Abstract
Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature Tc (ref. 1). Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin S = 0 (ref. 2), although they can also form parallel spin-triplet Cooper pairs with S = 1 and an odd parity wavefunction3. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation4,5. Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations3, uranium-based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity6. Indeed, UTe2, which has a Tc ≈ 1.6 K (refs. 7,8), has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability7,8,9,10,11,12,13,14, although it also has antiferromagnetic (AF) spin fluctuations15,16. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe2 is coupled to a sharp magnetic excitation, termed resonance17,18,19,20,21,22,23, at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability17,18,19,20,21,22,23, its observation in UTe2 suggests that AF spin fluctuations may also induce spin-triplet pairing24 or that electron pairing in UTe2 has a spin-singlet component.
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The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.
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Acknowledgements
P.D. thanks D. Natelson, W. P. Halperin, N. Butch and J. Paglione for discussions. E.M.N. and Q.S. acknowledge discussions with H. Hu, S. Paschen and J.-X. Zhu. The INS work at Rice is supported by the US DOE, BES under grant no. DE-SC0012311 (P.D.). Part of the material characterization efforts at Rice is supported by the Robert A. Welch Foundation grant nos C-1839 (P.D.). Work performed by R.E.B. at the National High Magnetic Field Laboratory was supported by National Science Foundation Cooperative Agreement No. DMR-1644779 and the State of Florida. Synthesis of crystalline materials and measurements by R.E.B. were supported by the Center for Actinide Science and Technology (CAST), an Energy Frontier Research Center (EFRC) funded by the US DOE, BES, under grant no. DE-SC0016568. Research at UC San Diego was supported by the US DOE, BES under grant no. DEFG02-04-ER46105 (single-crystal growth) and US NSF under grant no. DMR-1810310 (characterization of physical properties). The theory work at Rice has primarily been supported by the US DOE, BES under award no. DE-SC0018197, with travel support provided by the Robert A. Welch Foundation grant no. C-1411. Q.S. acknowledges the hospitality of the Aspen Center for Physics, which is supported by NSF grant no. PHY-1607611. E.M.N. was supported by an ASU startup grant. A portion of this research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by ORNL.
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P.D. and M.B.M. conceived the project. R.E.B. grew the single crystals and made specific-heat measurements on the crystals. The single crystals of UTe2 were aligned using Laue X-ray diffraction by C.D., Y.D., C.M. and A.J.B. and characterized by means of powder X-ray diffraction by C.M., A.J.B. and Y.D. at UCSD. The INS experiments were carried out by A.P. in remote discussion with C.D. and P.D. The data analysis was carried out by C.D. and P.D. E.M.N. and Q.S. contributed to the theoretical idea that AF spin fluctuations may facilitate spin-triplet superconductivity. The paper was written by P.D., C.D., R.E.B., E.M.N and Q.S., and all coauthors made comments on the paper.
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Extended data figures and tables
Extended Data Fig. 1 Pictures of the UTe2 single crystals used in the INS experiment.
a, A typical piece of UTe2 single crystal of 10 mm by 3 mm by 3 mm in size. The direction of the longest edge is the intersection of [1, 1, 0] plane and [0, 0, 1] plane. b, c, 27 pieces of UTe2 single crystals co-aligned on two oxygen-free Cu sample plates. The total mass is 0.9 grams.
Extended Data Fig. 2 Summary of temperature-dependent heat capacity C/T for single-crystal specimens of UTe2.
a, Comparison of C/T versus T for two representative crystals of UTe2. One crystal shows a single superconducting phase transition whereas the other shows two features. Several other crystals were measured, which all show similar behavior. b, The electronic component of the heat capacity Ce/T, which was obtained by subtracting the low temperature phonon heat capacity βT2, which was obtained by fitting the data for T > Tc using the expression C/T = γ + βT2. The normal state electronic coefficient of the heat capacity γ is indicated by the horizontal dotted blue line. An equal entropy construction is also indicated by dotted blue lines to determine Tc and the ideal size of the heat-capacity jump ΔC/Tc.
Extended Data Fig. 3 X-ray Laue pattern of the [0, 0, 1] plane of UTe2.
Pattern is shown for one of the samples used in the experiment.
