Letter
Open Access

Anisotropic field-induced changes in the superconducting order parameter of $UT e_{2}$

Sangyun Lee ^1,2,*, Andrew J. Woods ^1,3,*, P. F. S. Rosa ¹, S. M. Thomas ¹, E. D. Bauer ¹, Shi-Zeng Lin ¹, and R. Movshovich ^1,†

¹Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
²Department of Physics and National High Magnetic Field Laboratory High B/T Facility, University of Florida, Gainesville, Florida 32611–8440, USA
³MagLab DC-Field Facility, Florida State University, Tallahassee, Florida 32310, USA

^*These authors contributed equally to this work.
^†Contact author: roman@lanl.gov

PDF

Phys. Rev. Research 7, L022053 – Published 4 June, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022053

Abstract

$UT e_{2}$ is a newly discovered unconventional superconductor, where electron Cooper pairs combine into a spin-triplet ground state. We study the specific heat $C$ (H,T) of a high-quality $UT e_{2}$ single crystal, with a single anomaly at a high superconducting transition temperature $T_{c} = 2.1$ K and a low residual Sommerfeld coefficient $γ_{0}$ . Applying magnetic fields up to 12 T along the crystallographic axes $a, b$ , and $c$ , we observe highly anisotropic behavior in $γ_{0} (H)$ . Below 4 T, $γ_{0} (H) \approx γ 0 + λ i \sqrt H$ ( $i = a, b, c$ ), which is expected for an unconventional superconductor with nodes on the Fermi surface away from the direction of the magnetic field. At 4 T ( $a$ and $b$ axes) and 5.5 T ( $c$ axis), distinctive changes in the behavior of $γ_{0} (H)$ suggest that a stable low-field ground state begins to evolve above 4 T. The data analysis indicates that the nodes are located near the $a - b$ plane, with possible order parameters $d_{B 2 u} + i ɛ d_{B 1 u}$ or $d_{B 2 u} + i ɛ d_{Au}$ . Our findings support $B_{2 u}$ as the primary superconducting order parameter in $UT e_{2}$ .

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (62)

