Single-Component Superconductivity in UTe₂ at Ambient Pressure

The pairing symmetry in unconventional superconductors constrains microscopic pairing mechanisms and can yield topological superconducting states. UTe₂ exhibits extremely high upper critical fields and other signatures consistent with spin-triplet, odd-parity superconductivity, but the detailed symmetry of its order parameter has been debated. Prior reports of two superconducting transitions and time-reversal symmetry breaking suggested a multi-component order parameter. More recent, higher-purity samples often show a single transition at ambient pressure, raising questions about the earlier interpretation. The central research question is whether UTe₂ hosts a single-component or multi-component superconducting order parameter. Because multi-component order parameters couple to shear strains (leading to discontinuities in shear elastic moduli at Tc), while single-component order parameters do not, measuring elastic moduli across Tc provides a direct and symmetry-based probe of order parameter degeneracy and structure.

Previous studies reported evidence for unconventional superconductivity in UTe₂, including large Hc2, power-law thermodynamics, and possible time-reversal symmetry breaking at Tc. Two distinct superconducting transitions observed in some samples and under pressure led to proposals of multi-component order parameters (e.g., combinations of odd-parity representations such as {B2u, B3u}). STM, microwave impedance, Kerr effect, penetration depth, and NMR studies have been interpreted within various one- and two-component scenarios, some with chiral or nonunitary character. However, improved sample quality has often yielded a single thermodynamic transition, and some works suggested inhomogeneity as a cause of split transitions at ambient pressure. Table I in the paper summarizes proposed odd-parity order parameters, their dimensionality, and whether they predict shear discontinuities. The lack of a definitive order-parameter assignment from prior measurements motivates a direct elastic-modulus-based thermodynamic probe.

- Samples and transitions: Three UTe₂ single crystals were studied: S1 and S2 (single Tc ≈ 1.63 K and 1.70 K, respectively) and S3 (double Tc with Tc1 ≈ 1.64 K and Tc2 ≈ 1.60 K). - Technique: Phase-comparison pulse-echo ultrasound measurements of temperature-dependent elastic moduli were performed from ~1.3 K to ~1.9 K in an Oxford Instruments Heliox 3He refrigerator. Carrier frequencies ranged from ~500 MHz to 2.5 GHz. - Elastic moduli measured: All three compressional moduli (C11, C22, C33) and all three shear moduli (C44, C55, C66) were measured across Tc. Shear and compressional echoes were separated in time by their different velocities and identified with known mode velocities. - Transducers: Thin-film ZnO piezoelectric transducers were sputtered, providing both shear and longitudinal responses. Shear axes were aligned with crystallographic directions, verified via speed of sound and comparison with resonant ultrasound spectroscopy. - Sample preparation: Single crystals grown by chemical vapor transport; oriented via magnetic anisotropy and Laue diffraction; polished to produce parallel faces normal to (100), (010), and (001) as required by mode geometry. - Data analysis: The change in elastic modulus relative to the highest measured temperature T0 was tracked (Δc/c). Step discontinuities at Tc were identified by fitting polynomial backgrounds above and below Tc. Noise was estimated by RMS of background-subtracted normal-state data. An Ehrenfest analysis related modulus jumps δcij to the heat-capacity jump ΔC/T and dTc/dεij, enabling extraction of strain derivatives of Tc. Heat capacity was measured quasi-adiabatically on S3 to obtain ΔC/T at Tc. Consistency checks included echo selection and frequency dependence; no significant dependence was found.

