-singlet s- and d-wave and spin-triplet p-wave order parameters in anisotropic superconductors, phys. stat. sol. (b) 244, 3559 (2007)

    Article  ADS  Google Scholar 

  8. R. Gonczarek, M. Krzyzosiak, and A. Gonczarek, Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors, Eur. Phys. J. B 61(3), 299 (2008)

    Article  ADS  MATH  Google Scholar 

  9. D. Kasinathan, K. W. Lee, and W. E. Pickett, On heavy carbon doping of MgB2, Physica C 424(3–4), 116 (2005)

    Article  ADS  Google Scholar 

  10. J. Kortus, O. V. Dolgov, R. K. Kremer, and A. A. Golubov, Band filling and interband scattering effects in MgB2: Carbon versus aluminum doping, Phys. Rev. Lett. 94(2), 027002 (2005)

    Article  ADS  Google Scholar 

  11. W. S. Agrestini, C. Metallo, M. Filippi, L. Simonelli, G. Campi, C. Sanipoli, E. Liarokapis, S. De Negri, M. Giovannini, A. Saccone, A. Latini, and A. Bianconi, Substitution of Sc for Mg in MgB2: Effects on transition temperature and Kohn anomaly, Phys. Rev. B 70(13), 134514 (2004)

    Article  ADS  Google Scholar 

  12. H. Mori, T. Okano, M. Kamiya, M. Haemori, H. Suzuki, S. Tanaka, Y. Nishio, K. Kajita, and H. Moriyama, Bandwidth and band filling control in organic conductors, Physica C 357–360, 103 (2001)

    Article  Google Scholar 

  13. M. Mulak and R. Gonczarek, Structures of thermodynamic functions for S-paired fermi systems in parametric equations approach, Acta Phys. Pol. A 89(5–6), 689 (1996)

    Article  Google Scholar 

  14. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems, McGraw-Hill Book Company, 1971, §51

    Google Scholar 

  15. N. W. Ashcroft and N. D. Mermin, Solid State Physics, Holt, Rinehart and Winston, 1976, Ch. 34 Superconductivity

    Google Scholar 

  16. C. Kittel, Introduction to Solid State Physics, John Wiley and Sons, Inc. NY, 1966, Ch. 11

    MATH  Google Scholar 

  17. J. Spałek, Introduction to Condensed Matter Physics, Wydawnictwo Naukowe PWN SA, Warszawa, 2015, Ch. 17

    Google Scholar 

  18. H. Ibach and H. Lüth, Solid State Physics. An Introduction to Principles of Material Science, Berlin Heidelberg: Springer-Verlag, 1995, Ch. 10.5

    MATH  Google Scholar 

  19. M. Cyrot and D. Pavuna, Introduction to Superconductivity and High-Tc Materials, World Scientific Publ. Co. (London, New Jersey, Singapore, Hong Kong, Bangalore, Beijing, 1992), Ch. 7.1

    Book  Google Scholar 

  20. A. P. Durajski, R. Szczȩśniak, and Y. Li, Non-BCS thermodynamic properties of H2S superconductor, Physica C 515, 1 (2015)

    Article  ADS  Google Scholar 

  21. A. P. Durajski and R. Szczȩśniak, Estimation of the superconducting parameters for silane at high pressure, Mod. Phys. Lett. B 28(07), 1450052 (2014)

    Article  ADS  Google Scholar 

  22. R. Szczȩśniak, A. P. Durajski, M. W. Jarosik, Specific heat and thermodynamic critical field for calcium under the pressure at 120 GPa, Mod. Phys. Lett. B 26(08), 1250050 (2012)

    Article  ADS  MATH  Google Scholar 

  23. B. Lorenz, J. Cmaidalka, R. L. Meng, and C. W. Chu, Thermodynamic properties and pressure effect on the superconductivity in CaAlSi and SrAlSi, Phys. Rev. B 68(1), 014512 (2003)

    Article  ADS  Google Scholar 

  24. A. P. Durajski, Quantitative analysis of nonadiabatic effects in dense H3S and PH3 superconductors, Sci. Rep. 6(1), 38570 (2016)

    Article  ADS  Google Scholar 

  25. A. Drozdov, M. I. Eremets, I. A. Troyan, V. Ksenofontov, and S. I. Shylin, Conventional superconductivity at 203 kelvin at high pressures in the sulfur hydride system, Nature 525(7567), 73 (2015)