N. Read and D. Green, Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect, Phys. Rev. B 61, 10267 (2000).
D. A. Ivanov, Non-abelian statistics of half-quantum vortices in $p - wave$ superconductors, Phys. Rev. Lett. 86, 268 (2001).
M. Sato, Topological properties of spin-triplet superconductors and Fermi surface topology in the normal state, Phys. Rev. B 79, 214526 (2009).
M. Sato, Topological odd-parity superconductors, Phys. Rev. B 81, 220504(R) (2010).
D. Aoki et al., Spin-triplet superconductivity in $UT e_{2}$ and ferromagnetic superconductors, JPS Conf. Proc. 30, 011065 (2020).
S. Ran et al., Extreme magnetic field-boosted superconductivity, Nat. Phys. 15, 1250 (2019).
D. D. Osheroff, R. C. Richardson, and D. M. Lee, Evidence for a new phase of solid $H e_{3}$ , Phys. Rev. Lett. 28, 885 (1972).
A. J. Leggett, A theoretical description of the new phases of liquid ${}^{3}{He}$ , Rev. Mod. Phys. 47, 331 (1975).
Y. Maeno, A. Ikeda, and G. Mattoni, Thirty years of puzzling superconductivity in $S r_{2} Ru O_{4}$ , Nat. Phys. 20, 1712 (2024).
K. Ishida, H. Mukuda, Y. Kitaoka, K. Asayama, Z. Q. Mao, Y. Mori, and Y. Maeno, Spin-triplet superconductivity in $S r_{2} Ru O_{4}$ identified by ${}^{17}O$ Knight shift, Nature (London) 396, 658 (1998).
H. Tou, Y. Kitaoka, K. Ishida, K. Asayama, N. Kimura, Y. Onuki, and E. Yamamoto, Nonunitary spin-triplet superconductivity in $UP t_{3}$ : Evidence from ${}^{195}{P t}$ knight shift study, Phys. Rev. Lett. 80, 3129 (1998).
L. Jiao, S. Howard, S. Ren, Z. Wang, J. O. Rodriguez, M. Sigrist, Z. Wang, N. P. Butch, and V. Madhavan, Chiral superconductivity in heavy-fermion metal $UT e_{2}$ , Nature (London) 579, 523 (2020).
G. R Stewart, Z. Fisk, J. O. Willis, and J. L. Smith, Possibility of coexistence of bulk superconductivity and spin fluctuations in $UP t_{3}$ , Phys. Rev. Lett. 52, 679 (1984).
S. S. Saxena et al., Superconductivity on the border of itinerant-electron ferromagnetism in $UG e_{2}$ , Nature (London) 406, 587 (2000).
D. Aoki, A. Huxley, E. Ressouche, D. Braithwaite, J. Flouquet, J. P. Brison, E. Lhotel, and C. Paulsen, Coexistence of superconductivity and ferromagnetism in URhGe, Nature (London) 413, 613 (2001).
N. T. Huy, D. E. de Nijs, Y. K. Huang, and A. de Visser, Unusual upper critical field of the ferromagnetic superconductor UCoGe, Phys. Rev. Lett. 100, 077002 (2008).
S. M. Hayden, L. Taillefer, C. Vettier, and J. Flouquet, Antiferromagnetic order in $UP t_{3}$ under pressure: Evidence for a direct coupling to superconductivity, Phys. Rev. B 46, 8675 (1992).
D. Aoki, J. P. Brison, J. Flouquet, K. Ishida, G. Knebel, Y. Tokunaga, and Y. Yanase, Unconventional superconductivity in $UT e_{2}$ , J. Phys.: Condens. Matter 34, 243002 (2022).
See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022053 for more details.
S. Sundar, G. Gheidi, K. Akintola, A. M. Côté, S. R. Dunsiger, S. Ran, N. P. Butch, S. R. Saha, J. Paglione, and J. E. Sonier, Coexistence of ferromagnetic fluctuations and superconductivity in the actinide superconductor $UT e_{2}$ , Phys. Rev. B 100, 140502(R) (2019).
N. Azari et al., Absence of spontaneous magnetic fields due to time-reversal symmetry breaking in bulk superconducting $UT e_{2}$ , Phys. Rev. Lett. 131, 226504 (2023).
S. M. Thomas et al., Evidence for a pressure-induced antiferromagnetic quantum critical point in intermediate-valence $UT e_{2}$ , Sci. Adv. 6, 42 (2020).
W. Knafo et al., Incommensurate antiferromagnetism in $UT e_{2}$ under pressure, arXiv:2311.05455.
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 $UT e_{2}$ , Phys. Rev. Lett. 125, 237003 (2020).
