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High-TC Superconductivity in Hydrogen Clathrates Mediated by Coulomb Interactions Between Hydrogen and Central-Atom Electrons


The uniquely characteristic macrostructures of binary hydrogen-clathrate compounds MHn formed at high pressure, a cage of hydrogens surrounding a central-atom host, is theoretically predicted in various studies to include structurally stable phonon-mediated superconductors. High superconductive transition temperatures TC have thus far been measured for syntheses with M = La, Y, and Th. In compressed LaH10, independent studies report TC of 250 K and over 260 K, a maximum in TC with pressure P, and normal-state resistance scaling with temperature (suggesting unconventional pairing). According to reported band structure calculations of Fm\( \overline{3} \)m-phase LaH10, the La is anionic, with the chemical valence electrons appearing evenly split between La and H10. Thus, compressed LaH10 contains the combination of structure, charge separation, and optimal balanced allocation of valence electrons for supporting unconventional high-TC superconductivity mediated by Coulomb interactions between electronic charges associated with La and H10. A general expression for the optimal superconducting transition temperature for MHn clathrates is derived as TC0 = kB−1Λ[(n + v)/2A]1/2e2/ζ, where Λ is a universal constant, (n + v) is the chemical valence sum per formula unit, taking unity for H and v for atom M, A is the surface area of the H-polyhedron cage, and ζ is the mean distance between the M site and the centroids of the polyhedron faces. Applied to Fm\( \overline{3} \)m LaH10, TC0 values of  249.8(1.3) K and 260.7(2.0) K are found for the two experiments. Associated attributes of charge allocation, structure, effective Coulomb potential, and H-D isotope effect in TC of Fm\( \overline{3} \)m LaH10 and Im\( \overline{3} \)m H3S are discussed, along with a generalized prospective for Coulomb-mediated superconductivity in MHn.

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Fig. 1
Fig. 2


  1. 1.

    The layered FeH5, synthesized with no demonstration of superconductivity [32], is predicted to be superconducting in [33, 34] and non-superconducting in [35].

  2. 2.

    Note that here is a typographical error at the end of Section 3 (p. 5) of [41] which should read “ℓ = (A/σ)1/2 = 2.883 Å,” with the reported TC0 remaining unchanged.

  3. 3.

    Rule (1b) from [40] (see also [51]) reads that “The doping is shared equally between the hole and electron reservoirs, resulting in a factor of 1/2.”

  4. 4.

    Also presented in [16] are results of calculations for P63/mmc ThH9 from the Allen-Dynes formula extrapolated to 170 GPa, predicting TC of 125–147 K. For Fm\( \overline{3} \)m ThH10, the Allen-Dynes formula yields 160–193 K [10, 16].


  1. 1.

    Wang, H., Tse, J.S., Tanaka, K., Iitaka, T., Ma, Y.: Superconductive sodalite-like clathrate calcium hydride at high pressures. Proc. Nat. Acad. Sci. 109, 6463 (2012) Supplemental material

    ADS  Google Scholar 

  2. 2.

    Bi, T., Zarifi, N., Terpstra, T., Zurek, E.: The search for superconductivity in high pressure hydrides. In: Elsevier Reference Module in Chemistry, Molecular Sciences and Chemical Engineering. Reedijk, J. (ed), Elsevier (2019), pp. 1–36.

  3. 3.

    Zurek, E., Bi, T.: High-temperature superconductivity in alkaline and rare earth polyhydrides at high pressure: a theoretical perspective. J. Chem. Phys. 150, 050901 (2019)

    ADS  Google Scholar 

  4. 4.

    Flores-Livas, J.A., Boeri, L., Sanna, A., Profeta, G., Arita, R., Eremets, M.: A perspective on conventional high-temperature superconductors at high pressure: methods and materials. Phys. Rep. 856, 1 (2020)

    MathSciNet  ADS  Google Scholar 

  5. 5.

    Liu, H., Naumov, I.I., Hoffmann, R., Ashcroft, N.W., Hemley, R.J.: Potential high-TC superconducting lanthanum and yttrium hydrides at high pressure. Proc. Nat. Acad. Sci. 114, 6990 (2017)

    ADS  Google Scholar 

  6. 6.

    Peng, F., Sun, Y., Pickard, C.J., Needs, R.J., Wu, Q., Ma, Y.: Hydrogen clathrate structures in rare earth hydrides at high pressure: possible route to room-temperature superconductivity. Phys. Rev. Lett. 119, 107001 (2017) Supplemental material

    ADS  Google Scholar 

  7. 7.

    Li, Y., Hao, J., Liu, H., Tse, J.S., Wang, Y., Ma, Y.: Pressure-stabilized superconductive yttrium hydrides. Sci. Rep. 5, 09948 (2015)

    ADS  Google Scholar 

  8. 8.

    Heil, C., di Cataldo, S., Bachelet, G.B., Boeri, L.: Superconductivity in sodalite-like yttrium hydride clathrates. Phys. Rev. B. 99, 220502(R) (2019)

  9. 9.

