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Vanishing Phase Stiffness and Fluctuation-Dominated Superconductivity in
Phys. Rev. X 16, 041006 – Published 6 October, 2026
DOI: https://doi.org/10.1103/qjt6-hj2k
Abstract
Superconductivity in three dimensions is almost universally governed by Ginzburg-Landau mean-field theory, with critical fluctuations typically confined to within a few percent of the transition temperature (). We report that the heavy-fermion superconductor exhibits superconducting fluctuations that extend over a temperature range as wide as itself—the largest observed for any three-dimensional superconductor. Through ultrasound measurements of the elastic moduli and sound attenuation, we find that transitions from a mean-field-like state at ambient pressure to a fluctuation-dominated state at higher pressures. This regime is marked by elastic softening and an increase in sound attenuation that onsets well above , with the attenuation remaining anomalously high deep in the superconducting state. Our analysis suggests that these features stem from an extremely low superfluid phase stiffness. This results in a kinetic inductance as high as that of granular aluminum, but achieved in the clean limit. We propose a model where this exotic state is driven by dominant interband pairing mediated by ferromagnetic fluctuations, leading to “local” Cooper pairs with a coherence length of only a few lattice constants.
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synopsis
Elucidating Superconductivity with Ultrasound
Researchers measured a crystal’s elastic modulus and sound attenuation to infer the properties of two superconducting states.
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Popular Summary
The transition from a normal metal to superconductor usually happens abruptly as a function of temperature. Using ultrasound measurements, we found that the heavy-fermion superconductor behaves very differently: Signatures of superconductivity appear gradually and persist to temperatures more than twice the superconducting transition temperature. This unusually broad fluctuation regime is the largest yet observed in a three-dimensional superconductor.
Our results point to an unconventional form of superconductivity in which paired electrons remain tightly bound together over only a few atomic spacings. Such pairs produce an exceptionally large kinetic inductance, a property that is valuable for quantum technologies and is normally achieved by introducing disorder into a material. In contrast, realizes this behavior in a pristine crystal, highlighting clean heavy-fermion superconductors as a promising platform for quantum superconducting circuits.
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References (55)
- D. Braithwaite, M. Vališka, G. Knebel, G. Lapertot, J.-P. Brison, A. Pourret, M. E. Zhitomirsky, J. Flouquet, F. Honda, and D. Aoki, Multiple superconducting phases in a nearly ferromagnetic system, Commun. Phys. 2, 147 (2019).
- S. Ran, I.-L. Liu, Y. S. Eo, D. J. Campbell, P. M. Neves, W. T. Fuhrman, S. R. Saha, C. Eckberg, H. Kim, D. Graf, F. Balakirev, J. Singleton, J. Paglione, and N. P. Butch, Extreme magnetic field-boosted superconductivity, Nat. Phys. 15, 1250 (2019).
- G. Knebel, W. Knafo, A. Pourret, Q. Niu, M. Vališka, D. Braithwaite, G. Lapertot, M. Nardone, A. Zitouni, S. Mishra, I. Sheikin, G. Seyfarth, J.-P. Brison, D. Aoki, and J. Flouquet, Field-reentrant superconductivity close to a metamagnetic transition in the heavy-fermion superconductor , J. Phys. Soc. Jpn. 88, 063707 (2019).
- S. Ran, S. R. Saha, I.-L. Liu, D. Graf, J. Paglione, and N. P. Butch, Expansion of the high field-boosted superconductivity in under pressure, npj Quantum Mater. 6, 75 (2021).
- D. Aoki, M. Kimata, Y. J. Sato, G. Knebel, F. Honda, A. Nakamura, D. Li, Y. Homma, Y. Shimizu, W. Knafo, D. Braithwaite, M. Vališka, A. Pourret, J.-P. Brison, and J. Flouquet, Field-induced superconductivity near the superconducting critical pressure in , J. Phys. Soc. Jpn. 90, 074705 (2021).
- F. Theuss, A. Shragai, G. Grissonnanche, I. M. Hayes, S. R. Saha, Y. S. Eo, A. Suarez, T. Shishidou, N. P. Butch, J. Paglione, and B. J. Ramshaw, Single-component superconductivity in at ambient pressure, Nat. Phys. 20, 1124 (2024).
