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Superconducting properties of transition metal dichalcogenides in proximity to a conventional superconductor

Florian Kayatz1,2,*, Annica M. Black-Schaffer1,2, and Jorge Cayao1

  • 1Department of Physics and Astronomy, Uppsala University, Box 524, SE-751 20 Uppsala, Sweden
  • 2Wallenberg Initiative Materials Science for Sustainability, Uppsala University, SE-751 20 Uppsala, Sweden

  • *Contact author: florian.kayatz@physics.uu.se
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Phys. Rev. B 114, 194510 – Published 14 October, 2026

DOI: https://doi.org/10.1103/2kt6-vmbf

Abstract

Transition metal dichalcogenides (TMDs) hold relevance for spin-triplet superconducting phases due to their inherent Ising spin-orbit coupling, but the majority of studies have so far focused on oversimplified models. In this work, we consider a TMD monolayer using a three-orbital model with anisotropic couplings and investigate the emergent superconducting properties when it is placed in proximity to a conventional spin-singlet s-wave superconductor. We find that the multiorbital nature of the TMDs lead to superconducting gaps not only at zero energy but also at higher energies, so-called hybridization gaps, which exhibit a complex structure due to the anisotropic couplings, challenging their spectral measurement. Moreover, we find that the inherent Ising spin-orbit coupling induces a spin splitting and a spin polarization along the z direction, which correlates with the emergence of mixed spin-triplet superconducting pairs. These spin-triplet pair correlations appear in the monolayer as a proximity-induced effect due to the impact of the Ising spin-orbit field on conventional spin-singlet s-wave superconductivity. Taking realistic parameters for a MoS2 monolayer, we show that the Ising field is strong enough to induce spin-triplet pair correlations of the same magnitude as their spin-singlet counterparts. We also include Rashba spin-orbit coupling, naturally emerging in a heterostructure and find that it induces equal spin-triplet superconducting pairs that compete with the mixed spin-triplet pairs induced by the Ising spin-orbit coupling. Our findings help understand the superconducting properties of TMDs in proximity to conventional superconductors.

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References (89)