    Grishakov, K.S., Degtyarenko, N.N., Mazur, E.A.: Electron, phonon, and superconducting properties of yttrium and sulfur hydrides under high pressures. J. Exp. Theor. Phys. 128, 105 (2019)

    ADS  Google Scholar 

  10. 10.

    Kvashnin, A.G., Semenok, D.V., Kruglov, I.A., Wrona, I.A., Oganov, A.R.: High-temperature superconductivity in a Th-H system under pressure conditions. ACS Appl. Mater. Interfaces. 10, 43809 (2018)

    Google Scholar 

  11. 11.

    Geballe, Z.M., Liu, H., Mishra, A.K., Ahart, M., Somayazulu, M., Meng, Y., Baldini, M., Hemley, R.J.: Synthesis and stability of lanthanum superhydrides. Angew. Chem. Int. Ed. 57, 688 (2018)

    Google Scholar 

  12. 12.

    Drozdov, A.P., Kong, P.P., Minkov, V.S., Besedin, S.P., Kuzovnikov, M.A., Mozaffari, S., Balicas, L., Balakirev, F.F., Graf, D.E., Prakapenka, V.B., Greenberg, E., Knyazev, D.A., Tkacz, M., Eremets, M.I.: Superconductivity at 250 K in lanthanum hydride under high pressures. Nature. 569, 528 (2019) Supplemental material

    ADS  Google Scholar 

  13. 13.

    Somayazulu, M., Ahart, M., Mishra, A.K., Geballe, Z.M., Baldini, M., Meng, Y., Struzhkin, V.V., Hemley, R.J.: Evidence of superconductivity above 260 K in lanthanum superhydride at megabar pressures. Phys. Rev. Lett. 122, 027001 (2019) Supplemental material

    ADS  Google Scholar 

  14. 14.

    Kong, P. P., Minkov, V. S., Kuzovnikov, M. A., Besedin, S. P., Drozdov, A. P., Mozaffari, S., Balicas, L., Balakirev, F. F., Prakapenka, V. B., Greenberg, E., Knyazev, D. A., Eremets, M. I.: Superconductivity up to 243 K in yttrium hydrides under high pressure. arXiv:1909.10482v1 [cond-mat.supr-con] (2019)

  15. 15.

    Troyan, I. A., Semenok, D. V., Kvashnin, A. G., Ivanova, A. G., Prakapenka, V. B., Greenberg, E., Gavriliuk, A. G., Lyubutin, I. S., Struzhkin, V. V., Oganov, A. R.: Synthesis and superconductivity of yttrium hexahydride Im\( \overline{3} \)m YH6. arXiv:1908.01534v1 [cond-mat.supr-con] (2019)

  16. 16.

    Semenok, D.V., Kvashnin, A.G., Ivanova, A.G., Svitlyk, V., Fominski, V.Y., Sadakov, A.V., Sobolevskiy, O.A., Pudalov, V.M., Troyan, I.A., Oganov, A.R.: Superconductivity at 161 K in thorium hydride ThH10: synthesis and properties. Materials Today. 33, 36 (2020) Supplemental material

    Google Scholar 

  17. 17.

    Éliashberg, G.M.: Interactions between electrons and lattice vibrations in a superconductor. Zh. Eksp. Teor. Fiz. 38, 966 (1960) [Sov. Phys. JETP. 11, 696 (1960)]

  18. 18.

    Migdal, A.B.: Interaction between electrons and lattice vibrations in a normal metal. Zh. Eksp. Teor. Fiz. 34, 1438 (1958) [Sov. Phys. JETP. 7, 996 (1958)]

  19. 19.

    Allen, P.B., Dynes, R.C.: Transition temperature of strong-coupled superconductors reanalyzed. Phys. Rev. B. 12, 905 (1975)

    ADS  Google Scholar 

  20. 20.

    Duan, D., Yu, H., Xie, H., Cui, T.: Ab initio approach and its impact on superconductivity. J. Supercond. Nov. Magn. 32, 53 (2019)

    Google Scholar 

  21. 21.

    Semenok, D.V., Kruglov, I.A., Savkin, I.A., Kvashnin, A.G., Oganov, A.R.: On distribution of superconductivity in metal hydrides. Curr. Opinion Sol. State & Mater. Sci. 24 100808 (2020)

  22. 22.

    Liu, L., Wang, C., Yi, S., Kim, K.W., Kim, J., Cho, J.-H.: Microscopic mechanism of room-temperature superconductivity in compressed LaH10. Phys. Rev. B. 99, 140501(R) (2019)

  23. 23.

    Kruglov, I.A., Semenok, D.V., Song, H., Szczęśniak, R., Wrona, I.A., Akashi, R., Esfahani, M.M.D., Duan, D., Cui, T., Kvashnin, A.G., Oganov, A.R.: Superconductivity in LaH10 and LaH16. Phys. Rev. B. 101, 024508 (2020) Supplemental material

    ADS  Google Scholar 

  24. 24.

    Wang, C., Yi, S., Cho, J.-H.: Pressure dependence of the superconducting transition temperature of compressed LaH10. Phys. Rev. B. 100, 060502(R) (2019)

  25. 25.

