- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Inherent momentum-dependent gap structure of altermagnetic superconductors

Christian L. H. Rasmussen1, Jannik Gondolf1, Mats Barkman1, Mercè Roig2, Daniel F. Agterberg2, Andreas Kreisel1,3, and Brian M. Andersen1

PDF

Phys. Rev. B 113, 174513 – Published 14 May, 2026

DOI: https://doi.org/10.1103/wzch-zzwg

Abstract

Altermagnetic metals break time-reversal symmetry and feature spin-split Fermi surfaces generated by compensated Néel-ordered collinear magnetic moments. Being metallic, such altermagnets may undergo a further instability at low temperatures to a superconducting state, and it is an interesting open question what the salient features are of such altermagnetic superconductors. We address this question on the basis of realistic microscopic models that capture the altermagnetic sublattice degree of freedom. We find that the sublattice structure can strongly affect the superconducting gap structure in altermagnetic superconductors. In particular, it imposes nodes in the gap on the Brillouin zone edges for superconductors stabilized by momentum-independent bare attraction channels. We contrast this to the case of superconductivity generated by extended range interactions where pairing is allowed on the Brillouin zone edges and both spin-singlet and equal-spin-pairing triplet states can be stabilized. Equal-spin-pairing triplet superconductivity is generically favored in the limit of large altermagnetic spin splitting of the bands compared to the superconducting gap scale, and features characteristic nonunitary properties arising from the altermagnetic order.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (67)

