Enhancement and reentrance of spin triplet superconductivity in UTe2 under pressure

Resonant Ultrasound Spectroscopy for Irregularly Shaped Samples and Its Application to Uranium Ditelluride

Resonant ultrasound spectroscopy (RUS) is a powerful technique for measuring the full elastic tensor of a given material in a single experiment. Previously, this technique was practically limited to regularly shaped samples such as rectangular parallelepipeds, spheres, and cylinders [W. M. Visscher et al. J. Acoust. Soc. Am. 90, 2154 (1991)JASMAN0001-496610.1121/1.401643]. We demonstrate a new method for determining the elastic moduli of irregularly shaped samples, extending the applicability of RUS to a much larger set of materials. We apply this new approach to the recently discovered unconventional superconductor UTe_{2} and provide its elastic tensor at both 300 and 4 kelvin.

A review of UTe2at high magnetic fields

Uranium ditelluride (UTe2) is recognized as a host material to unconventional spin-triplet superconductivity, but it also exhibits a wealth of additional unusual behavior at high magnetic fields. One of the most prominent signatures of the unconventional superconductivity is a large and anisotropic upper critical field that exceeds the paramagnetic limit. This superconductivity survives to 35 T and is bounded by a discontinuous magnetic transition, which itself is also field-direction-dependent. A different, reentrant superconducting phase emerges only on the high-field side of the magnetic transition, in a range of angles between the crystallographicbandcaxes. This review discusses the current state of knowledge of these high-field phases, the high-field behavior of the heavy fermion normal state, and other phases that are stabilized by applied pressure.

Superconducting spin reorientation in spin-triplet multiple superconducting phases of UTe2

Superconducting (SC) state has spin and orbital degrees of freedom, and spin-triplet superconductivity shows multiple SC phases because of the presence of these degrees of freedom. However, the observation of spin-direction rotation occurring inside the SC state (SC spin rotation) has hardly been reported. Uranium ditelluride, a recently found topological superconductor, exhibits various SC phases under pressure: SC state at ambient pressure (SC1), high-temperature SC state above 0.5 gigapascal (SC2), and low-temperature SC state above 0.5 gigapascal (SC3). We performed nuclear magnetic resonance (NMR) and ac susceptibility measurements on a single-crystal uranium ditelluride. The b axis spin susceptibility remains unchanged in SC2, unlike in SC1, and decreases below the SC2-SC3 transition with spin modulation. These unique properties in SC3 arise from the coexistence of two SC order parameters. Our NMR results confirm spin-triplet superconductivity with SC spin parallel to b axis in SC2 and unveil the remaining of spin degrees of freedom in SC uranium ditelluride.

Revealing a 3D Fermi Surface Pocket and Electron-Hole Tunneling in UTe_{2} with Quantum Oscillations

Spin triplet superconductor UTe_{2} is widely believed to host a quasi-two-dimensional Fermi surface, revealed by first-principles calculations, photoemission, and quantum oscillation measurements. An outstanding question still remains as to the existence of a three-dimensional Fermi surface pocket, which is crucial for our understanding of the exotic superconducting and topological properties of UTe_{2}. This 3D Fermi surface pocket appears in various theoretical models with different physics origins, but has not been unambiguously detected in experiment. Here for the first time we provide concrete evidence for a relatively isotropic, small Fermi surface pocket of UTe_{2} via quantum oscillation measurements. In addition, we observed high frequency quantum oscillations corresponding to electron-hole tunneling between adjacent electron and hole pockets. The coexistence of 2D and 3D Fermi surface pockets, as well as the breakdown orbits, provide a test bed for theoretical models and aid the realization of a unified understanding of the superconducting state of UTe_{2} from the first-principles approach.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Field Induced Multiple Superconducting Phases in UTe_{2} along Hard Magnetic Axis

The superconducting (SC) phase diagram in uranium ditelluride is explored under magnetic fields (H) along the hard magnetic b axis using a high-quality single crystal with T_{c}=2.1  K. Simultaneous electrical resistivity and ac magnetic susceptibility measurements discern low- and high-field SC (LFSC and HFSC, respectively) phases with contrasting field-angular dependence. Crystal quality increases the upper critical field of the LFSC phase, but the H^{*} of ∼15  T, at which the HFSC phase appears, is always the same through the various crystals. A phase boundary signature is also observed inside the LFSC phase near H^{*}, indicating an intermediate SC phase characterized by small flux pinning forces.

