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  • Letter
  • Open Access

Predicted superconductivity above 100 K in electride Li4Rh under high pressure

Zhiyao Guan1, Tian Cui1,2,*, and Da Li1,†

  • 1State Key Laboratory of High Pressure and Superhard Materials and Key Laboratory of Material Simulation Methods & Software of Ministry of Education, College of Physics, Jilin University, Changchun 130012, People's Republic of China
  • 2School of Physical Science and Technology, Ningbo University, Ningbo 315211, People's Republic of China

  • *Contact author: cuitian@nbu.edu.cn
  • †Contact author: dali@jlu.edu.cn

Phys. Rev. Research 7, L012077 – Published 21 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012077

Abstract

Although numerous high-pressure electride (HPE) superconductors have been reported, their superconducting transition temperatures (Tc) are low. No HPE superconductor with a Tc exceeding 100 K has been reported. Herein, we predicted a HPE superconductor, Li4Rh, with a high Tc=108.2 K at 300 GPa, making it the first HPE superconductor with a Tc exceeding 100 K. Li4Rh features strong hybridization between nonnuclear attractors (NNAs) and atoms near the Fermi level and a large, deformed cylindrical Fermi sheet. This Fermi sheet structure induces strong electron-phonon coupling (EPC) and allows a broad range of electrons and phonons with a wide range of q vectors to participate in EPC, resulting in high Tc. Unlike other HPE superconductors, the Tc of Li4Rh does not decrease with decreasing EPC but remains stable because the logarithmic average phonon frequency increases as the EPC strength decreases. This helps maintain Tc with increasing pressure with little fluctuation. The results indicate that HPEs with strong hybridization between NNAs and atoms near the Fermi level and with large and closed Fermi surfaces are more likely to exhibit high Tc, offering deep insights into HPE superconductivity and providing valuable guidance for future research into high-Tc electrides.

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References (58)