    Article  ADS  Google Scholar 

  26. M. Einaga, M. Sakata, T. Ishikawa, K. Shimizu, M. I. Eremets, A. P. Drozdov, I. A. Troyan, N. Hirao, and Y. Ohishi, Crystal structure of the superconducting phase of sulfur hydride, Nat. Phys. 12(9), 835 (2016)

    Article  Google Scholar 

  27. Y. Li, J. Hao, H. Liu, Y. Li, and Y. Ma, The metallization and superconductivity of dense hydrogen sulfide, J. Chem. Phys. 140(17), 174712 (2014)

    Article  ADS  Google Scholar 

  28. R. Gonczarek, M. Gładysiewicz, and M. Mulak, On possible formalism of anisotropic fermi liquid and BCS–type superconductivity, Int. J. Mod. Phys. B 15(05), 491 (2001)

    Article  ADS  Google Scholar 

  29. F. C. Zhang and T. M. Rice, Effective Hamiltonian for the superconducting Cu oxides, Phys. Rev. B 37(7), 3759 (1988)

    Article  ADS  Google Scholar 

  30. R. Szczȩśniak and A. P. Durajski, The thermodynamic properties of the high-pressure superconducting state in the hydrogen-rich compounds, Solid State Sci. 25, 45 (2013)

    Article  ADS  Google Scholar 

  31. R. Szczȩśniak and A. P. Durajski, Superconducting state above the boiling point of liquid nitrogen in the GaH3 compound, Supercond. Sci. Technol. 27(1), 015003 (2013)

    Article  Google Scholar 

  32. D. Y. Xing, M. Liu, Y. G. Wang, and J. Dong, Analytic approach to the antiferromagnetic van Hove singularity model for high-Tc superconductors, Phys. Rev. B 60(13), 9775 (1999)

    Article  ADS  Google Scholar 

  33. E. Pavarini, I. Dasgupta, T. Saha-Dasgupta, O. Jepsen, and O. K. Andersen, Band-structure trend in holedoped cuprates and correlation with Tc max, Phys. Rev. Lett. 87(4), 047003 (2001)

    Article  ADS  Google Scholar 

  34. O. K. Andersen, A. I. Liechtenstein, O. Jepsen, and F. Paulsen, LDA energy bands, low-energy hamiltonians, t′, t″, tΛ(k), and JΛ, J. Phys. Chem. Solids 56(12), 1573 (1995)

    Article  ADS  Google Scholar 

  35. O. K. Andersen, S. Y. Savrasov, O. Jepsen, and A. I. Liechtenstein, Out-of-plane instability and electronphonon contribution tos- and d-wave pairing in hightemperature superconductors; LDA linear-response calculation for doped CaCuO2 and a generic tight-binding model, J. Low Temp. Phys. 105(3–4), 285 (1996)

    Article  ADS  Google Scholar 

  36. R. Gonczarek and M. Krzyzosiak, Some universal relations between the gap and thermodynamic functions plausible for various models of superconductors, phys. stat. sol. (b) 238, 29 (2003)

    Article  ADS  Google Scholar 

  37. R. Szczȩśniak, A. P. Durajski, and L. Herok, Theoretical description of the SrPt3P superconductor in the strongcoupling limit, Phys. Scr. 89(12), 125701 (2014)

    Article  ADS  Google Scholar 

  38. R. Szczȩśniak and A. P. Durajski, The Energy Gap in the (Hg1-xSnx)Ba2Ca2Cu3O8+y Superconductor, Journal of Superconductivity and Novel Magnetism 27(6), 1363 (2014)

    Article  Google Scholar 

  39. R. Szczȩśniak and A. P. Durajski, Thermodynamics of the superconducting state in calcium at 200 GPa, Journal of Superconductivity and Novel Magnetism 25(2), 399 (2012)

    Article  Google Scholar 

  40. M. Krzyzosiak, R. Gonczarek, A. Gonczarek, and L. Jacak, Applications of the conformal transformation method in studies of composed superconducting systems, Front. Phys. 11(6), 117407 (2016)

