This paper is directed to study the isotope effects of some superconducting materials that have a strong coupling coefficient λ > 1.5, and focuses on new superconducting materials whose critical temperature is close to room temperature, specifically LaH10-LaD10 and H3S-D3S systems. The Eliashberg-McMillan (EM) model and the recent Gor’kov-Kresin (GK) model for evaluating the isotope effects coefficient α were examined for these systems. The predicted values of α as a function of pressure, as compared to experimental values led to inference that these two models, despite their importance and simplicity, cannot be considered complete. These models can be used to calculate isotope effect of most superconducting materials with strong coupling coefficients but with critical reliability. The significance of studying the isotope effect lies in the possibility of identifying the interatomic forces that control the properties of superconducting materials such as electrons-mediated phonons and Coulomb interactions.
References
[1]
Onnes, H.K. (1911) The Superconductivity of Mercury. Commun. Phys. Lab. Univ, Leiden, Nos. 119, 120, 122.
[2]
Bendorz, J.G. and Müller, K.A. (1986) Possible High Tc Superconductivity in the Ba–La–Cu–O System. Zeitschrift fur Physik B Condensed Matter, 64, 189-193. https://doi.org/10.1007/BF01303701
[3]
Drozdov, A.P., Kong, P.P., Minkov, V.S., Besedin, S.P., Kuzovnikov, M.A., Mozaffari, S., et al. (2019) Superconductivity at 250K in Lanthanum Hydride under High Pressure. Nature, 569, 528-531. https://doi.org/10.1038/s41586-019-1201-8
[4]
Wigner, E. and Huntington, H.B. (1935) On the Possibility of a Metallic Modification of Hydrogen. Journal of Chemical Physics, 3, 764-770. https://doi.org/10.1063/1.1749590
[5]
McMahan, J.M. and Ceperley, D.M. (2011) Ground-State Structures of Atomic Metallic Hydrogen. Physical Review Letters, 106, Article ID: 165302.
[6]
Drozdov, A.P., Eremets, M.I., Troyan, I.A., Ksenofontov, V. and Shylin, S.I. (2015) Conventional Superconductivity at 203 K at High Pressures in the Sulfur Hydride System. Nature, 525, 73-76. https://doi.org/10.1038/nature14964
[7]
Duan, D., Liu, Y., Tian, F., Li, D., Huang, X., Zhao, Z., et al. (2014) Pressure-Induced Metallization of Dense (H2S)2H2 with High-Tc Superconductivity. Scientific Reports, 4, Article No. 6968. https://doi.org/10.1038/srep06968
[8]
Huang, W.M. and Lin, H.H. (2019) Anomalous Isotope Effect in Iron-Based Superconductors. Scientific Reports, 9, Article No. 5547. https://doi.org/10.1038/s41598-019-42041-z
[9]
Meissner, W. and Ochsenfeld, R. (1933) Ein neuer Effekt bei Eintritt der Supraleitfähigkeit. Naturwissenschaften, 21, 787-788. https://doi.org/10.1007/BF01504252
[10]
London, F. and London, H. (1935) The Electromagnetic Equations of the Superconductor. Proceedings of the Royal Society A, 149, 71-88.
[11]
Ginsburg, V.L. and Landau, L.D. (1950) On the Theory of Superconductivity. Sov. Phys. JETP, 20, Article No. 1064.
[12]
Barden, J., Cooper, L.N. and Schrieffer, J.R. (1957) Theory of Superconductivity. Physical Review Journals, 108, 1175-1204. https://doi.org/10.1103/PhysRev.108.1175
[13]
Snider, E., Dasenbrock-Gammon, N., McBride, R., Debessai, M., Vindana, H., Vencatasamy, K., et al. (2020) Room-Temperature Superconductivity in a Carbonaceous Sulfur Hydride. Nature, 586, 373-377. https://doi.org/10.1038/s41586-020-2801-z
[14]
Malik, M.A. and Malik, B.A. (2012) Isotope Effect as a Probe of the Role of Phonons in Conventional and High Temperature Superconductors. American Journal of Condensed Matter Physics, 2, 67-72. https://doi.org/10.5923/j.ajcmp.20120203.03
[15]
Rajagopalan, M., Selvamani, P., Vaitheeswaran, G., Kanchana, V. and Sundareswari, M. (2001) Calculation of Superconductivity Transition Temperature of MgB2. Solid State Communication, 120, 215-216. https://doi.org/10.1016/S0038-1098(01)00360-X
[16]
Huang, X.Q. (2011) Does the Isotope Effect of Mercury Support the BCS Theory? arXiv: 1102.1467v1.