- S. K. Lewin, C. E. Frank, S. Ran, J. Paglione, and N. P. Butch, A review of at high magnetic fields, Rep. Prog. Phys. 86, 114501 (2023).
- N. T. Huy, A. Gasparini, D. E. de Nijs, Y. Huang, J. C. P. Klaasse, T. Gortenmulder, A. de Visser, A. Hamann, T. Görlach, and H. v. Löhneysen, Superconductivity on the border of weak itinerant ferromagnetism in , Phys. Rev. Lett. 99, 067006 (2007).
- F. Lévy, I. Sheikin, B. Grenier, and A. D. Huxley, Magnetic field-induced superconductivity in the ferromagnet , Science 309, 1343 (2005).
- V. Zambra, A. Nathwani, M. Nauman, S. K. Lewin, C. E. Frank, N. P. Butch, A. Shekhter, B. J. Ramshaw, and K. A. Modic, Giant transverse magnetic fluctuations at the edge of re-entrant superconductivity in , Nat. Commun. 17, 3742 (2026).
- W. Knafo, G. Knebel, P. Steffens, K. Kaneko, A. Rosuel, J.-P. Brison, J. Flouquet, D. Aoki, G. Lapertot, and S. Raymond, Low-dimensional antiferromagnetic fluctuations in the heavy-fermion paramagnetic ladder compound , Phys. Rev. B 104, L100409 (2021).
- C. Duan, K. Sasmal, M. B. Maple, A. Podlesnyak, J.-X. Zhu, Q. Si, and P. Dai, Incommensurate spin fluctuations in the spin-triplet superconductor candidate , Phys. Rev. Lett. 125, 237003 (2020).
- T. Vasina, D. Aoki, A. Miyake, G. Seyfarth, A. Pourret, C. Marcenat, M. Amano Patino, G. Lapertot, J. Flouquet, J.-P. Brison, D. Braithwaite, and G. Knebel, Connecting high-field and high-pressure superconductivity in , Phys. Rev. Lett. 134, 096501 (2025).
- Y. Xu, Y. Sheng, and Y. F. Yang, Quasi-two-dimensional Fermi surfaces and unitary spin-triplet pairing in the heavy fermion superconductor , Phys. Rev. Lett. 123, 217002 (2019).
- S. Kamat, J. Dans, S. Saha, A. D. Kokovin, J. Paglione, J. Schmalian, and B. J. Ramshaw, Thermodynamic discovery of tetracriticality and emergent multicomponent superconductivity in , arXiv:2603.17905.
- Z. Wu, J. Chen, T. I. Weinberger, A. Cabala, V. Sechovský, M. Vališka, P. L. Alireza, A. G. Eaton, and F. M. Grosche, Magnetic signatures of pressure-induced multicomponent superconductivity in , Phys. Rev. Lett. 134, 236501 (2025).
- S. Ran, C. Eckberg, Q.-P. Ding, Y. Furukawa, T. Metz, S. R. Saha, I.-L. Liu, M. Zic, H. Kim, J. Paglione, and N. P. Butch, Nearly ferromagnetic spin-triplet superconductivity, Science 365, 684 (2019).
- F. Theuss, A. Shragai, G. Grissonnanche, L. Peralta, G. d. l. F. Simarro, I. M. Hayes, S. R. Saha, Y. S. Eo, A. Suarez, A. C. Salinas, G. Pokharel, S. D. Wilson, N. P. Butch, J. Paglione, and B. J. Ramshaw, Absence of a bulk thermodynamic phase transition to a density wave phase in , Phys. Rev. B 110, 144507 (2024).
- S. Klotz, J.-C. Chervin, P. Munsch, and G. Le Marchand, Hydrostatic limits of 11 pressure transmitting media, J. Phys. D 42, 075413 (2009).
- D. Aoki, F. Honda, G. Knebel, D. Braithwaite, A. Nakamura, D. Li, Y. Homma, Y. Shimizu, Y. J. Sato, J.-P. Brison, and J. Flouquet, Multiple superconducting phases and unusual enhancement of the upper critical field in , J. Phys. Soc. Jpn. 89, 053705 (2020).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/qjt6-hj2k, which includes Refs. [22–28], for discussions of pressure homogeneity, background subtraction, data from a second sample, and a derivation of gaussian fluctuations.
