Single-Component Superconductivity in UTe₂ at Ambient Pressure

Determining the superconducting pairing symmetry is crucial for understanding Cooper pairing mechanisms and predicting topological states. While achieved for some materials (e.g., s-wave BCS superconductors, d-wave cuprates), it remains challenging for others, like Sr₂RuO₄. UTe₂ presents a particularly interesting case due to its extremely high upper critical field (*H*_c2) relative to its low critical temperature, suggesting unconventional superconductivity. The high *H*_c2 constrains the spin component to be spin-triplet and the orbital component to have odd parity. However, numerous possible odd-parity order parameters exist. The primary question addressed is the degeneracy of the orbital part: is it single- or multi-component? Evidence for a two-component order parameter arises from two distinct superconducting transitions in some samples and the onset of time-reversal symmetry breaking. This has led to proposals for exotic multi-component order parameters, potentially explaining observations like chiral surface states and anomalous conductivity. However, the appearance of only a single transition in higher-purity samples raises questions about the multi-component interpretation. Applying strain offers a way to distinguish between single- and multi-component order parameters, as only multi-component superconductors exhibit discontinuities in shear moduli due to additional degrees of freedom associated with the relative orientation and phase difference of the order parameters.

The literature review extensively discusses previous studies on UTe₂, highlighting conflicting results regarding the nature of its superconducting order parameter. Some studies reported two distinct superconducting transitions and time-reversal symmetry breaking, suggesting a multi-component order parameter. These findings supported proposals for exotic, multi-component states with topological structures. Other research, however, observed only a single transition in high-purity samples, challenging the multi-component interpretation. The review also covers different theoretical models proposed to explain these contradictory results. Existing studies exploring the effect of strain on UTe₂'s superconductivity were also discussed to support the experimental approach proposed in the current study.

The study employed pulse-echo ultrasound to measure the temperature dependence of six elastic moduli (three compressional and three shear) in three UTe₂ samples: one with two superconducting transitions and two with a single transition. The samples were carefully aligned and polished before the measurements. Thin-film ZnO piezoelectric transducers, capable of generating both shear and longitudinal sound waves, were used. Measurements were performed in a ³He refrigerator using a phase-comparison pulse-echo technique. The phase of each echo was analyzed to determine the relative change in speed of sound as a function of temperature, which was then converted to the relative change in elastic moduli. Specific heat measurements were also conducted on the double-transition sample using a quasi-adiabatic method. A quantitative analysis of the elastic moduli discontinuities was performed using Ehrenfest relations, which relate these discontinuities to the specific heat discontinuity and the derivative of the critical temperature with respect to strain. Density functional theory (DFT) calculations were performed to investigate the electronic structure and orbital character of UTe₂, and a tight-binding model was developed to capture the key features of the Fermi surface. These calculations aided in proposing a specific order parameter compatible with the experimental data.

The key finding is the absence of thermodynamic discontinuities in the shear elastic moduli for both single- and double-transition samples. This directly demonstrates that UTe₂ possesses a single-component superconducting order parameter. Discontinuities were observed in the compressional moduli, particularly c₃₃, consistent with all superconductors. The magnitude of the discontinuity in c₃₃ was similar in both single and double-transition samples, with the double-transition sample exhibiting two closely spaced discontinuities. Specific heat measurements confirmed the double-peak feature in the double-transition sample. The analysis of compressional moduli revealed that superconductivity is significantly more sensitive to strain along the *a* and *c* axes than along the *b* axis. Ehrenfest analysis quantitatively determined these strain sensitivities. DFT and tight-binding model calculations showed that the superconducting gap is either weak or absent on the tellurium-dominant electron Fermi surface. Based on the experimental findings and the calculated electronic structure, the authors propose that the single-component order parameter is most likely the B_2u representation, implying either *p_y* or *p_yz* wave superconductivity.

The absence of shear modulus discontinuities strongly refutes the multi-component order parameter hypothesis, ruling out all two-component scenarios that couple bilinearly to strain. This challenges interpretations of previous observations of time-reversal symmetry breaking and chiral surface states, which were attributed to a multi-component order parameter. The finding of a single-component order parameter in UTe₂, which also has an odd-parity, spin-triplet order parameter and point nodes in the superconducting gap, leaves only three possibilities (B_1u representations). The authors suggest the B_2u order parameter as the most likely candidate, based on the observed strain sensitivity and the calculated Fermi surface, with nodes along *k_y*. The insensitivity to strain along the *b* axis is attributed to the asymmetric crystal structure where strain affects the uranium-uranium distances more than the tellurium-tellurium distances. Future experiments that directly measure the gap nodes are needed to confirm this conclusion.

This study provides strong experimental evidence for a single-component, likely B_2u, superconducting order parameter in UTe₂. This challenges previous interpretations of UTe₂ as a multi-component superconductor and implies that phenomena such as time-reversal symmetry breaking may require re-evaluation. Future work should focus on directly determining the orientation of nodes in the superconducting gap to further confirm the proposed B_2u order parameter. The search for multi-component superconductors continues, but this work shows that existing interpretations should be revisited in light of more refined experimental data.

The study focuses on ambient pressure measurements. The behavior of UTe₂ under pressure, where multi-transition behavior has been reported, remains to be fully explored. Also, the relatively small size of the discontinuities observed in some elastic moduli might lead to some uncertainties in quantitative analysis, particularly concerning the less sensitive *b* axis. Further investigations might need to be carried out with improved measurement techniques to ascertain the findings. Additionally, the proposed B_2u order parameter is based on indirect evidence; direct measurements of the gap structure are needed for definitive confirmation.