  1. J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, and J. Akimitsu, Superconductivity at 39 K in magnesium diboride, Nature (London) 410, 63 (2001).
  2. S. Kamal, R. Liang, A. Hosseini, D. A. Bonn, and W. N. Hardy, Magnetic penetration depth and surface resistance in ultrahigh-purity YBa2Cu3O7 crystals, Phys. Rev. B 58, R8933 (1998).
  3. U. Dionne, É. Bourgault, A. K. Dubé, D. Bradley, F. J. M. Chartier, R. Dandage, S. Dibyachintan, P. C. Després, G. D. Gish, N. T. H. Pham et al., Protein context shapes the specificity of SH3 domain-mediated interactions in vivo, Nat. Commun. 12, 1597 (2021).
  4. L. Ma, K. Wang, Y. Xie, X. Yang, Y. Wang, M. Zhou, H. Liu, X. Yu, Y. Zhao, H. Wang et al., High-temperature superconducting phase in clathrate calcium hydride CaH6 up to 215 K at a pressure of 172 GPa, Phys. Rev. Lett. 128, 167001 (2022).
  5. P. Bhattacharyya, W. Chen, X. Huang, S. Chatterjee, B. Huang, B. Kobrin, Y. Lyu, T. J. Smart, M. Block, E. Wang et al., Imaging the Meissner effect in hydride superconductors using quantum sensors, Nature (London) 627, 73 (2024).
  6. A. P. 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 (London) 525, 73 (2015).
  7. A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari, L. Balicas, F. F. Balakirev, D. E. Graf, V. B. Prakapenka et al., Superconductivity at 250 K in lanthanum hydride under high pressures, Nature (London) 569, 528 (2019).
  8. Z. Zhao, S. Zhang, T. Yu, H. Xu, A. Bergara, and G. Yang, Predicted pressure-induced superconducting transition in electride Li6P, Phys. Rev. Lett. 122, 097002 (2019).
  9. X.-L. He, W. Zhao, Y. Xie, A. Hermann, R. J. Hemley, H. Liu, and Y. Ma, Predicted hot superconductivity in LaSc2H24 under pressure, Proc. Natl. Acad. Sci. USA. 121, e2401840121 (2024).
  10. H. Wang, J. S. Tse, K. Tanaka, T. Iitaka, and Y. Ma, Superconductive sodalite-like clathrate calcium hydride at high pressures, Proc. Natl. Acad. Sci. USA. 109, 6463 (2012).
  11. M.-S. Miao and R. Hoffmann, High pressure electrides: A predictive chemical and physical theory, Acc. Chem. Res. 47, 1311 (2014).
  12. Y. Zhao, A. Bergara, X. Zhang, F. Li, Y. Liu, and G. Yang, Interstitial anionic electrons favoring superconductivity in Li-As electrides, Phys. Rev. B 108, 104505 (2023).
  13. Z. Guo, A. Bergara, X. Zhang, X. Li, S. Ding, and G. Yang, Superconductivity in Li8Hn electrides: The effect of interstitial anionic electrons on electron-phonon coupling, Phys. Rev. B 109, 134505 (2024).
  14. X. Zhang, Y. Zhao, A. Bergara, and G. Yang, Superconducting Li10Se electride under pressure, J. Chem. Phys. 156, 194112 (2022).
  15. X. Zhang, F. Li, A. Bergara, and G. Yang, Pressure-induced superconductivity in Li-Te electrides, Phys. Rev. B 104, 134505 (2021).
  16. X. Wang, Y. Wang, J. Wang, S. Pan, Q. Lu, H.-T. Wang, D. Xing, and J. Sun, Pressure stabilized lithium-aluminum compounds with both superconducting and superionic behaviors, Phys. Rev. Lett. 129, 246403 (2022).
  17. X. Zhang, Y. Yao, S. Ding, A. Bergara, F. Li, Y. Liu, X.-F. Zhou, and G. Yang, Superconductivity in Li8Au electride, Phys. Rev. B 107, L100501 (2023).
  18. Z. Wan, W. Xu, T. Yang, and R. Zhang, As-Li electrides under high pressure: Superconductivity, plastic, and superionic states, Phys. Rev. B 106, L060506 (2022).
  19. S. Shao, W. Zhu, J. Lv, Y. Wang, Y. Chen, and Y. Ma, The exotically stoichiometric compounds in Al–S system under high pressure, npj Comput. Mater. 6, 11 (2020).
  20. C. Kokail, C. Heil, and L. Boeri, Search for high- Tc conventional superconductivity at megabar pressures in the lithium-sulfur system, Phys. Rev. B 94, 060502(R) (2016).
  21. Z. Liu, D. Duan, Q. Zhuang, and T. Cui, High-temperature superconductivity in electrides dominated by hybridized p-orbital-like electride states, Phys. Rev. B 108, L100507 (2023).
  22. Q. Lu, C. Ding, Q. Jia, S. Pan, J. Shi, Y. Han, J. Wang, X. Wang, D. Xing, and J. Sun, Superconducting, plastic, and superionic states driven by four-membered lithium rings in a high-pressure lithium-lead compound, Phys. Rev. B 109, L180507 (2024).
  23. W. Xu, D. Yan, L. Zhu, Y. Wang, L. Kong, B. Yang, and B. Xu, Prediction of stable structure and unique charge transfer in Li–Pt intermetallic compounds under pressure, J. Mater. Res. Technol. 33, 3818 (2024).
  24. Y. Zhou, Q. Xu, C. Zhu, Q. Li, H. Liu, H. Wang, and J. S. Tse, Predicted lithium–iron compounds under high pressure, RSC Adv. 6, 66721 (2016).
  25. M. Jiang, Y. Tian, Y. Liang, X. Zhong, and H. Liu, The exotically stoichiometric compounds and superconductivity of lithium-copper systems under high pressure, J. Phys. Chem. Lett. 13, 9250 (2022).
  26. H. Liu, J. Wang, Q. Li, and C. Chen, Prediction of LinCd compounds with unusual stoichiometry and valence states, Phys. Rev. Mater. 4, 123604 (2020).
  27. Y. Wang, J. Lv, L. Zhu, and Y. Ma, Crystal structure prediction via particle-swarm optimization, Phys. Rev. B 82, 094116 (2010).
  28. X. Shao, J. Lv, P. Liu, S. Shao, P. Gao, H. Liu, Y. Wang, and Y. Ma, A symmetry-orientated divide-and-conquer method for crystal structure prediction, J. Chem. Phys. 156, 014105 (2022).