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, Science 306, 666 (2004).
  2. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature (London) 438, 197 (2005).
  3. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry's phase in graphene, Nature (London) 438, 201 (2005).
  4. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Two-dimensional atomic crystals, Proc. Natl. Acad. Sci. USA 102, 10451 (2005).
  5. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Electronics and optoelectronics of two-dimensional transition metal dichalcogenides, Nat. Nanotechnol. 7, 699 (2012).
  6. J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2D materials, Nat. Rev. Mat. 1, 16055 (2016).
  7. E. C. Ahn, 2D materials for spintronic devices, npj 2D Mater. Appl. 4, 17 (2020).
  8. Z. Y. Zhu, Y. C. Cheng, and U. Schwingenschlögl, Giant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors, Phys. Rev. B 84, 153402 (2011).
  9. P. A. Frigeri, D. F. Agterberg, and M. Sigrist, Spin susceptibility in superconductors without inversion symmetry, New J. Phys. 6, 115 (2004).
  10. B. T. Zhou, K. Taguchi, Y. Kawaguchi, Y. Tanaka, and K. T. Law, Spin-orbit coupling induced valley Hall effects in transition-metal dichalcogenides, Commun. Phys. 2, 26 (2019).
  11. G. Tang, C. Bruder, and W. Belzig, Magnetic field-induced “mirage” gap in an Ising superconductor, Phys. Rev. Lett. 126, 237001 (2021).
  12. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides, Phys. Rev. Lett. 108, 196802 (2012).
  13. R. F. Frindt, Superconductivity in ultrathin NbSe2 layers, Phys. Rev. Lett. 28, 299 (1972).
  14. X. Xi, L. Zhao, Z. Wang, H. Berger, L. Forró, J. Shan, and K. F. Mak, Strongly enhanced charge-density-wave order in monolayer NbSe2, Nat. Nanotechnol. 10, 765 (2015).
  15. X. Xi, Z. Wang, W. Zhao, J.-H. Park, K. T. Law, H. Berger, L. Forró, J. Shan, and K. F. Mak, Ising pairing in superconducting NbSe2 atomic layers, Nat. Phys. 12, 139 (2016).
  16. S. C. de la Barrera, M. R. Sinko, D. P. Gopalan, N. Sivadas, K. L. Seyler, K. Watanabe, T. Taniguchi, A. W. Tsen, X. Xu, D. Xiao, and B. M. Hunt, Tuning Ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalcogenides, Nat. Commun. 9, 1427 (2018).
  17. J. M. Lu, O. Zheliuk, I. Leermakers, N. F. Q. Yuan, U. Zeitler, K. T. Law, and J. T. Ye, Evidence for two-dimensional Ising superconductivity in gated MoS2, Science 350, 1353 (2015).
  18. Y. Saito, Y. Nakamura, M. S. Bahramy, Y. Kohama, J. Ye, Y. Kasahara, Y. Nakagawa, M. Onga, M. Tokunaga, T. Nojima, Y. Yanase, and Y. Iwasa, Superconductivity protected by spin–valley locking in ion-gated MoS2, Nat. Phys. 12, 144 (2016).
  19. A. M. Clogston, Upper limit for the critical field in hard superconductors, Phys. Rev. Lett. 9, 266 (1962).
  20. B. S. Chandrasekhar, A note on the maximum critical field of high-field superconductors, Appl. Phys. Lett. 1, 7 (1962).
  21. M. Smidman, M. B. Salamon, H. Q. Yuan, and D. F. Agterberg, Superconductivity and spin-orbit coupling in non-centrosymmetric materials: A review, Rep. Prog. Phys. 80, 036501 (2017).
  22. E. Bauer and M. Sigrist, Non-Centrosymmetric Superconductors: Introduction and Overview (Springer, Berlin, 2012).
  23. D. Möckli and M. Khodas, Ising superconductors: Interplay of magnetic field, triplet channels, and disorder, Phys. Rev. B 101, 014510 (2020).
  24. D. Wickramaratne, S. Khmelevskyi, D. F. Agterberg, and I. I. Mazin, Ising superconductivity and magnetism in NbSe2, Phys. Rev. X 10, 041003 (2020).