    Errea, I., Belli, F., Monacelli, L., Sanna, A., Koretsune, T., Tadano, T., Bianco, R., Calandra, M., Arita, R., Mauri, F., Flores-Livas, J.A.: Quantum crystal structure in the 250 K superconducting lanthanum hydride. Nature. 578, 66 (2020)

    ADS  Google Scholar 

  26. 26.

    Quan, Y., Ghosh, S.S., Pickett, W.E.: Compressed hydrides as metallic hydrogen superconductors. Phys. Rev. B. 100, 184505 (2019) Supplemental material

    ADS  Google Scholar 

  27. 27.

    Takabayashi, Y., Ganin, A.Y., Jeglič, P., Arčon, D., Takano, T., Iwasa, Y., Ohishi, Y., Takata, M., Takeshita, N., Prassides, K., Rosseinsky, M.J.: The disorder-free non-BCS superconductor Cs3C60 emerges from an antiferromagnetic insulator parent state. Science. 323, 1585 (2009)

    ADS  Google Scholar 

  28. 28.

    Hemley, R. J., Ahart, M., Liu, H., Somayazulu, M.: Road to room-temperature superconductivity: TC above 260 K in lanthanum superhydride under pressure. arXiv:1906.03462v1 [cond-mat.supr-con] (2019)

  29. 29.

    Struzhkin, V., Li, B., Ji, C., Chen, X.-J., Prakapenka, V., Greenberg, E., Troyan, I., Gavriliuk, A.: Mao, H-k.: Superconductivity in La and Y hydrides: remaining questions to experiment and theory. Matter Radiat. Extremes. 5, 028201 (2020)

  30. 30.

    Sun, D., Minkov, V. S., Kong, P., Drozdov, A., Mozaffari, S., Balicas, L., Eremets, M., Balakirev, F.: High field phase diagram of LaH10. Abstract M40.0004, APS March Meeting (2020)

  31. 31.

    Harshman, D.R., Mills Jr., A.P.: Concerning the nature of high-TC superconductivity: survey of experimental properties and implication for interlayer pairing. Phys. Rev. B. 45, 10684 (1992)

    ADS  Google Scholar 

  32. 32.

    Pépin, C.M., Geneste, G., Dewaele, A., Mezouar, M., Loubeyre, P.: Synthesis of FeH5: a layered structure with atomic hydrogen slabs. Science. 357, 382 (2017)

    ADS  Google Scholar 

  33. 33.

    Majumdar, A., Tse, J.S., Wu, M., Yao, Y.: Superconductivity in FeH5. Phys. Rev. B. 96, 201107(R) (2017)

  34. 34.

    Kvashnin, A.G., Kruglov, I.A., Semenok, D.V., Oganov, A.R.: Iron superhydrides FeH5 and FeH6: stability, electronic properties and superconductivity. J. Phys. Chem. C. 122, 4731 (2018)

    Google Scholar 

  35. 35.

    Heil, C., Bachelet, G.B., Boeri, L.: Absence of superconductivity in iron polyhydrides at high pressures. Phys. Rev. B. 97, 214510 (2018)

    ADS  Google Scholar 

  36. 36.

    Zurek, E.: Pushing towards room-temperature superconductivity. Physics. 12, 1 (2019)

    Google Scholar 

  37. 37.

    Kagan, M.Y., Bianconi, A.: Fermi-Bose mixtures and BCS-BEC crossover in high-TC superconductors. Condens. Matter. 4, 51 (2019)

    Google Scholar 

  38. 38.

    Otto, H.H.: Super-hydrides of lanthanum and yttrium: on optimal conditions for achieving near room temperature superconductivity. World J. Condens. Matter Phys. 9, 22 (2019)

    ADS  Google Scholar 

  39. 39.

    Talantsev, E.F.: Classifying hydrogen-rich superconductors. Mater. Res. Express. 6, 106002 (2019)

    ADS  Google Scholar 

  40. 40.

    Harshman, D.R., Fiory, A.T., Dow, J.D.: Theory of high-TC superconductivity: transition temperature. J. Phys. Condens. Matter. 23, 295701 (2011) Corrigendum: J. Phys. Condens. Matter 23, 349501 (2011)

  41. 41.

    Harshman, D.R., Fiory, A.T.: Compressed H3S: inter-sublattice Coulomb coupling in a high-TC superconductor. J. Phys. Condens. Matter. 29, 445702 (2017)

    ADS  Google Scholar 

  42. 42.

    Harshman, D.R., Fiory, A.T.: On the isotope effect in compressed H3S and D3S. Supercond. Sci. Technol. 30, 045011 (2017)

    ADS  Google Scholar 

  43. 43.

    Gurvitch, M., Fiory, A.T.: Resistivity of La1.825Sr0.175CuO4 and YBa2Cu3O7 to 1100 K: absence of saturation and its implications. Phys. Rev. Lett. 59, 1337 (1987)

    ADS  Google Scholar 

  44. 44.

    Legros, A., Benhabib, S., Tabis, W., Laliberté, F., Dion, M., Lizaire, M., Vignolle, B., Vignolles, D., Raffy, H., Li, Z.Z., Auban-Senzier, P., Doiron-Leyraud, N., Fournier, P., Colson, D., Taillefer, L., Proust, C.: Universal T-linear resistivity and Planckian dissipation in overdoped cuprates. Nature Phys. 15, 142 (2019)

    ADS  Google Scholar 

  45. 45.