    Article  MATH  Google Scholar 

  41. R. Baquero, D. Quesada, and C. Trallero-Giner, BCSuniversal ratios within the Van Hove scenario, Physica C 271(1–2), 122 (1996)

    Article  ADS  Google Scholar 

  42. M. Mulak and R. Gonczarek, Discontinuous phase transitions in S-paired Fermi systems, Acta Physica Polonica A 92, 1177 (1997)

    Article  Google Scholar 

  43. R. Gonczarek, M. Krzyzosiak, and M. Mulak, Valuation of characteristic ratios for high-Tc superconductors with anisotropic gap in the conformal transformation method, J. Phys. A 37(18), 4899 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. R. Gonczarek, M. Gładysiewicz, and M. Mulak, Equilibrium states and thermodynamical properties of d-wave paired HTSC in the tight-binding model, phys. stat. sol. (b) 233, 351 (2002)

    Article  ADS  Google Scholar 

  45. R. Gonczarek and M. Mulak, Enhancement of critical temperature of superconductors implied by the local fluctuation of EDOS, Phys. Lett. A 251(4), 262 (1999)

    Article  ADS  Google Scholar 

  46. J. Bouvier and J. Bok, The gap symmetry and fluctuations in high Tc superconductors, Eds. J. Bok, G. Deutscher, D. Pavuna, and S. Wolf, Plenum Press, New York, 1998, p. 37

    Google Scholar 

  47. R. Baquero, D. Quesada, and C. Trallero-Giner, BCSuniversal ratios within the Van Hove scenario, Physica C 271(1–2), 122 (1996)

    Article  ADS  Google Scholar 

  48. R. Gonczarek, M. Krzyzosiak, A. Gonczarek, and L. Jacak, New classes of integrals inherent in the mathematical structure of extended equations describing superconducting systems, Int. J. Mod. Phys. B 29(17), 1550117 (2015)

    Article  ADS  MATH  Google Scholar 

  49. R. Gonczarek, M. Krzyzosiak, A. Gonczarek, and L. Jacak, On new families of integrals in analytical studies of superconductors within the conformal transformation method, Adv. Condens. Matter Phys. 2015, 1 (2015)

    Article  MATH  Google Scholar 

  50. A. Bianconi and M. Filippi, Feshbach Shape Resonances in Multiband high Tc Superconductors in: Symmetry and Heterogeneity in High Temperature Superconductors, Ed. A. Bianconi, NATO Science Series (II): Mathematics, Physics and Chemistry- Vol. 2014, Springer 2006, Ch. 1.2

    Chapter  Google Scholar 

  51. J. K. Ren, X. B. Zhu, H. F. Yu, Y. Tian, H. F. Yang, C. Z. Gu, N. L. Wang, Y. F. Ren, and S. P. Zhao, Energy gaps in Bi2Sr2CaCu2O8+d cuprate superconductors, Sci. Rep. 2(1), 248 (2012)

    Article  ADS  Google Scholar 

  52. T. J. Reber, S. Parham, N. C. Plumb, Y. Cao, H. Li, Z. Sun, Q. Wang, H. Iwasawa, M. Arita, J. S. Wen, Z. J. Xu, G. D. Gu, Y. Yoshida, H. Eisaki, G. B. Arnold, and D. S. Dessau, Pairing, pair-breaking, and their roles in setting the Tc of cuprate high temperature superconductors, arXiv: 1508.06252v1 (2015)

    Google Scholar 

Download references

Acknowledgements

This research was supported by Ministry of Science and Higher Education (Poland) in 2017–2018.

Author information

Authors and Affiliations

  1. Faculty of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Ryszard Gonczarek & Lucjan Jacak

  2. University of Michigan–Shanghai Jiao Tong University Joint Institute, 800 Dongchuan Road, Shanghai, 200240, China

    Mateusz Krzyzosiak

  3. Faculty of Computer Science and Management, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Adam Gonczarek

Authors
  1. Ryszard Gonczarek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mateusz Krzyzosiak
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Adam Gonczarek
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Lucjan Jacak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mateusz Krzyzosiak.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gonczarek, R., Krzyzosiak, M., Gonczarek, A. et al. Analytical assessment of some characteristic ratios for s-wave superconductors. Front. Phys. 13, 137403 (2018). https://doi.org/10.1007/s11467-017-0739-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-017-0739-x

Keywords

Search

Navigation