  25. D. Wickramaratne, M. Haim, M. Khodas, and I. I. Mazin, Magnetism-driven unconventional effects in Ising superconductors: Role of proximity, tunneling, and nematicity, Phys. Rev. B 104, L060501 (2021).
  26. D. Wickramaratne and I. I. Mazin, Ising superconductivity: A first-principles perspective, Appl. Phys. Lett. 122, 240503 (2023).
  27. J. Siegl, A. Bleibaum, W. Wan, M. Kurpas, J. Schliemann, M. M. Ugeda, M. Marganska, and M. Grifoni, Friedel oscillations and chiral superconductivity in monolayer NbSe2, Nat. Commun. 16, 8228 (2025).
  28. T. Sohier, M. Gibertini, I. Martin, and A. F. Morpurgo, Unconventional gate-induced superconductivity in transition-metal dichalcogenides, Phys. Rev. Res. 7, 013290 (2025).
  29. D. Möckli and M. Khodas, Robust parity-mixed superconductivity in disordered monolayer transition metal dichalcogenides, Phys. Rev. B 98, 144518 (2018).
  30. D. Shaffer, J. Kang, F. J. Burnell, and R. M. Fernandes, Crystalline nodal topological superconductivity and Bogolyubov Fermi surfaces in monolayer NbSe2, Phys. Rev. B 101, 224503 (2020).
  31. D. Möckli and M. Khodas, Magnetic-field induced s+if pairing in Ising superconductors, Phys. Rev. B 99, 180505(R) (2019).
  32. Y.-T. Hsu, A. Vaezi, M. H. Fischer, and E.-A. Kim, Topological superconductivity in monolayer transition metal dichalcogenides, Nat. Commun. 8, 14985 (2017).
  33. S. Das, H. Paudyal, E. R. Margine, D. F. Agterberg, and I. I. Mazin, Electron-phonon coupling and spin fluctuations in the Ising superconductor NbSe2, npj Comput. Mater. 9, 66 (2023).
  34. S. Roy, A. Kreisel, B. M. Andersen, and S. Mukherjee, Unconventional superconductivity in monolayer transition metal dichalcogenides, Phys. Rev. B 113, 014506 (2026).
  35. R. Holm and W. Meissner, Messungen mit Hilfe von flüssigem Helium. XIII, Z. Phys. 74, 715 (1932).
  36. A. I. Buzdin, Proximity effects in superconductor-ferromagnet heterostructures, Rev. Mod. Phys. 77, 935 (2005).
  37. F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Odd triplet superconductivity and related phenomena in superconductor-ferromagnet structures, Rev. Mod. Phys. 77, 1321 (2005).
  38. Y. Tanaka, M. Sato, and N. Nagaosa, Symmetry and topology in superconductors–odd-frequency pairing and edge states–, J. Phys. Soc. Jpn. 81, 011013 (2012).
  39. J. Cayao, C. Triola, and A. M. Black-Schaffer, Odd-frequency superconducting pairing in one-dimensional systems, Eur. Phys. J. Spec. Top. 229, 545 (2020).
  40. G. A. Bobkov, K. A. Bokai, M. M. Otrokov, A. M. Bobkov, and I. V. Bobkova, Gate-controlled proximity effect in superconductor/ferromagnet van der Waals heterostructures, Phys. Rev. Mater. 8, 104801 (2024).
  41. D. J. Trainer, B. Wang, F. Bobba, N. Samuelson, X. Xi, J. Zasadzinski, J. Nieminen, A. Bansil, and M. Iavarone, Proximity-induced superconductivity in monolayer MoS2, ACS Nano 14, 2718 (2020).
  42. G. Xu, J. Wang, B. Yan, and X.-L. Qi, Topological superconductivity at the edge of transition-metal dichalcogenides, Phys. Rev. B 90, 100505(R) (2014).
  43. R.-L. Chu, G.-B. Liu, W. Yao, X. Xu, D. Xiao, and C. Zhang, Spin-orbit-coupled quantum wires and Majorana fermions on zigzag edges of monolayer transition-metal dichalcogenides, Phys. Rev. B 89, 155317 (2014).
  44. R. Wakatsuki and K. T. Law, Proximity effect and Ising superconductivity in superconductor/transition metal dichalcogenide heterostructures, arXiv:1604.04898.
  45. L. P. Gor'kov and E. I. Rashba, Superconducting 2D system with lifted spin degeneracy: Mixed singlet-triplet state, Phys. Rev. Lett. 87, 037004 (2001).