    Zaanen, J.: Planckian dissipation, minimal viscosity and the transport in cuprate strange metals. SciPost Phys. 6, 061 (2019)

    MathSciNet  ADS  Google Scholar 

  46. 46.

    Kamarás, K., Herr, S.L., Porter, C.D., Tache, N., Tanner, D.B., Etemad, S., Venkatesan, T., Chase, E., Inam, A., Wu, X.D., Hegde, M.S., Dutta, B.: In a clean high-TC superconductor you do not see the gap. Phys. Rev. Lett. 64, 84 (1990) Erratum: Phys. Rev. Lett. 64, 1692 (1990)

  47. 47.

    Fiory, A.T., Hebard, A.F., Eick, R.H., Mankiewich, P.M., Howard, R.E., O’Malley, M.L.: Metallic and superconducting surfaces of YBa2Cu3O7 probed by electrostatic charge modulation of epitaxial films. Phys. Rev. Lett. 65, 3441 (1990)

    ADS  Google Scholar 

  48. 48.

    Romero, D.B., Porter, C.D., Tanner, D.B., Forro, L., Mandrus, D., Mihaly, L., Carr, G.L., Williams, G.P.: Quasiparticle damping in Bi2Sr2CaCu2O8 and Bi2Sr2CuO6. Phys. Rev. Lett. 68, 1590 (1992)

  49. 49.

    Harshman, D.R., Fiory, A.T.: High-TC superconductivity in Cs3C60 compounds governed by local Cs – C60 Coulomb interactions. J. Phys. Condens. Matter. 29, 145602 (2017)

    ADS  Google Scholar 

  50. 50.

    Harshman, D.R., Fiory, A.T.: Charge compensation and optimal stoichiometry in superconducting (CaxLa1–x)(Ba1.75–xLa0.25+x)Cu3Oy. Phys. Rev. B. 86, 144533 (2012)

  51. 51.

    Harshman, D.R., Fiory, A.T.: Superconducting interaction charge in thallium-based high-TC cuprates: roles of cation oxidation state and electronegativity. J. Phys. Chem. Sol. 85, 106 (2015)

    ADS  Google Scholar 

  52. 52.

    Harshman, D.R., Fiory, A.T.: The superconducting transition temperatures of Fe1+xSe1–y, Fe1+xSe1–yTey and (K/Rb/Cs)zFe2–xSe2. J. Phys. Condens. Matter. 24, 135701 (2012)

    ADS  Google Scholar 

  53. 53.

    Harshman, D.R., Fiory, A.T.: Comment on “superconductivity in electron-doped layered TiNCl with variable interlayer coupling”. Phys. Rev. B. 90, 186501 (2014)

    ADS  Google Scholar 

  54. 54.

    Harshman, D.R., Fiory, A.T.: Modeling intercalated group-4-metal nitride halide superconductivity with interlayer Coulomb coupling. J. Supercond. Nov. Magn. 28, 2967 (2015)

    Google Scholar 

  55. 55.

    Harshman, D.R., Fiory, A.T.: High-TC superconductivity originating from interlayer Coulomb coupling in gate-charged twisted bilayer graphene Moiré superlattices. J. Supercond. Nov. Magn. 33, 367 (2020)

  56. 56.

    Mozaffari, S., Sun, D., Minkov, V.S., Drozdov, A.P., Knyazev, D., Betts, J.B., Einaga, M., Shimizu, K., Eremets, M.I., Balicas, L., Balakirev, F.F.: Superconducting phase diagram of H3S under high magnetic fields. Nat. Commun. 10, 2522 (2019)

    ADS  Google Scholar 

  57. 57.

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

    ADS  Google Scholar 

  58. 58.

    Oh, H., Coh, S., Cohen, M. L.: Comparative study of high-TC superconductivity in H3S and H3P. arXiv:1606.09477v2 [cond-mat.supr-con] (2016)

  59. 59.

    Duan, D., Liu, Y., Tian, F., Li, D., Huang, X., Zhao, Z., Yu, H., Liu, B., Tian, W., Cui, T.: Pressure-induced metallization of dense (H2S)2H2 with high-TC superconductivity. Sci. Rep. 4, 6968 (2014)

    ADS  Google Scholar 

  60. 60.

    Papaconstantopoulos, D.A., Klein, B.M., Mehl, M.J., Pickett, W.E.: Cubic H3S around 200 GPa: an atomic hydrogen superconductor stabilized by sulfur. Phys. Rev. B. 91, 184511 (2015)

    ADS  Google Scholar 

  61. 61.

    Boeri, L., Bachelet, G.B.: Viewpoint: the road to room-temperature conventional superconductivity. J. Phys. Condens. Matter. 31, 234002 (2019)

    ADS  Google Scholar 

  62. 62.