  1. S. Hayami, Y. Yanagi, and H. Kusunose, Momentum-dependent spin splitting by collinear antiferromagnetic ordering, J. Phys. Soc. Jpn. 88, 123702 (2019).
  2. K.-H. Ahn, A. Hariki, K.-W. Lee, and J. Kuneš, Antiferromagnetism in RuO2 as d-wave Pomeranchuk instability, Phys. Rev. B 99, 184432 (2019).
  3. L. Šmejkal, R. González-Hernández, T. Jungwirth, and J. Sinova, Crystal time-reversal symmetry breaking and spontaneous Hall effect in collinear antiferromagnets, Sci. Adv. 6, eaaz8809 (2020).
  4. L.-D. Yuan, Z. Wang, J.-W. Luo, E. I. Rashba, and A. Zunger, Giant momentum-dependent spin splitting in centrosymmetric low-Z antiferromagnets, Phys. Rev. B 102, 014422 (2020).
  5. I. I. Mazin, K. Koepernik, M. D. Johannes, R. González-Hernández, and L. Šmejkal, Prediction of unconventional magnetism in doped FeSb2, Proc. Natl. Acad. Sci. USA 118, e2108924118 (2021).
  6. L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X 12, 040501 (2022).
  7. L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X 12, 031042 (2022).
  8. S. Bhowal and N. A. Spaldin, Ferroically ordered magnetic octupoles in d-wave altermagnets, Phys. Rev. X 14, 011019 (2024).
  9. S. Reimers, L. Odenbreit, L. Šmejkal, V. N. Strocov, P. Constantinou, A. B. Hellenes, R. J. Ubiergo, W. H. Campos, V. K. Bharadwaj, A. Chakraborty, et al., Direct observation of altermagnetic band splitting in CrSb thin films, Nat. Commun. 15, 2116 (2024).
  10. J. Ding, Z. Jiang, X. Chen, Z. Tao, Z. Liu, T. Li, J. Liu, J. Sun, J. Cheng, J. Liu, Y. Yang, R. Zhang, L. Deng, W. Jing, Y. Huang, Y. Shi, M. Ye, S. Qiao, Y. Wang, Y. Guo, et al., Large band splitting in g-wave altermagnet CrSb, Phys. Rev. Lett. 133, 206401 (2024).
  11. J. Krempaský, L. Šmejkal, S. W. D'Souza, M. Hajlaoui, G. Springholz, K. Uhlířová, F. Alarab, P. C. Constantinou, V. Strocov, D. Usanov, et al., Altermagnetic lifting of Kramers spin degeneracy, Nature (London) 626, 517 (2024).
  12. S. Lee, S. Lee, S. Jung, J. Jung, D. Kim, Y. Lee, B. Seok, J. Kim, B. G. Park, L. Šmejkal, C.-J. Kang, and C. Kim, Broken Kramers degeneracy in altermagnetic MnTe, Phys. Rev. Lett. 132, 036702 (2024).
  13. T. Osumi, S. Souma, T. Aoyama, K. Yamauchi, A. Honma, K. Nakayama, T. Takahashi, K. Ohgushi, and T. Sato, Observation of a giant band splitting in altermagnetic MnTe, Phys. Rev. B 109, 115102 (2024).
  14. O. Fedchenko, J. Minár, A. Akashdeep, S. W. D'Souza, D. Vasilyev, O. Tkach, L. Odenbreit, Q. Nguyen, D. Kutnyakhov, N. Wind, et al., Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2, Sci. Adv. 10, eadj4883 (2024).
  15. R. Soto-Garrido and E. Fradkin, Pair-density-wave superconducting states and electronic liquid-crystal phases, Phys. Rev. B 89, 165126 (2014).
  16. D. Chakraborty and A. M. Black-Schaffer, Zero-field finite-momentum and field-induced superconductivity in altermagnets, Phys. Rev. B 110, L060508 (2024).
  17. S. Sumita, M. Naka, and H. Seo, Fulde-Ferrell-Larkin-Ovchinnikov state induced by antiferromagnetic order in κ-type organic conductors, Phys. Rev. Res. 5, 043171 (2023).
  18. S. B. Hong, M. J. Park, and K.-M. Kim, Unconventional p-wave and finite-momentum superconductivity induced by altermagnetism through the formation of Bogoliubov Fermi surface, Phys. Rev. B 111, 054501 (2025).
  19. G. B. Sim and J. Knolle, Pair density waves and supercurrent diode effect in altermagnets, Phys. Rev. B 112, L020502 (2025).
  20. H. Hu, Z. Liu, and X.-J. Liu, Unconventional superconductivity of an altermagnetic metal: Polarized BCS and inhomogeneous FFLO states, Phys. Rev. B 112, 184501 (2025).
  21. K. Mukasa and Y. Masaki, Finite-momentum superconductivity in two-dimensional altermagnets with a Rashba-type spin–orbit coupling, J. Phys. Soc. Jpn. 94, 064705 (2025).