  29. A. R. Oganov and C. W. Glass, Crystal structure prediction using ab initio evolutionary techniques: Principles and applications, J. Chem. Phys. 124, 244704 (2006).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012077 for computational methods and details; crystal structures of predicted Li-Rh compounds; phonon dispersion spectrum of predicted structures at various pressures; electron localization function; Brillouin zone and Fermi surfaces; estimated Tc values of Li4Rh with various Coulomb pseudopotentials; distribution of λq; vibration modes; Fermi nesting function; phonon dispersion relationships, projected phonon density of states (PHDOS), Eliashberg spectral function α2F(ω), and EPC parameter; normalized quasiparticle density of states; λ of different frequency regions; electronic band structure and partial density of states, which also contains Refs. [52, 53, 54, 55, 56, 57, 58].
  31. R. C. Dynes, McMillan's equation and the Tc of superconductors, Solid State Commun. 10, 615 (1972).
  32. P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B 12, 905 (1975).
  33. G. Profeta, C. Franchini, N. N. Lathiotakis, A. Floris, A. Sanna, M. A. L. Marques, M. Lüders, S. Massidda, E. K. U. Gross, and A. Continenza, Superconductivity in lithium, potassium, and aluminum under extreme pressure: A first-principles study, Phys. Rev. Lett. 96, 047003 (2006).
  34. A. Sanna, C. Pellegrini, and E. K. U. Gross, Combining eliashberg theory with density functional theory for the accurate prediction of superconducting transition temperatures and gap functions, Phys. Rev. Lett. 125, 057001 (2020).
  35. M. Kawamura, Y. Hizume, and T. Ozaki, Benchmark of density functional theory for superconductors in elemental materials, Phys. Rev. B 101, 134511 (2020).
  36. B. Lv, X. Y. Zhu, B. Lorenz, F. Y. Wei, Y. Y. Xue, Z. P. Yin, G. Kotliar, and C. W. Chu, Superconductivity in the Mn5Si3-type Zr5Sb3 system, Phys. Rev. B 88, 134520 (2013).
  37. Y. Zhang, B. Wang, Z. Xiao, Y. Lu, T. Kamiya, Y. Uwatoko, H. Kageyama, and H. Hosono, Electride and superconductivity behaviors in Mn5Si3-type intermetallics, npj Quantum Mater. 2, 45 (2017).
  38. S. Dilmi, S. Saib, and N. Bouarissa, Band structure, electron-phonon interaction and superconductivity of yttrium hypocarbide, Curr. Appl Phys. 18, 1338 (2018).
  39. J. Zhang, G. Chen, and H. Liu, Stable structures and superconductivity in a Y-Si system under high pressure, J. Phys. Chem. Lett. 12, 10388 (2021).
  40. Q. Wang, W. Cui, K. Gao, J. Chen, T. Gu, M. Liu, J. Hao, J. Shi, and Y. Li, Pressure-stabilized superconducting electride Li5C, Phys. Rev. B 106, 054519 (2022).
  41. B. Sa, R. Xiong, C. Wen, Y.-L. Li, P. Lin, Q. Lin, M. Anpo, and Z. Sun, Electronic anisotropy and superconductivity in one-dimensional electride Ca3Si, J. Phys. Chem. C 124, 7683 (2020).
  42. X. Li, A. Hermann, F. Peng, J. Lv, Y. Wang, H. Wang, and Y. Ma, Stable lithium argon compounds under high pressure, Sci. Rep. 5, 16675 (2015).
  43. K. Zhao, Q. Wang, H. Li, B. Gao, S. Wei, L. Zhu, H. Xu, H. Liu, and S. Zhang, Superconductivity in dense scandium-based phosphides, Phys. Rev. B 108, 174513 (2023).
  44. K. Zhao, H. Yu, Q. Yang, W. Li, F. Han, H. Liu, and S. Zhang, Emerging yttrium phosphides with tetrahedron phosphorus and superconductivity under high pressures, Chem. Eur. J. 27, 17420 (2021).
  45. Z. Wan, C. Zhang, T. Yang, W. Xu, and R. Zhang, Predicted superconductivity and superionic state in the electride Li5N under high pressure, New J. Phys. 24, 113012 (2022).
  46. Z. Shao, D. Duan, L. Wang, H. Song, H. Yu, Y. Yao, and T. Cui, First-principles investigation of rhodium hydrides under high pressure, Phys. Rev. B 104, 054110 (2021).
  47. W. Kohn, Image of the Fermi surface in the vibration spectrum of a metal, Phys. Rev. Lett. 2, 393 (1959).
  48. S. Piscanec, M. Lazzeri, F. Mauri, A. C. Ferrari, and J. Robertson, Kohn anomalies and electron-phonon interactions in graphite, Phys. Rev. Lett. 93, 185503 (2004).
  49. Y. An, J. Chen, Z. Wang, J. Li, S. Gong, C. Ma, T. Wang, Z. Jiao, R. Wu, J. Hu et al., Topological and nodal superconductor kagome magnesium triboride, Phys. Rev. Mater. 7, 014205 (2023).
  50. T. G. Saunderson, J. F. Annett, B. Újfalussy, G. Csire, and M. Gradhand, Gap anisotropy in multiband superconductors based on multiple scattering theory, Phys. Rev. B 101, 064510 (2020).
  51. Z. Zhang, T. Cui, M. J. Hutcheon, A. M. Shipley, H. Song, M. Du, V. Z. Kresin, D. Duan, C. J. Pickard, and Y. Yao, Design principles for high-temperature superconductors with a hydrogen-based alloy backbone at moderate pressure, Phys. Rev. Lett. 128, 047001 (2022).
  52. V. Wang, N. Xu, J.-C. Liu, G. Tang, and W.-T. Geng, VASPKIT: A user-friendly interface facilitating high-throughput computing and analysis using vasp code, Comput. Phys. Commun. 267, 108033 (2021).
  53. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  54. G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
  55. M. Kawamura, FermiSurfer: Fermi-surface viewer providing multiple representation schemes, Comput. Phys. Commun. 239, 197 (2019).
  56. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo et al., quantum espresso: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
  57. P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
  58. M. G. Alex, S. Amy, J. Anubhav, and M. G. Sinéad, IFermi: A python library for Fermi surface generation and analysis, J. Open Source Softw. 6, 3089 (2021).

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