- Shear moduli: No thermodynamic discontinuities in any shear elastic modulus (C44, C55, C66) were observed at Tc in either single- or double-transition samples, within a sensitivity of a few parts in 10^7. This directly rules out uniform-parity, multi-component superconducting order parameters at ambient pressure. - Compressional moduli: Clear step discontinuities at Tc were seen in compressional moduli: • C33: ~40 parts per million (ppm) step in single-Tc samples; in the double-Tc sample, two distinct C33 discontinuities separated by ~40 mK whose sum matches the single-Tc discontinuity. • C11: ~20 ppm step (about half of C33). • C22: at most ~1 ppm step, much smaller than C11 and C33. - Single vs double transitions: The absence of shear jumps in the double-Tc sample, together with the additivity of C33 jumps across the two transitions, indicates a single-component order parameter and suggests the two transitions share a common origin (e.g., local strain or impurities) rather than distinct superconducting states. - Strain sensitivity (Ehrenfest analysis): Using ΔC/T ≈ 196 ± 18 mJ/(mol K^2) and measured δc/c, the derivatives of Tc with respect to uniaxial strain were extracted (signs inferred from uniaxial stress literature): • dTc/dεxx ≈ −0.23 ± 0.02 K/% strain (from C11) • dTc/dεyy ≈ −0.07 ± 0.02 K/% strain (from C22) • dTc/dεzz ≈ +0.34 ± 0.02 K/% strain (from C33) This shows superconductivity is strongly sensitive to a- and c-axis compression, but comparatively insensitive to b-axis strain. - Order parameter assignment: Combining symmetry constraints (no shear jumps) with nodal evidence from prior works and the observed anisotropic strain sensitivity, the data favor a single-component, odd-parity B2u representation (e.g., p_y or p_yz), with point nodes oriented along k_y and a larger gap on uranium-dominant Fermi-surface sheets than on tellurium-dominant ones.

The lack of shear-modulus discontinuities at Tc constitutes thermodynamic evidence for a single-component order parameter in UTe₂ at ambient pressure, ruling out multi-component uniform-parity scenarios that would couple bilinearly to shear strain. This conclusion holds for both single- and double-transition samples; the double C33 jump additivity implies a common superconducting state below the lower transition, consistent with inhomogeneous strain or impurity-induced splitting rather than two distinct order parameters. Considering strong evidence for odd-parity, spin-triplet pairing and nodal behavior, and the pronounced sensitivity of Tc to a- and c-axis strains compared to b-axis strain, a single-component B2u order parameter is most compatible with the data. This assignment is further motivated by the Fermi-surface topology and orbital content: uranium-chain dominated sheets are likely more strongly coupled to superconductivity than tellurium-chain dominated ones. The single-component conclusion also constrains interpretations of reported time-reversal symmetry breaking signals and chiral surface states, suggesting these observations may need reevaluation or could arise under different conditions (e.g., under pressure) where multi-component states might emerge.

Ultrasound measurements of all six elastic moduli across Tc in UTe₂ reveal discontinuities in compressional moduli but none in shear moduli for both single- and double-transition samples. This symmetry-based thermodynamic result demonstrates a single-component superconducting order parameter at ambient pressure. Ehrenfest analysis shows Tc is most sensitive to a- and c-axis compression and weakly sensitive to b-axis strain. Considering prior evidence for odd parity and nodal gaps, the findings strongly suggest a single-component B2u order parameter (e.g., p_y or p_yz). Future work should directly determine the nodal orientation and investigate whether pressure or other tuning parameters can stabilize multi-component states that might reconcile reports of time-reversal symmetry breaking and chiral signatures.

- The study focuses on ambient pressure; under hydrostatic pressure, UTe₂ often exhibits two transitions, and a multi-component order parameter may emerge in that regime. - While shear-modulus discontinuities would indicate multi-component order, their absence only rules out bilinear shear coupling; mixed-parity states (e.g., s + ip) that avoid shear jumps cannot be fully excluded, though they lack experimental support here. - Exact node orientation is inferred indirectly; direct phase-sensitive or momentum-resolved gap measurements would be required for definitive confirmation. - The origin of two sharp transitions in some ambient-pressure samples remains unresolved (local strain or impurities are suggested), and why only two transitions typically appear rather than a distribution is an open question. - Affiliation of certain coauthors is not explicitly tagged in the provided text, but does not affect scientific conclusions.