    Salke, N.P., Esfahani, M.M.D., Zhang, Y., Kruglov, I.A., Zhou, J., Wang, Y., Greenberg, E., Prakapenka, V.B., Liu, J., Oganov, A.R., Lin, J.-F.: Synthesis of clathrate cerium superhydride CeH9 at 80-100 GPa with atomic hydrogen sublattice. Nat. Commun. 10, 4453 (2019)

    ADS  Google Scholar 

  63. 63.

    Zhou, D., Semenok, D.V., Duan, D., Xie, H., Chen, W., Huang, X., Li, X., Liu, B., Oganov, A.R., Cui, T.: Superconducting praseodymium superhydrides. Sci. Adv. 5, eaax6849 (2020)

    ADS  Google Scholar 

  64. 64.

    Kim, D.Y., Scheicher, R.H., Ahuja, R.: Predicted high-temperature superconducting state in the hydrogen-dense transition-metal hydride YH3 at 40 K and 17.7 GPa. Phys. Rev. Lett. 103, 077002 (2009)

  65. 65.

    Jarosik, M.W., Szczęśniak, R., Wrona, I.A., Kostrzewa, M.: Non-BCS superconducting state in yttrium hydride at a record low value of the external pressure. Sol. State Commun. 250, 5 (2017)

  66. 66.

    Ohmura, A., Machida, A., Watanuki, T., Aoki, K., Nakano, S., Takemura, K.: Infrared spectroscopic study of the band-gap closure in YH3 at high pressure. Phys. Rev. B. 73, 104105 (2006)

    ADS  Google Scholar 

  67. 67.

    Kume, T., Ohura, H., Sasaki, S., Shimizu, H., Ohmura, A., Machida, A., Watanuki, T., Aoki, K., Takemura, K.: High-pressure study of YH3 by Raman and visible absorption spectroscopy. Phys. Rev. B. 76, 024107 (2007)

    ADS  Google Scholar 

  68. 68.

    Soerensen, G., Gygax, S.: Evaluation of oxygen isotope experiments on Pr-, Ca-, and Zn-substituted YBa2Cu3O7. Phys. Rev. B. 51, 11848 (1995)

    ADS  Google Scholar 

  69. 69.

    Harshman, D.R., Dow, J.D., Fiory, A.T.: Isotope effect in high-TC superconductors. Phys. Rev. B. 77, 024523 (2008)

    ADS  Google Scholar 

  70. 70.

    Harshman, D.R., Dow, J.D., Fiory, A.T.: Reply to “comment on ‘isotope effect in high-TC superconductors’”. Phys. Rev. B. 80, 136502 (2009)

    ADS  Google Scholar 

  71. 71.

    Shao, Z., Duan, D., Ma, Y., Yu, H., Song, H., Xie, H., Li, D., Tian, F., Liu, B., Cui, T.: Unique phase diagram and superconductivity of calcium hydrides at high pressures. Inorg. Chem. 58, 2558 (2019)

    Google Scholar 

  72. 72.

    Qian, S., Sheng, X., Yan, X., Chen, Y., Song, B.: Theoretical study of stability and superconductivity of ScHn (n = 4–8) at high pressure. Phys. Rev. B. 96, 094513 (2017)

    ADS  Google Scholar 

  73. 73.

    Semenok, D., Kvashnin, A.G., Kruglov, I.A., Oganov, A.R.: Actinium hydrides AcH10, AcH12 and AcH16 as high-temperature conventional superconductors. J. Phys. Chem. Lett. 9, 1920 (2018)

    Google Scholar 

  74. 74.

    Li, X., Huang, X., Duan, D., Pickard, C.J., Zhou, D., Xie, H., Zhuang, Q., Huang, Y., Zhou, Q., Liu, B., Cui, T.: Polyhydride CeH9 with an atomic-like hydrogen clathrate structure. Nat. Commun. 10, 3461 (2019)

    ADS  Google Scholar 

  75. 75.

    Peña-Alvarez, M., Binns, J., Hermann, A., Kelsall, L.C., Dalladay-Simpson, P., Gregoryanz, E., Howie, R.T.: Praseodymium polyhydrides synthesized at high temperatures and pressures. Phys. Rev. B. 100, 184109 (2019)

  76. 76.

    Gor’kov, L.P., Kresin, V.Z.: Colloquium: high pressure and road to room temperature superconductivity. Rev. Mod. Phys. 90, 011001 (2018)

    MathSciNet  ADS  Google Scholar 

  77. 77.

    Baldassarre, L., Perucchi, A., Mitrano, M., Nicoletti, D., Marini, C., Pontiroli, D., Mazzani, M., Aramini, M., Riccó, M., Giovannetti, G., Capone, M., Lupi, S.: The strength of the electron electron correlation in Cs3C60. Sci. Rep. 5, 15240 (2015)

    ADS  Google Scholar 

  78. 78.

    Capitani, F., Langerome, B., Brubach, J.-B., Roy, P., Drozdov, A., Eremets, M.I., Nicol, E.J., Carbotte, J.P., Timusk, T.: Spectroscopic evidence of a new energy scale for superconductivity in H3S. Nat. Phys. 13, 859 (2017)

    Google Scholar 

  79. 79.