W. Knafo et al., Low-dimensional antiferromagnetic fluctuations in the heavy-fermion paramagnetic ladder compound $UT e_{2}$ , Phys. Rev, B 104, L100409 (2021).
G. Nakamine et al., Superconducting properties of heavy fermion $UT e_{2}$ revealed by ${}^{125}{T e}$ -nuclear magnetic resonance, J. Phys. Soc. Jpn. 88, 113703 (2019).
H. Fujibayashi et al., Superconducting order parameter in $UT e_{2}$ determined by knight shift measurement, J. Phys. Soc. Jpn. 91, 043705 (2022).
G. Nakamine et al., Anisotropic response of spin susceptibility in the superconducting state of $UT e_{2}$ probed with ${}^{125}{Te} − NMR$ measurement, Phys. Rev. B 103, L100503 (2021).
W. Knafo, M. Vališka, D. Braithwaite, G. Lapertot, G. Knebel, A. Pourret, J. P. Brison, J. Flouquet, and D. Aoki, Magnetic-field-induced phenomena in the paramagnetic superconductor $UT e_{2}$ , J. Phys. Soc. Jpn. 88, 063705 (2019).
A. Miyake, Y. Shimizu, Y. J. Sato, D. Li, A. Nakamura, Y. Homma, F. Honda, J. Flouquet, M. Tokunaga, and D. Aoki, Metamagnetic transition in heavy fermion superconductor $UT e_{2}$ , J. Phys. Soc. Jpn. 88, 063706 (2019).
Q. Niu et al., Evidence of Fermi surface reconstruction at the metamagnetic transition of the strongly correlated superconductor $UT e_{2}$ , Phys. Rev. Res. 2, 033179 (2020).
T. Metz et al., Point-node gap structure of the spin-triplet superconductor $UT e_{2}$ , Phys. Rev. B 100, 220504(R) (2019).
S. Bae, H. Kim, Y. S. Eo, S. Ran, I. Liu, W. T. Fuhrman, J. Paglione, N. P. Butch, and S. M. Anlage, Anomalous normal fluid response in a chiral superconductor $UT e_{2}$ , Nat. Comm. 12, 2644 (2021).
S. Kittaka et al., Y. Shimizu, T. Sakakibara, A. Nakamura, D. Li, Y. Homma, F. Honda, D. Aoki, and K. Machida, Orientation of point nodes and nonunitary triplet pairing tuned by the easy-axis magnetization in $UT e_{2}$ , Phys. Rev. Res. 2, 032014(R) (2020).
I. M. Hayes et al., Multicomponent superconducting order parameter in $UT e_{2}$ , Science 373, 797 (2021).
D. Aoki et al., First Observation of the de haas–van alphen effect and fermi surfaces in the unconventional superconductor $UT e_{2}$ , J. Phys. Soc. Jpn. 91, 083704 (2022).
P. F. S. Rosa, A. Weiland, S. S. Fender, B. L. Scott, F. Ronning, J. D. Thompson, E. D. Bauer, and S. M. Thomas, Single thermodynamic transition at 2 K in superconducting $UT e_{2}$ single crystals, Commun. Mater. 3, 33 (2022).
H. Sakai, P. Opletal, Y. Tokiwa, E. Yamamoto, Y. Tokunaga, S. Kambe, and Y. Haga, Single crystal growth of superconducting $UT e_{2}$ by molten salt flux method, Phys. Rev. Mater. 6, 073401 (2022).
M. O. Ajeesh, M. Bordelon, C. Girod, S. Mishra, F. Ronning, E. D. Bauer, B. Maiorov, J. D. Thompson, P. F. S. Rosa, and S. M. Thomas, Fate of time-reversal symmetry breaking in $UT e_{2}$ , Phys. Rev. X 13, 041019 (2023).
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 $UT e_{2}$ at ambient pressure, Nat. Phys. 20, 1124 (2024).
H. Matsumura et al., Large reduction in the a-axis knight shift on $UT e_{2}$ with $T_{c} = 2.1$ K, J. Phys. Soc. Jpn. 92, 063701 (2023).
K. Ishihara et al., Chiral superconductivity in $UT e_{2}$ probed by anisotropic low-energy excitations, Nat. Commun. 14, 2966 (2023).
E. I. Blount, Symmetry properties of triplet superconductors, Phys. Rev. B 32, 2935 (1985).
S. Kobayashi, K. Shiozaki, Y. Tanaka, and M. Sato, Topological Blount's theorem of odd-parity superconductors, Phys. Rev. B 90, 024516 (2014).
G. Knebel et al., Field-reentrant superconductivity close to a metamagnetic transition in the heavy-fermion superconductor $UT e_{2}$ , J. Phys. Soc. Jpn. 88, 063707 (2019).