Unconventional superconductivity in UTe2

The novel spin-triplet superconductor candidate UTe₂was discovered only recently at the end of 2018 and already attracted enormous attention. We review key experimental and theoretical progress which has been achieved in different laboratories. UTe₂is a heavy-fermion paramagnet, but following the discovery of superconductivity, it has been expected to be close to a ferromagnetic instability, showing many similarities to the U-based ferromagnetic superconductors, URhGe and UCoGe. This view might be too simplistic. The competition between different types of magnetic interactions and the duality between the local and itinerant character of the 5fUranium electrons, as well as the shift of the U valence appear as key parameters in the rich phase diagrams discovered recently under extreme conditions like low temperature, high magnetic field, and pressure. We discuss macroscopic and microscopic experiments at low temperature to clarify the normal phase properties at ambient pressure for field applied along the three axis of this orthorhombic structure. Special attention will be given to the occurrence of a metamagnetic transition atH_m= 35 T for a magnetic field applied along the hard magnetic axisb. Adding external pressure leads to strong changes in the magnetic and electronic properties with a direct feedback on superconductivity. Attention is paid on the possible evolution of the Fermi surface as a function of magnetic field and pressure. Superconductivity in UTe₂is extremely rich, exhibiting various unconventional behaviors which will be highlighted. It shows an exceptionally huge superconducting upper critical field with a re-entrant behavior under magnetic field and the occurrence of multiple superconducting phases in the temperature-field-pressure phase diagrams. There is evidence for spin-triplet pairing. Experimental indications exist for chiral superconductivity and spontaneous time reversal symmetry breaking in the superconducting state. Different theoretical approaches will be described. Notably we discuss that UTe₂is a possible example for the realization of a fascinating topological superconductor. Exploring superconductivity in UTe₂reemphasizes that U-based heavy fermion compounds give unique examples to study and understand the strong interplay between the normal and superconducting properties in strongly correlated electron systems.

Evidence for a pressure-induced antiferromagnetic quantum critical point in intermediate-valence UTe2

UTe2 is a recently discovered unconventional superconductor that has attracted much interest because of its potentially spin-triplet topological superconductivity. Our ac calorimetry, electrical resistivity, and x-ray absorption study of UTe2 under applied pressure reveals key insights on the superconducting and magnetic states surrounding pressure-induced quantum criticality at P c1 = 1.3 GPa. First, our specific heat data at low pressures, combined with a phenomenological model, show that pressure alters the balance between two closely competing superconducting orders. Second, near 1.5 GPa, we detect two bulk transitions that trigger changes in the resistivity, which are consistent with antiferromagnetic order, rather than ferromagnetism. Third, the emergence of magnetism is accompanied by an increase in valence toward a U4+ (5f 2) state, which indicates that UTe2 exhibits intermediate valence at ambient pressure. Our results suggest that antiferromagnetic fluctuations may play a more substantial role on the superconducting state of UTe2 than previously thought.

Composition dependence of the superconducting properties of UTe2

A better understanding of the synthesis conditions, composition and physical properties of UTe2are required to interpret previously reported unconventional superconductivity. Here we report how the superconducting properties of single crystals depend on the ratio of elements present in their synthesis by chemical vapour transport. We have obtained crystals with the highest reported ambient pressureTcand a larger superconducting heat capacity jump from a growth with a U:Te ratio different from that widely used in the literature. For these crystals, the ratio of residual heat capacity in the superconducting state to that of the normal state,γ*/γN, is significantly lower than 0.5, reported elsewhere. An upturn in the heat capacity below 200 mK is also reduced compared to other studies and is well described by a Schottky anomaly and residual Sommerfeld term rather than quantum critical behaviour.

Enhancement and reentrance of spin triplet superconductivity in UTe2 under pressure

Spin triplet superconductivity in the Kondo lattice UTe2 appears to be associated with spin fluctuations originating from incipient ferromagnetic order. Here we show clear evidence of twofold enhancement of superconductivity under pressure, which discontinuously transitions to magnetic order, likely of ferromagnetic nature, at higher pressures. The application of a magnetic field tunes the system back across a first-order phase boundary. Straddling this phase boundary, we find another example of reentrant superconductivity in UTe2. As the superconductivity and magnetism exist on two opposite sides of the first-order phase boundary, our results indicate other microscopic mechanisms may be playing a role in stabilizing spin triplet superconductivity in addition to spin fluctuations associated with magnetism.