    Carbotte, J.P., Nicol, E.J., Timusk, T.: Spectroscopic signatures of phonons in high pressure superconducting hydrides. Phys. Rev. B. 100, 094505 (2019)

    ADS  Google Scholar 

  80. 80.

    Bill, A., Morawitz, H., Kresin, V.Z.: Electronic collective modes and superconductivity in layered conductors. Phys. Rev. B. 68, 144519 (2003)

    ADS  Google Scholar 

  81. 81.

    Shipley, A. M., Hutcheon, M. J., Johnson, M. S., Needs, R. J., Pickard, C. J.: Stability and superconductivity of lanthanum and yttrium decahydrides. arXiv:2001.05305v2 [cond-mat.supr-con] (2020)

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The authors are grateful for support from the College of William and Mary, New Jersey Institute of Technology, and the University of Notre Dame. We also acknowledge helpful information provided by Dr. F. Peng.


This study was supported by Physikon Research Corporation (Project No. PL-206) and the New Jersey Institute of Technology.

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Correspondence to Dale R. Harshman.

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The following appendix sections present and analyze results for the pressure variation in TC, normal-state resistance, pressure dependence of the lattice parameter, and accuracy and systematic error of the model, based on this work and published data.

A1 Pressure Variation in TC

A comprehensive plot of available experimental data [12, 13, 29] and theoretical results [4,5,6, 21,22,23,24,25,26] pertaining to the variation of TC with pressure P in LaH10 is presented in Fig. 3. Open circle symbols shown for P ∈ (140, 218) GPa and TC ∈ (243, 251) K are transcriptions of experimental data from Fig. 1 inset of [12] (error bars omitted for clarity). The arched trend in TC vs. P, noted in [12], comprises points with highest TC at 251.5 and 251.3 K (error bars ± 1 K) corresponding to P at 166 and 172 GPa (± 2 GPa), respectively (data for sample 5 in [12]). Taking rounded averages and uncertainties, the values 251(1) K and 169(4) GPa thus determine the experimentally measured optimal TC and P, respectively, shown in the first row of Table 1.

Fig. 3

Plot of transition temperature TC vs. pressure P for Fm\( \overline{3} \)m LaH10 (marked with source references). Larger green symbols denote experimental data from [12, 13, 29]; smaller blue symbols and connecting lines represent theoretical results from [4,5,6, 21,22,23,24,25,26]. Magenta star symbols are at TC0 and P as given in Table 1

Although experimental measurements of TC are not specified in [13], full superconducting resistance transition curves for cooling and warming of sample A are presented in Fig. 3 therein. Onset values of TC are determined herein to about ± 1 K uncertainty from the intersection of tangents drawn through the linear-in-T normal-state region (see Section A2) and the more steeply sloped region just below the transition onset. This method yields TC of 262(1) and 247(1) K for cooling and warming, respectively, and is shown as the filled square symbols in Fig. 3, where horizontal error bars span the pressures of 188 and 196 GPa associated with the data (i.e., P = 192 ± 4 GPa). The higher TC for cooling is assumed to be closer to optimal and therefore entered in the second row of Table 1. Coincidentally, Fig. 3 shows by way of comparison that the onset TC for warming lies in the region of the lower TC observed in the data from [12] (sample 6 therein). Other resistance-vs.-temperature data in [13] show resistance drops suggesting onsets of superconducting behavior (full transitions not displayed). Figure 4 in [13] shows a resistance drop at 280 K for 0.1 mA applied current and 195 GPa pressure for sample F. Figure S4 in [13] shows drops at 257, 282, and 276 K for pressures of 190, 195, and 202 GPa, respectively, for sample B. Additionally, a small jump at 240 K (at assumed 179 GPa) is described for sample G [13]. The five open square symbols in Fig. 3 represent these other temperatures and pressures drawn from [13]. Cross symbols represent data from Fig. 10 of [29].

Fig. 4

Distributions of experimental and theoretical results for TC of Fm\( \overline{3} \)m LaH10, as presented in Fig. 3 and Table 1. Normalized histograms show distributions in TC from experiments (solid green) and phonon theories (dashed blue). Vertical pink bars denote TC0 presented in Table 1 (bar width denotes uncertainty)

Small symbols in Fig. 3 display results of theoretical calculations of TC for LaH10 from strong electron-phonon coupling based on Migdal-Éliashberg theory, density functional theory, or ab initio methods (labels distinguish the source references [4,5,6, 21,22,23,24,25,26], exclusive of ranges in theoretical stability study of [81]). Results calculated at multiple values of P, connected by broken lines, show that the electron-phonon mechanism reproducibly predicts that TC has a monotonically decreasing dependence on P with average slope ΔTCP ≈ − 0.30 ± 0.08 K/GPa [5, 23,24,25,26], a finding with theoretical basis [26]. The dotted line in Fig. 3 illustrates the linear extrapolation from the calculated point (diamond symbol) to the range of experimental pressure that is used in [22]. Superconducting density functional theory (SCDFT), as applied in [23], predicts TC = 271 K at P = 200 GPa, whereas SCDFT applied in [25] predicts a much lower TC = 214 K (interpolated to P = 200 GPa).

