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1. Thermal conductivity of nonunitary triplet superconductors: application to UTe2

   https://doi.org/10.3389/fphy.2024.1397524  

   Mishra, Vivek; Wang, Ge; Hirschfeld, P J (June 2024, Frontiers in Physics)

   Considerable evidence shows that the heavy fermion material UTe₂is a spin-triplet superconductor, possibly manifesting time-reversal symmetry breaking, as measured by Kerr effect below the critical temperature, in some samples. Such signals can arise due to a chiral orbital state or possible nonunitary pairing. Although experiments at low temperatures appear to be consistent with point nodes in the spectral gap, the detailed form of the order parameter and even the nodal positions are not yet determined. Thermal conductivity measurements can extend to quite low temperatures, and varying the heat current direction should be able to provide information on the order parameter structure. Here, we derive a general expression for the thermal conductivity of a spin-triplet superconductor and use it to compare the low-temperature behavior of various states proposed for UTe₂. 

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2. Pair wave function symmetry in UTe ₂ from zero-energy surface state visualization

   https://doi.org/10.1126/science.adk7219  

   Gu, Qiangqiang; Wang, Shuqiu; Carroll, Joseph P; Zhussupbekov, Kuanysh; Broyles, Christopher; Ran, Sheng; Butch, Nicholas P; Horn, Jarryd A; Saha, Shanta; Paglione, Johnpierre; et al (May 2025, Science)

   Although nodal spin-triplet topological superconductivity appears probable in uranium ditelluride (UTe₂), its superconductive order parameter Δ_kremains unestablished. In theory, a distinctive identifier would be the existence of a superconductive topological surface band, which could facilitate zero-energy Andreev tunneling to an s-wave superconductor and also distinguish a chiral from a nonchiral Δ_kthrough enhanced s-wave proximity. In this study, we used s-wave superconductive scan tips and detected intense zero-energy Andreev conductance at the UTe₂(0-11) termination surface. Imaging revealed subgap quasiparticle scattering interference signatures witha-axis orientation. The observed zero-energy Andreev peak splitting with enhanced s-wave proximity signifies that Δ_kof UTe₂is a nonchiral state:B_1u,B_2u, orB_3u. However, if the quasiparticle scattering along theaaxis is internodal, then a nonchiralB_3ustate is the most consistent for UTe₂. 

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3. Evidence for even parity unconventional superconductivity in Sr ₂ RuO ₄

   https://doi.org/10.1073/pnas.2025313118  

   Chronister, Aaron; Pustogow, Andrej; Kikugawa, Naoki; Sokolov, Dmitry A.; Jerzembeck, Fabian; Hicks, Clifford W.; Mackenzie, Andrew P.; Bauer, Eric D.; Brown, Stuart E. (June 2021, Proceedings of the National Academy of Sciences)

   Unambiguous identification of the superconducting order parameter symmetry in ${\text{Sr}}_2{\text{RuO}}_4$has remained elusive for more than a quarter century. While a chiral p-wave ground state analogue to superfluid³He-A was ruled out only very recently, other proposed triplet-pairing scenarios are still viable. Establishing the condensate magnetic susceptibility reveals a sharp distinction between even-parity (singlet) and odd-parity (triplet) pairing since the superconducting condensate is magnetically polarizable only in the latter case. Here field-dependent¹⁷O Knight shift measurements, being sensitive to the spin polarization, are compared to previously reported specific heat measurements for the purpose of distinguishing the condensate contribution from that due to quasiparticles. We conclude that the shift results can be accounted for entirely by the expected field-induced quasiparticle response. An upper bound for the condensate magnetic response of <10% of the normal state susceptibility is sufficient to exclude all purely odd-parity candidates. 

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4. Anomalous normal fluid response in a chiral superconductor UTe2

   https://doi.org/10.1038/s41467-021-22906-6  

   Bae, Seokjin; Kim, Hyunsoo; Eo, Yun Suk; Ran, Sheng; Liu, I-lin; Fuhrman, Wesley T.; Paglione, Johnpierre; Butch, Nicholas P.; Anlage, Steven M. (May 2021, Nature Communications)

   Abstract Chiral superconductors have been proposed as one pathway to realize Majorana normal fluid at its boundary. However, the long-sought 2D and 3D chiral superconductors with edge and surface Majorana normal fluid are yet to be conclusively found. Here, we report evidence for a chiral spin-triplet pairing state of UTe₂with surface normal fluid response. The microwave surface impedance of the UTe₂crystal was measured and converted to complex conductivity, which is sensitive to both normal and superfluid responses. The anomalous residual normal fluid conductivity supports the presence of a significant normal fluid response. The superfluid conductivity follows the temperature behavior predicted for an axial spin-triplet state, which is further narrowed down to a chiral spin-triplet state with evidence of broken time-reversal symmetry. Further analysis excludes trivial origins for the observed normal fluid response. Our findings suggest that UTe₂can be a new platform to study exotic topological excitations in higher dimension. 

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5. Inhomogeneous high temperature melting and decoupling of charge density waves in spin-triplet superconductor UTe2

   https://doi.org/10.1038/s41467-024-48844-7  

   LaFleur, Alexander; Li, Hong; Frank, Corey E; Xu, Muxian; Cheng, Siyu; Wang, Ziqiang; Butch, Nicholas P; Zeljkovic, Ilija (May 2024, Nature Communications)

   Abstract Charge, spin and Cooper-pair density waves have now been widely detected in exotic superconductors. Understanding how these density waves emerge — and become suppressed by external parameters — is a key research direction in condensed matter physics. Here we study the temperature and magnetic-field evolution of charge density waves in the rare spin-triplet superconductor candidate UTe₂using scanning tunneling microscopy/spectroscopy. We reveal that charge modulations composed of three different wave vectors gradually weaken in a spatially inhomogeneous manner, while persisting to surprisingly high temperatures of 10–12 K. We also reveal an unexpected decoupling of the three-component charge density wave state. Our observations match closely to the temperature scale potentially related to short-range magnetic correlations, providing a possible connection between density waves observed by surface probes and intrinsic bulk features. Importantly, charge density wave modulations become suppressed with magnetic field both below and above superconductingT_cin a comparable manner. Our work points towards an intimate connection between hidden magnetic correlations and the origin of the unusual charge density waves in UTe₂. 

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