  46. M. Sato, Y. Takahashi, and S. Fujimoto, Non-Abelian topological order in s-wave superfluids of ultracold fermionic atoms, Phys. Rev. Lett. 103, 020401 (2009).
  47. C. R. Reeg and D. L. Maslov, Proximity-induced triplet superconductivity in Rashba materials, Phys. Rev. B 92, 134512 (2015).
  48. B. T. Zhou, N. F. Q. Yuan, H.-L. Jiang, and K. T. Law, Ising superconductivity and Majorana fermions in transition-metal dichalcogenides, Phys. Rev. B 93, 180501(R) (2016).
  49. J. Cayao and A. M. Black-Schaffer, Odd-frequency superconducting pairing in junctions with Rashba spin-orbit coupling, Phys. Rev. B 98, 075425 (2018).
  50. M. Haim, D. Möckli, and M. Khodas, Signatures of triplet correlations in density of states of Ising superconductors, Phys. Rev. B 102, 214513 (2020).
  51. J. Linder and A. V. Balatsky, Odd-frequency superconductivity, Rev. Mod. Phys. 91, 045005 (2019).
  52. C. Triola, J. Cayao, and A. M. Black-Schaffer, The role of odd-frequency pairing in multiband superconductors, Ann. Phys. 532, 1900298 (2020).
  53. Y. Tanaka, S. Tamura, and J. Cayao, Theory of Majorana zero modes in unconventional superconductors, Prog. Theor. Exp. Phys. 2024, 08C105 (2024).
  54. Y. Fukaya, B. Lu, K. Yada, Y. Tanaka, and J. Cayao, Superconducting phenomena in systems with unconventional magnets, J. Phys.: Condens. Matter 37, 313003 (2025).
  55. A. Singh, S. Voltan, K. Lahabi, and J. Aarts, Colossal proximity effect in a superconducting triplet spin valve based on the half-metallic ferromagnet CrO2, Phys. Rev. X 5, 021019 (2015).
  56. G.-B. Liu, W.-Y. Shan, Y. Yao, W. Yao, and D. Xiao, Three-band tight-binding model for monolayers of group-VIB transition metal dichalcogenides, Phys. Rev. B 88, 085433 (2013).
  57. L. Komendová, A. V. Balatsky, and A. M. Black-Schaffer, Experimentally observable signatures of odd-frequency pairing in multiband superconductors, Phys. Rev. B 92, 094517 (2015).
  58. C. Triola, D. M. Badiane, A. V. Balatsky, and E. Rossi, General conditions for proximity-induced odd-frequency superconductivity in two-dimensional electronic systems, Phys. Rev. Lett. 116, 257001 (2016).
  59. L. Komendová and A. M. Black-Schaffer, Odd-frequency superconductivity in Sr2RuO4 measured by Kerr rotation, Phys. Rev. Lett. 119, 087001 (2017).
  60. S. Tamura, S. Nakosai, A. M. Black-Schaffer, Y. Tanaka, and J. Cayao, Bulk odd-frequency pairing in the superconducting Su-Schrieffer-Heeger model, Phys. Rev. B 101, 214507 (2020).
  61. J. Cayao, C. Triola, and A. M. Black-Schaffer, Floquet engineering bulk odd-frequency superconducting pairs, Phys. Rev. B 103, 104505 (2021).
  62. S. Ilić, J. S. Meyer, and M. Houzet, Spectral properties of disordered Ising superconductors with singlet and triplet pairing in in-plane magnetic fields, Phys. Rev. B 108, 214510 (2023).
  63. J. Cayao, P. Burset, and Y. Tanaka, Controllable odd-frequency Cooper pairs in multisuperconductor Josephson junctions, Phys. Rev. B 109, 205406 (2024).
  64. P.-H. Fu, S. Mondal, J.-F. Liu, and J. Cayao, Light-induced Floquet spin-triplet Cooper pairs in unconventional magnets, SciPost Phys. 20, 059 (2026).
  65. P.-H. Fu, S. Mondal, J.-F. Liu, Y. Tanaka, and J. Cayao, Floquet engineering spin triplet states in unconventional magnets, Phys. Rev. Lett. 136, 066703 (2026).
  66. W. Chen, Q. Zhu, Y. Zhou, and J. An, Topological Ising pairing states in monolayer and trilayer TaS2, Phys. Rev. B 100, 054503 (2019).