The magenta star symbols in Fig. 3 are the results for TC0 given in Table 1 at the values of P indicated. These two points define a positive change ΔTCP = + 0.47 K/GPa, in contrast to negative variations predicted in electron-phonon theory [5, 22, 24,25,26].

The distributions of the TC values from Fig. 3 are cast in Fig. 4 in the form of histograms corresponding to the experiments (solid green) and phonon theories (dashed blue) normalized to the number of points (30 and 27, respectively), and with bin sizes of 5 K and 10 K, respectively. Statistical averages and ± standard deviations of the distributions are as follows: TC = 251 ± 10 K (experiments) and 245 ± 26 K (phonon theories); P = 174 ± 27 GPa (experiments) and 232 ± 52 GPa (phonon theories). Theoretical pressure dependence suggests shifting the statistical average for the phonon theories as TC = 263 ± 29 K at P → 174 GPa. Pre-experimental theories include predictions of 274 and 286 K at 210 GPa in [5] and 288 K at 200 GPa in [6], which may be compared with resistance drops [13] or magnetic onsets [29] at temperatures of 276–283 K and pressures of 185–202 GPa, and represented by the smaller histogram fragment in Fig. 4. The two pink vertical bars (and widths) in Fig. 4 represent the values of TC0 (and uncertainties) given in Table 1.

Figure 5 is a comprehensive plot of TC vs. P for YH6 (circle symbols) and YH9 (square symbols) where the larger green circles and squares denote experimental data in [14, 15]. The smaller blue circles and filled squares denote theoretical results for YH6 [6,7,8,9, 14] and YH9 [6], respectively. Asterisk symbols in the legend express the caveat that phases other than those indicated are determined from X-ray data analysis (e.g., YH4) [14]. Statistical averages and ± standard deviations of samples identified as YH6 in [14, 15] are TC = 219 ± 5 K and P = 188 ± 28 GPa; statistics for the YH6 phonon theories are TC = 245 ± 47 K and P = 176 ± 75 GPa. The “dome” trend in TC vs. P for YH9 with maximum TC = 243 K at P = 201 GPa is noted in [14] (filled symbols, before change in P; open symbols, after change in P); phonon theory predicts TC = 253–287 at P = 150 GPa [6].

Fig. 5

Plot of transition temperature TC vs. pressure P for Im\( \overline{3} \)m YH6 and P63/mmc YH9 (marked with source references), denoted by circular and square symbols, respectively. Larger green symbols denote experimental data [14, 15]; smaller blue symbols and connecting lines represent phonon theories [6,7,8,9, 15]

A2 Normal-State Resistance

Unique features signifying unconventional high-TC superconductivity are a linear temperature dependence in the normal-state resistivity, ρN(T) ∝ T, and the absence of saturation at high temperature, such that the negative curvature of ρN(T) for conventional strong electron-phonon coupled metals is absent [43]. Such unconventional behavior in ρN(T), observed in optimally and overdoped high-TC cuprates, is ascribed generally to “Planckian” dissipation phenomena [44, 45]. Superconducting LaH10 and YH9 are exemplary of this behavior for T > TC, as can be seen in Fig. 6 showing resistance vs. temperature for (a) Fm\( \overline{3} \)m LaH10 sample 3 from Fig. 1 of [12] (blue curve, P = 150 GPa, TC ~ 249 K) and (b) P63/mmc YH9 sample 2 from Fig. 1a of [14] (red curve, P = 201 GPa, TC = 243 K). Dotted lines illustrate linear dependence for T > TC extrapolating to the origin. Resistance of LaH10 sample A in [13] (Fig. 3 therein, cooling curve) and Im\( \overline{3} \)m YH6 sample M1 in [15] are also consistent with normal-state linearity in T. Table 3 summarizes normalized normal-state slopes obtained from the temperature dependence of the resistance RN(T) reported for various samples of La, Y, and Th superhydrides and H3S, defined as S = [TC/RN(TC)] (ΔRNT) in terms of slope ΔRNT taken asymptotically above TC and RN(TC) as extrapolated to TC. Resistance in applied magnetic fields, which depress the superconducting transition, shows linear-in-T extending to T < TC; S = 0.91 at 9 Tesla is obtained for sample 3 from Fig. 2(a) in [12], and extension to above 60 Tesla is reported in [30]. Extrapolated residual resistance ratio is given by RN(0)/RN(TC) = 1 – S. The statistical distribution in S with bin size 0.25 is shown in Fig. 7 (from Table 3 and near unity S assumed from [30]), indicating that highest probability occurs at S ≈ 1. Ideally, S approaches unity for (unconventional) optimal high-TC superconductors.

