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Landau Theory for Pair Density Modulation in Fe(Te,Se) Flakes

Po-Jui Chen1 and Piers Coleman1,2,*

  • *Contact author: pcoleman@physics.rutgers.edu

Phys. Rev. Lett. 137, 016501 – Published 29 June, 2026

DOI: https://doi.org/10.1103/n7xg-dbfz

Abstract

Motivated by recent scanning tunneling microscopy (STM) experiments reporting a pair-density modulation (PDM) in flakes of FeTe0.55Se0.45, we develop a Landau theory to elucidate its physical origin. We analyze the PDM in terms of screw and glide symmetries, interpreting it as a hybridized state of two order parameters with opposite glide and screw parity. To explain the absence of PDM in the bulk, we argue that the breaking of glide symmetry at the surface allows nematic order to selectively stabilize the PDM in thin flakes. From these symmetry constraints, we show that the opposing glide and screw parities of the condensate favor a site-based, rather than bond-based, pairing mechanism. Thus, the discovery of PDM in superconducting flakes suggests that the pairing in iron-based superconductors is local to the iron atoms, possibly driven by Hunds coupling. We argue that the mismatch in Knight shift between the even and odd parity order parameters will lead to a magnetic-field enhancement of the PDM at low fields, and a reentrant triplet phase at high fields that can be tested in STM experiments.

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References (36)

  1. A. I. Coldea, Electronic nematic states tuned by isoelectronic substitution in bulk FeSe1−x  Sx, Front. Phys. 8, 594500 (2021).
  2. R. M. Fernandes and A. V. Chubukov, Low-energy microscopic models for iron-based superconductors: A review, Rep. Prog. Phys. 80, 014503 (2017).
  3. T. Hanaguri, S. Niitaka, K. Kuroki, and H. Takagi, Unconventional s-wave superconductivity in Fe(Se,Te), Science 328, 474 (2010).
  4. A. Chubukov, Pairing mechanism in Fe-based superconductors, Annu. Rev. Condens. Matter Phys. 3, 57 (2012).
  5. I. I. Mazin, D. J. Singh, M. D. Johannes, and M. H. Du, Unconventional superconductivity with a sign reversal in the order parameter of LaFeAsO1−xFx, Phys. Rev. Lett. 101, 057003 (2008).
  6. G. R. Stewart, Superconductivity in iron compounds, Rev. Mod. Phys. 83, 1589 (2011).
  7. Y. Liu, T. Wei, G. He, Y. Zhang, Z. Wang, and J. Wang, Pair density wave state in a monolayer high-Tc iron-based superconductor, Nature (London) 618, 934 (2023).
  8. R. M. Fernandes, A. I. Coldea, H. Ding, I. R. Fisher, P. J. Hirschfeld, and G. Kotliar, Iron pnictides and chalcogenides: A new paradigm for superconductivity, Nature (London) 601, 35 (2022).
  9. Y. Zhang, L. Yang, C. Liu, W. Zhang, and Y.-S. Fu, Visualizing uniform lattice-scale pair density wave in single-layer FeSe/SrTiO3 films, arXiv:2406.05693.
  10. C. Ding, Z. Xu, X. Jiao, Q. Hu, W. Zhao, L. Yang, K. Jiang, J.-F. Jia, L. Wang, J. Hu, and Q.-K. Xue, Sublattice dichotomy in monolayer FeSe superconductor, Phys. Rev. Lett. 136, 066502 (2026).
  11. L. Kong, M. Papaj, H. Kim, Y. Zhang, E. Baum, H. Li, K. Watanabe, T. Taniguchi, G. Gu, P. A. Lee, and S. Nadj-Perge, Cooper-pair density modulation state in an iron-based superconductor, Nature (London) 640, 55 (2025).
  12. T. Wei, Y. Liu, W. Ren, Z. Liang, Z. Wang, and J. Wang, Observation of superconducting pair density modulation within lattice unit cell, Chin. Phys. Lett. 42, 027404 (2025).
  13. C. Song, H. Bai, Z. Zhou, L. Han, H. Reichlova, J. H. Dil, J. Liu, X. Chen, and Feng Pan, Altermagnets as a new class of functional materials, Nat. Rev. Mater. 10, 473 (2025).
  14. P. Fulde and R. A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev. 135, A550 (1964).
  15. A. I. Larkin and Y. N. Ovchinnikov, Nonuniform state of superconductors, Zh. Eksp. Teor. Fiz. 47, 1136 (1964).
  16. Z. Dai, Y.-H. Zhang, T. Senthil, and P. A. Lee, Pair-density waves, charge-density waves, and vortices in high-Tc cuprates, Phys. Rev. B 97, 174511 (2018).
  17. Y. Wang, D. F. Agterberg, and A. Chubukov, Interplay between pair- and charge-density-wave orders in underdoped cuprates, Phys. Rev. B 91, 115103 (2015).
  18. M. H. Fischer, F. Loder, and M. Sigrist, Superconductivity and local noncentrosymmetricity in crystal lattices, Phys. Rev. B 84, 184533 (2011).
  19. J. Hu, Iron-based superconductors as odd-parity superconductors, Phys. Rev. X 3, 031004 (2013).
  20. Technically, this is a glide mirror, a combination of a half translation and a mirror reflection. For ease of description, we shall simply adopt the term “glide.”