- G. Blatter, Vortices in high-temperature superconductors, Rev. Mod. Phys. 66, 1125 (1994).
- E. H. Brandt, The flux-line lattice in superconductors, Rep. Prog. Phys. 58, 1465 (1995).
- A. Larkin and A. Varlamov, Theory of Fluctuations in Superconductors, International Series of Monographs on Physics (Oxford University Press, Oxford, 2005).
- S. Nakamura, T. Goto, Y. Isikawa, S. Sakatsume, and M. Kasaya, Elastic properties of dense Kondo compounds CeNiSn and CePdSn, J. Phys. Soc. Jpn. 60, 2305 (1991).
- Y. P. Varshni, Temperature dependence of the elastic constants, Phys. Rev. B 2, 3952 (1970).
- H. Kim, I.-L. Liu, W.-C. Lin, Y. S. Eo, S. Ran, N. P. Butch, and J. Paglione, Tuning a magnetic energy scale with pressure and field in , Commun. Mater. 6, 6 (2025).
- M. Kardar, Statistical Physics of Fields (Cambridge University Press, Cambridge, England, 2007).
- F. S. Khan and P. B. Allen, Sound attenuation by electrons in metals, Phys. Rev. B 35, 1002 (1987).
- D. Thuillier, Multipolar Fermi surface deformations in probed by resistivity and sound attenuation: A window into electron viscosity and the collision operator, Phys. Rev. Lett. 135, 146302 (2025).
- D. J. Bishop, C. M. Varma, B. Batlogg, E. Bucher, Z. Fisk, and J. L. Smith, Ultrasonic attenuation in , Phys. Rev. Lett. 53, 1009 (1984).
- B. Batlogg, D. Bishop, B. Golding, C. M. Varma, Z. Fisk, J. L. Smith, and H. R. Ott, -shaped ultrasound-attenuation peak in superconducting , Phys. Rev. Lett. 55, 1319 (1985).
- K. Miyake and C. M. Varma, Landau-Khalatnikov damping of ultrasound in heavy-fermion superconductors, Phys. Rev. Lett. 57, 1627 (1986).
- F. Theuss, S. Ghosh, T. Chen, O. Tchernyshyov, S. Nakatsuji, and B. J. Ramshaw, Strong magnetoelastic coupling in (). Phys. Rev. B 105, 174430 (2022).
- T. Vasina, M. Pfeiffer, R. Borth, M. Nicklas, M. A. Patino, G. Lapertot, J.-P. Brison, E. Hassinger, G. Knebel, and D. Braithwaite, Quantitative thermodynamic study of superconducting and normal states in under pressure, arXiv:2603.29760.
- W. Knafo, G. Knebel, P. Steffens, K. Kaneko, A. Rosuel, J.-P. Brison, J. Flouquet, D. Aoki, G. Lapertot, and S. Raymond, Low-dimensional antiferromagnetic fluctuations in the heavy-fermion paramagnetic ladder compound , Phys. Rev. B 104, L100409 (2021).
- W. Knafo, T. Thebault, S. Raymond, P. Manuel, D. D. Khalyavin, F. Orlandi, E. Ressouche, K. Beauvois, G. Lapertot, K. Kaneko, D. Aoki, D. Braithwaite, and G. Knebel, Incommensurate antiferromagnetism in under pressure, Phys. Rev. X 15, 021075 (2025).
- T. Shishidou, H. G. Suh, P. M. R. Brydon, M. Weinert, and D. F. Agterberg, Topological band and superconductivity in , Phys. Rev. B 103, 104504 (2021).
- H. Christiansen, M. Geier, B. M. Andersen, and A. Kreisel, Nodal superconducting gap structure and topological surface states of , Phys. Rev. B 112, 054510 (2025).
- J. Tei, T. Mizushima, and S. Fujimoto, Pairing symmetries of multiple superconducting phases in : Competition between ferromagnetic and antiferromagnetic fluctuations, Phys. Rev. B 109, 064516 (2024).
- K. V. Samokhin, Ginzburg-Landau energy of multiband superconductors with interband pairing, Phys. Rev. B 109, 134508 (2024).