Fig. 6

Resistance vs. temperature for (a) Fm\( \overline{3} \)m LaH10 sample 3 from Fig. 1 of [12] (blue curve) and (b) P63/mmc YH9 sample 2 from Fig. 1(a) of [14] (red curve). Dotted lines show extrapolations of normal-state resistance to the origin

Fig. 7

Statistical distribution of data for normalized normal-state resistance temperature slope parameter S from Table 3

Dissipation from inelastic electron scattering in the normal state is determined from the scattering rate formula τN−1 = ρNe2n/m, written in terms of density n and mass m of the carriers. An estimated ρN ~ 10−5 Ω cm at T ≈ 285 K is calculated for sample F in [13] from measured resistance ≈ 0.11 mΩ at 0.1 mA indicated in Fig. 4, thickness ~ 2 μm mentioned in the supplemental material of [13], and an assumed Van der Pauw factor of 4.53. Carrier density n is obtained from the charge fraction σ = 6.5 associated with H10 (6.5e per formula unit volume); m is derived from theoretical superconducting parameters as m = ħkF/vF = ħ2kF/πΔξ with theoretical gap Δ = 2.3 kBTC [22] and experimental coherence distance ξ = 1.7 nm (average determined in [12]); Fermi wave vector is determined as kF = (3π2n/g)1/3 with g = 2 (approximating the theoretical Fermi surface in [22] as two equal-area spheres). The Planckian dissipation energy evaluates to ħτN−1 ~ 4kBT from the above data for LaH10. Acknowledging that this analysis provides only a single order of magnitude estimation, the dissipation may be considered as similar to (1.3–2.3)kBT determined for optimal cuprate superconductors [46,47,48]. While conventional theory of strong electron-phonon scattering might mimic linearity for T between TC and 300 K, if designed with judicious choices of residual and saturation resistivities, it appears rather implausible in view of the preponderance of S ≈ 1 listed in Table 3 and displayed in Fig. 7.

A3 Pressure Dependence of the Lattice Parameter

X-ray diffraction is employed to determine volumes of LaH10 referenced to the fcc cubic cell for samples 2 and 3 in [12] and referenced per La for superconducting samples A–C and E–G in [13]. Samples 2 and 3 are reported to contain minority phase material [12]. Samples F and G are described as mixed phase [13]. Pressure dependence in the fcc lattice parameter a are plotted in Fig. 8 as filled circles (data from [12]) and filled squares ([13]). Square symbols inscribed with a white cross correspond to samples C and E for which no information on transition temperature is provided in [13]. The straight line is a linear fit (exclusive of the two white-crossed squares) to the relation a = a0 − sP with intercept a0 = 5.78 ± 0.15 Å, slope s = 0.00459 ± 0.000091 Å/GPa, and root-mean-square deviation of 0.043 Å between the data and the line. The fitted function is used to extract values of a, and therefrom d, A, ζ, ℓ, and TC0, at experimental optimal pressures (Table 1).

Fig. 8

Lattice parameter (face centered cubic) vs. pressure for Fm\( \overline{3} \)m LaH10 from X-ray data in [12] (circles) and [13] (squares). The solid line shows the linear dependence obtained by fitting the data exclusive of the two white-crossed squares (see text)

A4 Accuracy and Systematic Error of the Model

The accuracy of Eq. (1) rests on that of the constant Λ, which was originally obtained by fitting Λ in the right-hand side expression to experimental data for TC0 taken for the left-hand side. The fitted data included 31 phase-pure, optimal high-TC compounds, with superconducting transitions in the range 10.5 K ≤ TC ≤ 145 K [40]. Subsequently, 24 other compounds (see [41, 49,50,51,52,53,54,55]), optimized according to the developed criteria and inclusive of the two LaH10 samples, have been added to the list of optimal superconductors with TC values demonstrated to be in congruence with Eq. (1), bringing the total number to 55 from eleven disparate superconducting families (with TC ranging from ~ 2 to 260 K). Comparisons of TC0 calculated for LaH10 at 169(4) GPa [12] and at 192(4) GPa [13] with the measured average TC values (from Table 1) yield differential accuracies of 0.48% and 0.50%, respectively. The optimal transition temperatures are predicted with an overall statistical accuracy of ± 4.3% over a range in TC from ~ 2 to 260 K, with an average fractional deviation of 0.7%. These results are graphically represented in Fig. 9, which plots the measured optimal transition temperature TC vs. (ℓζ)−1, and compared with the theoretical expression for TC0 given in Eq. (1) represented by the solid line. Deviations of TC from the theoretical line have a root-mean-square average of 1.3 K. The statistical distribution of fractional deviation between calculated TC0 and measured TC is given in the inset of Fig. 9, where the dashed curve shows the fitted Gaussian form.

Fig. 9

Optimal measured transition temperatures TC vs. (ℓζ)−1 for 55 superconductors (grouped as per legend) are shown in comparison with calculated TC0 (solid line). Inset: statistical distribution of fractional deviation between calculated TC0 and measured TC; dashed curve shows fitted Gaussian form

Nearly abrupt superconducting transitions are also predicted theoretically for the hydrides LaH10 and H3S, by virtue of their being three-dimensional bulk crystals. One might assume that improved synthesis of the hydride samples would lead to sharper transitions, reduced uncertainty in determining TC and, in turn, the value of Λ.

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Harshman, D.R., Fiory, A.T. High-TC Superconductivity in Hydrogen Clathrates Mediated by Coulomb Interactions Between Hydrogen and Central-Atom Electrons. J Supercond Nov Magn 33, 2945–2961 (2020).

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  • LaH10
  • Superhydrides
  • Superconductivity
  • T C
  • Coulomb mediation