  22. I. V. Iorsh, Electron pairing by dispersive phonons in altermagnets: Reentrant superconductivity and continuous transition to finite momentum superconducting state, Phys. Rev. B 111, L220503 (2025).
  23. S. Sumita, M. Naka, and H. Seo, Phase-modulated superconductivity via altermagnetism, Phys. Rev. B 112, 144510 (2025).
  24. Z. Liu, H. Hu, and X.-J. Liu, Fulde-Ferrell-Larkin-Ovchinnikov states and topological Bogoliubov Fermi surfaces in altermagnets: An analytical study, Phys. Rev. B 113, 024518 (2026).
  25. S. Banerjee and M. S. Scheurer, Altermagnetic superconducting diode effect, Phys. Rev. B 110, 024503 (2024).
  26. D. Chakraborty and A. M. Black-Schaffer, Perfect superconducting diode effect in altermagnets, Phys. Rev. Lett. 135, 026001 (2025).
  27. Q. Cheng, Y. Mao, and Q.-F. Sun, Field-free Josephson diode effect in altermagnet/normal metal/altermagnet junctions, Phys. Rev. B 110, 014518 (2024).
  28. M. Roig, P. Kotetes, and B. M. Andersen, Superconducting diodes from magnetization gradients, Phys. Rev. B 109, 144503 (2024).
  29. A. Bose, S. Vadnais, and A. Paramekanti, Altermagnetism and superconductivity in a multiorbital t−J model, Phys. Rev. B 110, 205120 (2024).
  30. B. Brekke, A. Brataas, and A. Sudbø, Two-dimensional altermagnets: Superconductivity in a minimal microscopic model, Phys. Rev. B 108, 224421 (2023).
  31. V. S. de Carvalho and H. Freire, Unconventional superconductivity in altermagnets with spin-orbit coupling, Phys. Rev. B 110, L220503 (2024).
  32. K. Leraand, K. Mæland, and A. Sudbø, Phonon-mediated spin-polarized superconductivity in altermagnets, Phys. Rev. B 112, 104510 (2025).
  33. N. Parthenios, P. M. Bonetti, R. González-Hernández, W. H. Campos, L. Šmejkal, and L. Classen, Spin and pair density waves in two-dimensional altermagnetic metals, Phys. Rev. B 112, 214410 (2025).
  34. M. Khodas, S. Mu, I. I. Mazin, and K. D. Belashchenko, Tuning of altermagnetism by strain, Phys. Rev. B 113, 104422 (2026).
  35. K. Parshukov and A. P. Schnyder, Exotic superconducting states in altermagnets, arXiv:2507.10700.
  36. K. Monkman, J. Weng, N. Heinsdorf, A. Nocera, Y. Barlas, and M. Franz, Persistent spin currents in superconducting altermagnets, Phys. Rev. X 16, 011057 (2026).
  37. D. Zhu, Z.-Y. Zhuang, Z. Wu, and Z. Yan, Topological superconductivity in two-dimensional altermagnetic metals, Phys. Rev. B 108, 184505 (2023).
  38. T. F. Heung and M. Franz, Probing topological degeneracy on a torus using superconducting altermagnets, Phys. Rev. B 111, 205145 (2025).
  39. Y.-X. Li and C.-C. Liu, Majorana corner modes and tunable patterns in an altermagnet heterostructure, Phys. Rev. B 108, 205410 (2023).
  40. Y.-X. Li, Realizing tunable higher-order topological superconductors with altermagnets, Phys. Rev. B 109, 224502 (2024).
  41. S. A. A. Ghorashi, T. L. Hughes, and J. Cano, Altermagnetic routes to Majorana modes in zero net magnetization, Phys. Rev. Lett. 133, 106601 (2024).
  42. J. A. Ouassou, A. Brataas, and J. Linder, DC Josephson effect in altermagnets, Phys. Rev. Lett. 131, 076003 (2023).
  43. C. W. J. Beenakker and T. Vakhtel, Phase-shifted Andreev levels in an altermagnet Josephson junction, Phys. Rev. B 108, 075425 (2023).
  44. M. Papaj, Andreev reflection at the altermagnet-superconductor interface, Phys. Rev. B 108, L060508 (2023).
  45. S.-B. Zhang, L.-H. Hu, and T. Neupert, Finite-momentum Cooper pairing in proximitized altermagnets, Nat. Commun. 15, 1801 (2024).
  46. 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).
  47. N. Heinsdorf and M. Franz, Proximitizing altermagnets with conventional superconductors, Phys. Rev. B 113, L020501 (2026).
  48. M. Roig, A. Kreisel, Y. Yu, B. M. Andersen, and D. F. Agterberg, Minimal models for altermagnetism, Phys. Rev. B 110, 144412 (2024).