  21. K. Ishida, Y. Onishi, M. Tsujii, K. Mukasa, M. Qiu, M. Saito, Y. Sugimura, K. Matsuura, Y. Mizukami, K. Hashimoto, and T. Shibauchi, Pure nematic quantum critical point accompanied by a superconducting dome, Proc. Natl. Acad. Sci. U.S.A. 119, e2110501119 (2022).
  22. M. Papaj, L. Kong, S. Nadj-Perge, and P. A. Lee, Pair density modulation from glide symmetry breaking and nematic superconductivity, arXiv:2506.19903.
  23. The possibility of a relative phase ϕ between the two condensates requires introduction of a biquadratic Josephson coupling term −uJ(Δ+Δ−)2cos(2ϕ) into the interactions. However, so long as uJ>0 is positive, the phases of the order parameters do indeed lock together in the ground state, with ϕ=0,π corresponding to the two screw-degenerate ground states, and uJ can be reabsorbed into a redefinition of u˜±=u±−uJ (see Supplemental Material for details [24]).

  24. See Supplemental Material at http://link.aps.org/supplemental/10.1103/n7xg-dbfz for a detailed discussion of the phase diagram calculations using the Landau theory.
  25. H. Zhao, H. Li, L. Dong, B. Xu, J. Schneeloch, R. Zhong, M. Fang, G. Gu, J. Harter, S. D. Wilson, Z. Wang, and I. Zeljkovic, Nematic transition and nanoscale suppression of superconductivity in Fe(Te,Se), Nat. Phys. 17, 903 (2021).
  26. A. L. Szabó and A. Ramires, Superconductivity-induced improper orders in nonsymmorphic systems, Phys. Rev. B 110, L180503 (2024).
  27. P. W. Anderson, Further consequences of symmetry in heavy-electron superconductors, Phys. Rev. B 32, 499 (1985).
  28. T. Hazra and P. Coleman, Triplet pairing mechanisms from Hund’s-Kondo models: Applications to UTe2 and CeRh2As2, Phys. Rev. Lett. 130, 136002 (2023).
  29. Y. Komijani, E. König, and P. Coleman, Triplet pairing, orbital selectivity, and correlations in iron-based superconductors, Phys. Rev. B 112, 125120 (2025).
  30. P. Coleman, Y. Komijani, and E. J. König, Triplet resonating valence bond state and superconductivity in Hund’s metals, Phys. Rev. Lett. 125, 077001 (2020).
  31. T.-H. Lee, A. Chubukov, H. Miao, and G. Kotliar, Pairing mechanism in Hund’s metal superconductors and the universality of the superconducting gap to critical temperature ratio, Phys. Rev. Lett. 121, 187003 (2018).
  32. T. Hotta and K. Ueda, Odd-parity triplet pair induced by Hund’s rule coupling, Phys. Rev. Lett. 92, 107007 (2004).
  33. S. Khim, J. F. Landaeta, J. Banda, N. Bannor, M. Brando, P. M. R. Brydon, D. Hafner, R. Küchler, R. Cardoso-Gil, U. Stockert, A. P. Mackenzie, D. F. Agterberg, C. Geibel, and E. Hassinger, Field-induced transition within the superconducting state of CeRh2As2, Science 373, 1012 (2021).
  34. J. F. Landaeta, P. Khanenko, D. C. Cavanagh, C. Geibel, S. Khim, S. Mishra, I. Sheikin, P. M. R. Brydon, D. F. Agterberg, M. Brando, and E. Hassinger, Field-angle dependence reveals odd-parity superconductivity in CeRh2As2, Phys. Rev. X 12, 031001 (2022).
  35. C. Lee, D. F. Agterberg, and P. M. R. Brydon, Unified picture of superconductivity and magnetism in CeRh2As2, Phys. Rev. Lett. 135, 026003 (2025).
  36. P.-J. Chen and P. Coleman, Data for: A Landau theory for pair density modulation in Fe(Te,Se) flakes, Zenodo repository, 10.5281/zenodo.1234567 (2026).

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