W. Knafo, M. Nardone, M. Vališka, A. Zitouni, G. Lapertot, D. Aoki, G. Knebel, and D. Braithwaite, Comparison of two superconducting phases induced by a magnetic field in $UT e_{2}$ , Comms Phys 4, 40 (2021).
A. Rosuel et al., Field-induced tuning of the pairing state in a superconductor, Phys. Rev. X 13, 011022 (2023).
G. Nakamine et al., Inhomogeneous superconducting state probed by ${}^{125}{T e}$ NMR on $UT e_{2}$ , J. Phys. Soc. Jpn. 90, 064709 (2021).
D. Aoki, I. Sheikin, N. Marquardt, G. Lapertot, J. Flouquet, and G. Knebel, High field superconducting phases of ultra clean single crystal $UT e_{2}$ , J. Phys. Soc. Jpn. 93, 123702 (2024).
T. Helm et al., Field-induced compensation of magnetic exchange as the possible origin of reentrant superconductivity in $UT e_{2}$ , Nat. Commun. 15, 37 (2024).
S. K. Lewin, C. E. Frank, S. Ran, J. Paglione, and N. P. Butch, A review of $UT e_{2}$ at high magnetic fields, Rep. Prog. Phys. 86, 114501 (2023).
G. E. Volovik, On the vortex lattice transition in heavy-fermionic $UT e_{2}$ , J. Phys. C Solid State Phys. 21, L221 (1988).
P. Miranovic, N. Nakai, M. Ichioka, and K. Machida, Orientational field dependence of low-lying excitations in the mixed state of unconventional superconductors, Phys. Rev. B 68, 052501 (2003).
A. B. Vorontsov and I. Vekhter, Unconventional superconductors under a rotating magnetic field. I. Density of states and specific heat, Phys. Rev. B 75, 224501 (2007).
J. S. Kim, G. R. Stewart, Y. Liu, and T. A. Lograsso, Specific heat investigation for line nodes in heavily overdoped $B a_{1 - x} K_{x} F e_{2} A s_{2}$ , Phys. Rev. B 91, 214506 (2015).
It is possible that small amounts of disorder may move the nodes away from the high-symmetry axes expected in the case of a single-component order parameter. Such a possibility, explored in the context of FeAs-based superconductors, was not considered theoretically for heavy fermion superconductors.
J. J. Yu, Y. Yu, D. F. Agterberg, and S. Raghu, Theory of the low- and high-field superconducting phases of $UT e_{2}$ , Phys. Rev. B 107, 214510 (2023).
A. G. Eaton et al., Quasi-2D Fermi surface in the anomalous superconductor $UT e_{2}$ , Nat. Commun. 15, 223 (2024).
L. Miao et al., Low energy band structure and symmetries of $UT e_{2}$ from angle-resolved photoemission spectroscopy, Phys. Rev. Lett. 124, 076401 (2020).
Y. Moriya, T. Matsushita, M. G. Yamada, T. Mizushima, and S. Fujimoto, Intrinsic anomalous thermal Hall effect in the unconventional superconductor $UT e_{2}$ , J. Phys. Soc. Jpn. 91, 094710 (2022).
R. Willa, M. Hecker, R. M. Fernandes, and J. Schmalian, Inhomogeneous time-reversal symmetry breaking in $S r_{2} Ru O_{4}$ , Phys. Rev. B 104, 024511 (2021).
D. Mockli and A. Ramires, Superconductivity in disordered locally noncentrosymmetric materials: An application to $CeR h_{2} A s_{2}$ , Phys. Rev. B 104, 134517 (2021).

Phys. Rev. Research 7, L022053– Published 4 June, 2025

Vol. 7, Iss. 2 — June - August 2025

Received 7 October 2023
Accepted 1 May 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022053

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.

Published by the American Physical Society

Physical Review Research

Reuse & Permissions

Export citation

Export citation

Anisotropic field-induced changes in the superconducting order parameter of $UT e_{2}$

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (62)

Outline

Information

Filter

Filter

Article Lookup

Enter a citation

Anisotropic field-induced changes in the superconducting order parameter of UTe2

Abstract

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (62)

Anisotropic field-induced changes in the superconducting order parameter of $UT e_{2}$