  49. M. Roig, Y. Yu, R. C. Ekman, A. Kreisel, B. M. Andersen, and D. F. Agterberg, Quasisymmetry-constrained spin ferromagnetism in altermagnets, Phys. Rev. Lett. 135, 016703 (2025).
  50. D. Chakraborty and A. M. Black-Schaffer, Constraints on superconducting pairing in altermagnets, Phys. Rev. B 112, 014516 (2025).
  51. J. Gondolf, A. Kreisel, M. Roig, Y. Yu, D. F. Agterberg, and B. M. Andersen, Local signatures of altermagnetism, Phys. Rev. B 111, 174436 (2025).
  52. Y.-M. Wu, Y. Wang, and R. M. Fernandes, Intra-unit-cell singlet pairing mediated by altermagnetic fluctuations, Phys. Rev. Lett. 135, 156001 (2025).
  53. L. Bai, R.-W. Zhang, W. Feng, and Y. Yao, Anomalous Hall effect in type IV 2D collinear magnets, Phys. Rev. Lett. 135, 036702 (2025).
  54. M. Tian, C. Cui, Z. Zhang, J. Duan, W. Feng, and R.-W. Zhang, Symmetry classification of altermagnetism and emergence of type-IV magnetism in two dimensions, arXiv:2508.17864
  55. M. Roig, A. T. Rømer, P. J. Hirschfeld, and B. M. Andersen, Revisiting superconductivity in the extended one-band Hubbard model: Pairing via spin and charge fluctuations, Phys. Rev. B 106, 214530 (2022).
  56. The triplet state would be stabilized for this set of parameters even in the absence of altermagnetic order. However, as we will demonstrate below, for tz≠0 and Nz≠0, features unique to altermagnetism will be imprinted on the triplet state.
  57. A. T. Rømer, I. Eremin, P. J. Hirschfeld, and B. M. Andersen, Superconducting phase diagram of itinerant antiferromagnets, Phys. Rev. B 93, 174519 (2016).
  58. C. N. Breiø, A. Kreisel, M. Roig, P. J. Hirschfeld, and B. M. Andersen, Time-reversal symmetry breaking from lattice dislocations in superconductors, Phys. Rev. B 109, 014505 (2024).
  59. B. M. Andersen, A. Kreisel, and P. J. Hirschfeld, Spontaneous time-reversal symmetry breaking by disorder in superconductors, Front. Phys. 12, 1353425 (2024).
  60. S. J. De, T. Pereg-Barnea, and K. Agarwal, Nanoscale defects as probes of time-reversal symmetry breaking, Phys. Rev. X 16, 011001 (2026).
  61. M. Uchida, T. Nomoto, M. Musashi, R. Arita, and M. Kawasaki, Superconductivity in uniquely strained RuO2 films, Phys. Rev. Lett. 125, 147001 (2020).
  62. J. P. Ruf, H. Paik, N. J. Schreiber, H. P. Nair, L. Miao, J. K. Kawasaki, J. N. Nelson, B. D. Faeth, Y. Lee, B. H. Goodge, et al., Strain-stabilized superconductivity, Nat. Commun. 12, 59 (2021).
  63. C. A. Occhialini, L. G. P. Martins, S. Fan, V. Bisogni, T. Yasunami, M. Musashi, M. Kawasaki, M. Uchida, R. Comin, and J. Pelliciari, Strain-modulated anisotropic electronic structure in superconducting RuO2 films, Phys. Rev. Mater. 6, 084802 (2022).
  64. N. Wadehra, B. Z. Gregory, S. Zhang, N. Schnitzer, Y. Iguchi, Y. E. Li, B. Pamuk, D. A. Muller, A. Singer, K. M. Shen, and D. G. Schlom, Strain-induced superconductivity in RuO2(100) thin-films, Commun. Mater. 6, 135 (2025).
  65. B. Jiang, M. Hu, J. Bai, Z. Song, C. Mu, G. Qu, W. Li, W. Zhu, H. Pi, Z. Wei, et al., A metallic room-temperature d-wave altermagnet, Nat. Phys. 21, 754 (2025).
  66. R. B. Regmi, H. Bhandari, B. Thapa, Y. Hao, N. Sharma, J. McKenzie, X. Chen, A. Nayak, M. El Gazzah, B. G. Márkus, et al., Altermagnetism in the layered intercalated transition metal dichalcogenide CoNb4Se8, Nat. Commun. 16, 4399 (2025).
  67. A. De Vita, C. Bigi, D. Romanin, M. D. Watson, V. Polewczyk, M. Zonno, F. Bertran, M. B. Petersen, F. Motti, G. Vinai, et al., Optical switching in a layered altermagnet, arXiv:2502.20010.

Outline

Information

Phys. Rev. B 113, 174513– Published 14 May, 2026
  • Received 14 November 2025
  • Revised 6 February 2026
  • Accepted 16 March 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation