Interplay between altermagnetism and superconductivity in two dimensions: intertwined symmetries and singlet-triplet mixing
Source abstract
Abstract
We study the interplay between altermagnetism and unconventional superconductivity for two-dimensional square- and triangular-lattice systems. Our approach is based on an effective single particle Hamiltonian which mimics the alternating spin splitting of the d - wave and i - wave altermagnetic state. By supplementing the model with intersite pairing term we characterize the principal features of the coexistent altermagnetic-superconducting state as well as the possibility of inducing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Our calculations show that the subtle interplay between the symmetries of the superconducting and altermagnetic order parameters as well as the shape/size of the Fermi surface lead to various types of anisotropic behaviors of the resultant non-zero momentum pairing, which has not been possible in the originally proposed FFLO state. Moreover, additional pairing symmetries appear leading to multi-component order parameter with singlet-triplet mixing. We discuss our result in the context of possible applications like, e.g., the superconducting diode.
Source: openalex_inverted_index · Quality: baseline
Research context
OpenAlex topics: Physics of Superconductivity and Magnetism · Rare-earth and actinide compounds · Iron-based superconductors research
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (48)
Show source-provided references
1. Šmejkal, L., Sinova, J. & Jungwirth, T. Emerging research landscape of altermagnetism. Phys. Rev. X 12, 040501 (2022).
2. Šmejkal, L., Sinova, J. & Jungwirth, T. Beyond conventional ferromagnetism and antiferromagnetism: a phase with nonrelativistic spin and crystal rotation symmetry. Phys. Rev. X 12, 031042 (2022).
3. Mazin, I. Editorial: altermagnetism—a new punch line of fundamental magnetism. Phys. Rev. X 12, 040002 (2022).
4. Mazin, I. Altermagnetism then and now. Physics 17, 4 (2024).10.1103/Physics.17.4 ↗
5. Song, C. et al. Altermagnets as a new class of functional materials. Nat. Rev. Mater.https://doi.org/10.1038/s41578-025-00779-1. (2025).10.1038/s41578-025-00779-1 ↗
6. Bai, L. et al. Altermagnetism: exploring new frontiers in magnetism and spintronics. Adv. Funct. Mater. 34, 2409327 (2024).10.1002/adfm.202409327 ↗
7. Ma, H.-Y. et al. Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current. Nat. Commun. 12, 2846 (2021).10.1038/s41467-021-23127-7 ↗
8. Fedchenko, O. et al. Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2. Sci. Adv. 10, eadj4883 (2024).10.1126/sciadv.adj4883 ↗
9. Jiang, B. et al. A metallic room-temperature d-wave altermagnet. Nat. Phys. 21, 754–759 (2025).10.1038/s41567-025-02822-y ↗
10. Sarkar, R. Altermagnet with a metallic touch. Nat. Phys. 21, 691–692 (2025).10.1038/s41567-025-02894-w ↗
11. Lee, S. et al. Broken Kramers degeneracy in altermagnetic mnte. Phys. Rev. Lett. 132, 036702 (2024).10.1103/PhysRevLett.132.036702 ↗
12. Zhu, Y.-P. et al. Observation of plaid-like spin splitting in a noncoplanar antiferromagnet. Nature 626, 523–528 (2024).10.1038/s41586-024-07023-w ↗
13. Zhang, F. et al. Crystal-symmetry-paired spin–valley locking in a layered room-temperature metallic altermagnet candidate. Nat. Phys. 21, 760–767 (2025).10.1038/s41567-025-02864-2 ↗
14. Jiang, B. et al. Discovery of a metallic room-temperature d-wave altermagnet. Nature Physics. 21, 754–759 (2025).10.1038/s41567-025-02822-y ↗
15. Zeng, S. & Zhao, Y.-J. Description of two-dimensional altermagnetism: categorization using spin group theory. Phys. Rev. B 110, 054406 (2024).10.1103/PhysRevB.110.054406 ↗
16. Mazin, I. I. Notes on altermagnetism and superconductivity. AAPPS Bulletin. 35, 18 (2022).10.1007/s43673-025-00158-6 ↗
17. Zeng, S. & Zhao, Y.-J. Bilayer stacking a-type altermagnet: A general approach to generating two-dimensional altermagnetism. Phys. Rev. B 110, 174410 (2024).10.1103/PhysRevB.110.174410 ↗
18. Eschrig, M. Spin-polarized supercurrents for spintronics: a review of current progress. Rep. Prog. Phys. 78, 104501 (2015).10.1088/0034-4885/78/10/104501 ↗
19. Linder, J. & Robinson, J. W. A. Superconducting spintronics. Nat. Phys. 11, 307–315 https://doi.org/10.1038/nphys3242 (2015).10.1038/nphys3242 ↗
20. Bergeret, F. S., Silaev, M., Virtanen, P. & Heikkilä, T. T. Colloquium: nonequilibrium effects in superconductors with a spin-splitting field. Rev. Mod. Phys. 90, 041001 (2018).10.1103/RevModPhys.90.041001 ↗
21. Flensberg, K., von Oppen, F. & Stern, A. Engineered platforms for topological superconductivity and Majorana zero modes. Nat. Rev. Mater. 6, 944–958 (2021).10.1038/s41578-021-00336-6 ↗
22. Narita, H. et al. Field-free superconducting diode effect in noncentrosymmetric superconductor/ferromagnet multilayers. Nat. Nanotechnol. 17, 823–828 (2022).10.1038/s41565-022-01159-4 ↗
23. Coronado, E. et al. Coexistence of superconductivity and magnetism by chemical design. Nat. Chem. 2, 1031–1036 (2010).10.1038/nchem.898 ↗
24. Matsuda, Y. & Shimahara, H. Fulde-ferrell-larkin-ovchinnikov state in heavy fermion superconductors. J. Phys. Soc. Jpn. 76, 051005 (2007).10.1143/JPSJ.76.051005 ↗
25. Si, Q., Yu, R. & Abrahams, E. High-temperature superconductivity in iron pnictides and chalcogenides. Nat. Rev. Mater. 1, 16017 (2016).10.1038/natrevmats.2016.17 ↗
26. Zhang, S.-B., Hu, L.-H. & Neupert, T. Finite-momentum cooper pairing in proximitized altermagnets. Nat. Commun. 15, 1801 (2024).10.1038/s41467-024-45951-3 ↗
27. Chakraborty, D. & Black-Schaffer, A. M. Zero-field finite-momentum and field-induced superconductivity in altermagnets. Phys. Rev. B 110, L060508 (2024).10.1103/PhysRevB.110.L060508 ↗
28. de Carvalho, V. S. & Freire, H. Unconventional superconductivity in altermagnets with spin-orbit coupling. Phys. Rev. B 110, L220503 (2024).10.1103/PhysRevB.110.L220503 ↗
29. Sumita, S., Naka, M. & Seo, H. Phase-modulated superconductivity via altermagnetism. Phys. Rev. B 112, 144510 (2025).10.1103/3k12-2467 ↗
30. Sim, G. & Knolle, J. Pair density waves and supercurrent diode effect in altermagnets. Phys. Rev. B 112. https://doi.org/10.1103/b7rh-v7nq (2025).10.1103/b7rh-v7nq ↗
31. Mukasa, K. & Masaki, Y. Finite-momentum superconductivity in two-dimensional altermagnets with a rashba-type spin-orbit coupling. J. Phys. Soc. Jpn. 94, 064705 (2025).10.7566/JPSJ.94.064705 ↗
32. Banerjee, S. & Scheurer, M. S. Altermagnetic superconducting diode effect. Phys. Rev. B 110, 024503 (2024).10.1103/PhysRevB.110.024503 ↗
33. Chakraborty, D. & Black-Schaffer, A. M. Perfect superconducting diode effect in altermagnets. Phys. Rev. Lett. 135, 026001 (2025).10.1103/cv8s-tk4c ↗
34. Fukaya, Y., Lu, B., Yada, K., Tanaka, Y. & Cayao, J. Superconducting phenomena in systems with unconventional magnets. J. Phys. Condens. Matter 37, 313003 (2025).10.1088/1361-648X/adf1cf ↗
35. Bose, A., Vadnais, S. & Paramekanti, A. Altermagnetism and superconductivity in a multiorbital t − j model. Phys. Rev. B 110, 205120 (2024).10.1103/PhysRevB.110.205120 ↗
36. León, A., Autieri, C., Brumme, T. & González, J. W. Hybrid d/p-wave altermagnetism in ca3ru2o7 and strain-controlled spin splitting. npj Quantum Mater. 10, 98 (2025).10.1038/s41535-025-00814-y ↗
37. Sumita, S., Naka, M. & Seo, H. Fulde-ferrell-larkin-ovchinnikov state induced by antiferromagnetic order in κ-type organic conductors. Phys. Rev. Res. 5, 043171 (2023).10.1103/PhysRevResearch.5.043171 ↗
38. Jiang, K., Wu, X., Hu, J. & Wang, Z. Nodeless high-Tc superconductivity in the highly overdoped cuo2 monolayer. Phys. Rev. Lett. 121, 227002 (2018).10.1103/PhysRevLett.121.227002 ↗
39. Zhong, Y. et al. Nodeless pairing in superconducting copper-oxide monolayer films on bi2sr2cacu2o8+δ. Sci. Bull. 61, 1239–1247 (2016).10.1007/s11434-016-1145-4 ↗
40. Zegrodnik, M., Wójcik, P. & Spałek, J. Superconducting dome with extended s-wave pairing symmetry in the heavily hole-overdoped copper-oxide planes. Phys. Rev. B 103, 144511 (2021).10.1103/PhysRevB.103.144511 ↗
41. Zegrodnik, M. & Wójcik, P. Superconducting dome in laalo3/srtio3 interfaces as a direct consequence of the extended s-wave symmetry of the gap. Phys. Rev. B 102, 085420 (2020).10.1103/PhysRevB.102.085420 ↗
42. Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550–A563 (1964).10.1103/PhysRev.135.A550 ↗
43. Larkin, A. I. & Ovchinnikov, Y. N. Nonuniform state of superconductors. Zh. Eksp. Teor. Fiz. 47, 1136–1146 (1964).
44. Zegrodnik, M. & Wójcik, P. Interplay between extended s-wave symmetry of the gap and spin-orbit coupling in the low electron concentration regime of quasi-two-dimensional superconductors. Phys. Rev. B 106, 184508 (2022).10.1103/PhysRevB.106.184508 ↗
45. Li, S., Zhang, Y., Bahri, A., Zhang, X. & Jia, C. Altermagnetism and strain induced altermagnetic transition in cairo pentagonal monolayer. npj Quantum Mater. 10, 83 (2025).10.1038/s41535-025-00793-0 ↗
46. Beida, W. et al. Chiral split magnons in metallic g-wave altermagnets: insights from many-body perturbation theory. npj Quantum Mater. 10, 97 (2025).10.1038/s41535-025-00818-8 ↗
47. Zegrodnik, M. & Biborski, A. Mixed singlet-triplet superconducting state within the moiré t − j − u model applied to twisted bilayer wse2. Phys. Rev. B 108, 064506 (2023).10.1103/PhysRevB.108.064506 ↗
48. Akbar, W., Biborski, A., Rademaker, L. & Zegrodnik, M. Topological superconductivity with mixed singlet-triplet pairing in moiré transition metal dichalcogenide bilayers. Phys. Rev. B 110, 064516 (2024).10.1103/PhysRevB.110.064516 ↗