[17]
Vora, A.M. (2008) Modified Transition Temperature Equationuation for Superconductors. Chinese Physics Letters, 25, 2162-2164.
[18]
Durajski, A.P., Szczęśniak, R., Li, Y., Wang, C. and Cho, J.-H. (2020) Isotope Effect in Superconducting Lanthanum Hydride under High Compression. Physical Review B, 101, Article ID: 214501. https://doi.org/10.1103/PhysRevB.101.214501
[19]
Eliashberg, G.M. (1960) Interactions between Electrons and Lattice Vibrations in a Superconductor. Soviet Physics—JETP, 11, 696-702.
[20]
Talantsev, E.F. (2020) Advanced McMillan’s Equationuation and Its Application for the Analysis of Highly-Compressed Superconductors. arXiv: 2002.12859.
[21]
McMillan, W.L. (1968) Transition Temperature of Strong-Coupled Superconductors. Physical Review, 167, 331-344. https://doi.org/10.1103/PhysRev.167.331
[22]
Dynes, R.C. (1972) McMillan’s Equationuation and the Tc of Superconductors. Solid State Communications, 10, 615-618. https://doi.org/10.1016/0038-1098(72)90603-5
[23]
Allen, P.B. and Dynes, R.C. (1975) Transition Temperature pf Strongly-Coupled Superconductors Reanalyzed. Physical Review B, 12, 905-922. https://doi.org/10.1103/PhysRevB.12.905
[24]
Gor’kov, L.P. and Kresin, V.Z. (2016) Pressure and High-Tc Superconductivity in Sulfur Hydrides. Scientific Reports, 6, Article No. 25608. https://doi.org/10.1038/srep25608
[25]
Struzhkin, V., et al. (2020) Superconductivity in La and Y Hydrides: Remaining Questions to Experiment and Theory. Matter and Radiation at Extremes, 5, Article ID: 028201. https://doi.org/10.1063/1.5128736
[26]
Liu, H., Naumov, I.I., Hoffmann, R., Ashcroft, N.W. and Hemley, R.J. (2017) Potential High-Tc Superconductivity Lanthanum and Yttrium Hydrides at High Pressure. Proceedings of the National Academy of Sciences of the United States of America, 114, 6990-6995. https://doi.org/10.1073/pnas.1704505114
[27]
Somazulu, M., Ahart, M., Mishra, A.K., Geballe, Z.M., Baldini, M., Meng, Y., et al. (2019) Evidence for Superconductivity above 260 K in Lanthanum Super Hydride at Megabar Pressure. Physical Review Letters, 122, Article ID: 027001. https://doi.org/10.1103/PhysRevLett.122.027001
[28]
Errea, I., Belli, F., Monacelli, L., Sanna, A., Koretsune, T., Tadano, T., et al. (2020) Quantum Crystal Structure in the 250 K Superconducting Lanthanum Hydride. Nature, 578, 66-69. https://doi.org/10.1038/s41586-020-1955-z
[29]
Einaga, M., Sakata, M., Ishikawa, T., Shimizu, K., Eremets, M., Drozdov, A., et al. (2016) Crystal Structure of the Superconducting Phase of Sulfur Hydride. Nature Physics, 12, 835-838. https://doi.org/10.1038/nphys3760
[30]
Huang, X., Wang, X., Duan, D., Sundqvist, B., Li, X., Huang, Y., et al. (2019) High-Temperature Superconductivity in Sulfur Hydride Evidenced by Alternating-Current Magnetic Susceptibility. National Science Review, 6, 713-718. https://doi.org/10.1093/nsr/nwz061