- D. Vijayan Ambika, Q.-P. Ding, C. E. Frank, S. Ran, N. P. Butch, and Y. Furukawa, Enhancement of antiferromagnetic spin fluctuations in under pressure revealed by NMR, Phys. Rev. B 113, 014510 (2026).
- D. V. Ambika, Q.-P. Ding, K. Rana, C. E. Frank, E. L. Green, S. Ran, N. P. Butch, and Y. Furukawa, Possible coexistence of antiferromagnetic and ferromagnetic spin fluctuations in the spin-triplet superconductor revealed by NMR under pressure, Phys. Rev. B 105, L220403 (2022).
- A. Rosuel, C. Marcenat, G. Knebel, T. Klein, A. Pourret, N. Marquardt, Q. Niu, S. Rousseau, A. Demuer, G. Seyfarth, G. Lapertot, D. Aoki, D. Braithwaite, J. Flouquet, and J. P. Brison, Field-induced tuning of the pairing state in a superconductor, Phys. Rev. X 13, 011022 (2023).
- T. I. Weinberger, D. Shaffer, Z. Wu, D. V. Chichinadze, J. Pu, G. Li, R. Zhou, Y. Skourski, D. Graf, A. Cabala, V. Sechovsky, M. Valiska, M. P. Kwasigroch, F. M. Grosche, and A. G. Eaton, Metamagnetism in : The roles of itinerancy and localization, arXiv:2606.27913.
- C. Krellner, S. Hartmann, A. Pikul, N. Oeschler, J. G. Donath, C. Geibel, F. Steglich, and J. Wosnitza, Violation of critical universality at the antiferromagnetic phase transition of , Phys. Rev. Lett. 102, 196402 (2009).
- V. Grinenko et al., State with spontaneously broken time-reversal symmetry above the superconducting phase transition, Nat. Phys. 17, 1254 (2021).
- T. M. Bretz-Sullivan, R. M. Lewis, A. L. Lima-Sharma, D. Lidsky, C. M. Smyth, C. T. Harris, M. Venuti, S. Eley, and T.-M. Lu, High kinetic inductance NbTiN superconducting transmission line resonators in the very thin film limit, Appl. Phys. Lett. 121, 052602 (2022).
- S. Kamat, J. Dans, S. Saha, D. F. Agterberg, J. Paglione, and B. J. Ramshaw, Dataset for “Vanishing Phase Stiffness and Fluctuation-Dominated Superconductivity in ”, Github, https://github.com/CHiLL-Ramshaw/manuscripts-supporting_data/tree/2f152da924c294dfc4c06ac37db01ddcde2f2905/2026_UTe2_Vanishing.
- M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63, 239 (1991).
- S. Liu and L. A. Wray, Density functional theory based investigation of heavy fermion band candidates in triplet superconductor , arXiv:2410.03840.
- K. Ishihara, M. Roppongi, M. Kobayashi, K. Imamura, Y. Mizukami, H. Sakai, P. Opletal, Y. Tokiwa, Y. Haga, K. Hashimoto, and T. Shibauchi, Chiral superconductivity in probed by anisotropic low-energy excitations, Nat. Commun. 14, 2966 (2023).
- N. Sharma, M. Toole, J. McKenzie, F. Cheng, M. M. Bordelon, S. M. Thomas, P. F. S. Rosa, Y.-T. Hsu, and X. Liu, Observation of persistent zero modes and superconducting vortex doublets in , ACS Nano 19, 31539 (2025).
- B. J. Ramshaw, J. Day, B. Vignolle, D. LeBoeuf, P. Dosanjh, C. Proust, L. Taillefer, R. Liang, W. N. Hardy, and D. A. Bonn, Vortex lattice melting and in underdoped , Phys. Rev. B 86, 174501 (2012).
- M. Kreidel, X. Chu, J. Balgley, A. Antony, N. Verma, J. Ingham, L. Ranzani, R. Queiroz, R. M. Westervelt, J. Hone, and K. C. Fong, Measuring kinetic inductance and superfluid stiffness of two-dimensional superconductors using high-quality transmission-line resonators, Phys. Rev. Res. 6, 043245 (2024).