  67. A.-Y. Lu, H. Zhu, J. Xiao, C.-P. Chuu, Y. Han, M.-H. Chiu, C.-C. Cheng, C.-W. Yang, K.-H. Wei, Y. Yang, Y. Wang, D. Sokaras, D. Nordlund, P. Yang, D. A. Muller, M.-Y. Chou, X. Zhang, and L.-J. Li, Janus monolayers of transition metal dichalcogenides, Nat. Nanotechnol. 12, 744 (2017).
  68. K. Lee, W. S. Yun, and J. D. Lee, Giant Rashba-type splitting in molybdenum-driven bands of MoS2/Bi(111) heterostructure, Phys. Rev. B 91, 125420 (2015).
  69. Y. Chen, C. Liu, and R. Li, Probing Rashba spin-orbit coupling by subcycle lightwave control of valley polarization, Phys. Rev. Res. 5, 013098 (2023).
  70. L. F. Mattheiss, Band structures of transition-metal-dichalcogenide layer compounds, Phys. Rev. B 8, 3719 (1973).
  71. X. Huang, Y. Xiao, R. Song, and N. Hao, Generic model with unconventional Rashba bands and giant spin galvanic effect, Phys. Rev. B 109, 195419 (2024).
  72. Yu. A. Bychkov and E. I. Rashba, Properties of a 2D electron gas with lifted spectral degeneracy, JETP Lett. 39, 66 (1984).
  73. A. Zagoskin, Quantum Theory of Many-body Systems: Techniques and Applications (Springer, Berlin, 2014).
  74. G. D. Mahan, Many-Particle Physics (Springer Science & Business Media, New York, 2013).
  75. M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63, 239 (1991).
  76. J. J. He, K. Hiroki, K. Hamamoto, and N. Nagaosa, Spin supercurrent in two-dimensional superconductors with Rashba spin-orbit interaction, Commun. Phys. 2, 128 (2019).
  77. S. Hüfner, Photoelectron Spectroscopy: Principles and Applications (Springer Science & Business Media, New York, 2013).
  78. B. Lv, T. Qian, and H. Ding, Angle-resolved photoemission spectroscopy and its application to topological materials, Nat. Rev. Phys. 1, 609 (2019).
  79. T. Yu, C. E. Matt, F. Bisti, X. Wang, T. Schmitt, J. Chang, H. Eisaki, D. Feng, and V. N. Strocov, The relevance of ARPES to high-Tc superconductivity in cuprates, npj Quantum Mater. 5, 46 (2020).
  80. J. A. Sobota, Y. He, and Z.-X. Shen, Angle-resolved photoemission studies of quantum materials, Rev. Mod. Phys. 93, 025006 (2021).
  81. G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion, Phys. Rev. B 25, 4515 (1982).
  82. J. C. Cuevas, A. Martín-Rodero, and A. L. Yeyati, Hamiltonian approach to the transport properties of superconducting quantum point contacts, Phys. Rev. B 54, 7366 (1996).
  83. J. Linder and J. W. A. Robinson, Superconducting spintronics, Nat. Phys. 11, 307 (2015).
  84. M. Eschrig, Spin-polarized supercurrents for spintronics: A review of current progress, Rep. Prog. Phys. 78, 104501 (2015).
  85. G. Yang, C. Ciccarelli, and J. W. A. Robinson, Boosting spintronics with superconductivity, APL Mater. 9, 050703 (2021).
  86. A. Mel'nikov, S. V. Mironov, A. V. Samokhvalov, and A. I. Buzdin, Superconducting spintronics: State of the art and prospects, Uspekhi Fiz. Nauk 192, 1339 (2022).
  87. E. Ahmed, S. Tamura, Y. Tanaka, and J. Cayao, Odd-frequency pairing due to Majorana and trivial Andreev bound states, Phys. Rev. B 111, 224508 (2025).
  88. E. Ahmed, Y. Tanaka, and J. Cayao, Anomalous proximity effect under Andreev and Majorana bound states, J. Supercond. Nov. Magn. 38, 220 (2025).
  89. F. Kayatz, Data for “Superconducting properties of transition metal dichalcogenides in proximity to a conventional superconductor” [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.18417351.

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Phys. Rev. B 114, 194510– Published 14 October, 2026
  • Received 5 February 2026
  • Revised 7 September 2026
  • Accepted 2 October 2026
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