Extended Data Fig. 4 Unsymmetrized raw data in the [H, K, 0] plane with Ei = 3.32 meV.
a–l, Constant-energy cuts of the unsymmetrized S(Q, E) with Ei = 3.32 meV at (a) 0.0 ± 0.1 meV and BT, (b) 0.0 ± 0.1 meV and 2 K, (c) 0.4 ± 0.1 meV and BT, (d) 0.4 ± 0.1 meV and 2 K, (e) 0.7 ± 0.1 meV and BT, (f) 0.7 ± 0.1 meV and 2 K, (g) 1.0 ± 0.1 meV and BT, (h) 1.0 ± 0.1 meV and 2 K, (i) 1.5 ± 0.1 meV and BT, (j) 1.5 ± 0.1 meV and 2 K, (k) 2.0 ± 0.1 meV and BT, (l) 2.0 ± 0.1meV and 2 K. The bin size is 0.035 r.l.u. along both H and K. The integration range is ±0.2 r.l.u. in L, and ±0.1 meV in E. The unit of the colour bars in Extended Data Figs. 4, 5, 6 is the same as that of Fig. 2b.
Extended Data Fig. 5 Unsymmetrized raw data in the [H, K, 0] plane with Ei = 12 meV.
a–d, Constant energy cuts of the unsymmetrized S(Q, E) with Ei = 12 meV and BT at (a) 0.0 ± 0.5 meV, (b) 3.25 ± 0.25 meV, (c) 5.25 ± 0.25 meV, (d) 7.25 ± 0.25 meV. The bin size is 0.04 r.l.u. along both H and K. The integration range is ±0.2 r.l.u. in L, and ±0.25 meV in E. The rings of scattering in a are from the nuclear (1, 1, 1) and (2, 0, 0) Bragg peaks of the Cu sample holder.
Extended Data Fig. 6 Unsymmetrized raw data, E–Q plots and one-dimensional energy cuts with Ei = 2.5 meV.
a–d, Constant energy cuts of the unsymmetrized S(Q, E) with Ei = 2.5 meV at (a) 0.25 to 0.3 meV and BT, (b) 0.25 to 0.3 meV and 3.5 K, (c) 1.05 to 1.1 meV and BT, (d) 1.05 to 1.1 meV and 3.5 K. The bin size is 0.02 r.l.u. along H and 0.03 r.l.u. along K. The integration range is ±0.3 r.l.u. in L. e, f, E–Q plots of the scattering function S(Q, E) with Ei = 2.5 meV at BT (e) and 3.5 K (f), respectively. The integration range is ±0.08 r.l.u. in H and ±0.3 r.l.u. in L, the bin size along K is 0.03 r.l.u., and the E step is 0.03 meV. g, One-dimensional cuts of the scattering function S(Q) with high temperature data (SHT(Q)) subtracted. The cuts are taken at Y1 along E taken at BT (blue), 0.4 K (red), 0.8 K (yellow), 1.2 K (purple), and 1.5 K (green) with Ei = 2.5 meV. The high-temperature data are taken at 3.5 K. At low energy the excitation at Y1 is not fully covered with this Ei, which causes the gap feature between 0.2 to 0.7 meV to be hard to observe in the subtracted one-dimensional data. Different temperature data in g are artificially shifted, with the dashed black line representing the base line for each temperature. The integration ranges in g are: ±0.08 r.l.u. in H, ±0.15 r.l.u. in K, and ±0.3 r.l.u. in L. The bin size in E is 0.04 meV.
Extended Data Fig. 7 Temperature dependence of the excitations at different Q positions.
a, b, One-dimensional cuts of S(E) with Ei = 3.32 meV at Bragg peak (1, −1, 0) along E at BT and 2 K, respectively. Incoherent background scattering integrated at Qbkg is plotted in green triangles. There are no FM spin fluctuation signals observed above the background. The broad peak around E = 0.7 meV is powder ring of scattering not associated with UTe2 (see Extended Data Fig. 4e, g). (c) One-dimensional cuts of S(E) with Ei = 3.32 meV at Y1 along E at 1.5, 1.8, and 2 K. There is no significant change in the quasielastic energy range for temperature close to and above Tc. d, e, One-dimensional cuts of S(E) with Ei = 3.32 meV (d) and 2.5 meV (e), respectively. The subtle increase of S(E) above Tc near 1.4 meV with Ei = 3.32 meV is just above one standard deviation, and is not observed with Ei = 2.5 meV. The integration ranges of the one-dimensional data in d, e are: ±0.1 r.l.u. in H, ±0.15 r.l.u. in K, and ±0.3 r.l.u. in L. The bin size in E is 0.04 meV.
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Duan, C., Baumbach, R.E., Podlesnyak, A. et al. Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2. Nature 600, 636–640 (2021). https://doi.org/10.1038/s41586-021-04151-5
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DOI: https://doi.org/10.1038/s41586-021-04151-5
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