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Spin-triplet superconductors potentially host topological excitations that are of interest for quantum information processing. We report the discovery of spin-triplet superconductivity in UTe₂, featuring a transition temperature of 1.6 kelvin and a very large and anisotropic upper critical field exceeding 40 teslas. This superconducting phase stability suggests that UTe₂ is related to ferromagnetic superconductors such as UGe₂, URhGe, and UCoGe. However, the lack of magnetic order and the observation of quantum critical scaling place UTe₂ at the paramagnetic end of this ferromagnetic superconductor series. A large intrinsic zero-temperature reservoir of ungapped fermions indicates a highly unconventional type of superconducting pairing.

Spin-triplet topological superconductors should exhibit many unprecedented electronic properties, including fractionalized electronic states relevant to quantum information processing. Although UTe 2 may embody such bulk topological superconductivity 1 – 11 , its superconductive order parameter Δ( k ) remains unknown 12 . Many diverse forms for Δ( k ) are physically possible 12 in such heavy fermion materials 13 . Moreover, intertwined 14 , 15 density waves of spin (SDW), charge (CDW) and pair (PDW) may interpose, with the latter exhibiting spatially modulating 14 , 15 superconductive order parameter Δ( r ), electron-pair density 16 – 19 and pairing energy gap 17 , 20 – 23 . Hence, the newly discovered CDW state 24 in UTe 2 motivates the prospect that a PDW state may exist in this material 24 , 25 . To search for it, we visualize the pairing energy gap with μeV-scale energy resolution using superconductive scanning tunnelling microscopy (STM) tips 26 – 31 . We detect three PDWs, each with peak-to-peak gap modulations of around 10 μeV and at incommensurate wavevectors P i =1,2,3 that are indistinguishable from the wavevectors Q i =1,2,3 of the prevenient 24 CDW. Concurrent visualization of the UTe 2 superconductive PDWs and the non-superconductive CDWs shows that every P i : Q i pair exhibits a relative spatial phase δϕ  ≈ π. From these observations, and given UTe 2 as a spin-triplet superconductor 12 , this PDW state should be a spin-triplet PDW 24 , 25 . Although such states do exist 32 in superfluid 3 He, for superconductors, they are unprecedented. A spin-triplet pair density wave is discovered in the candidate topological superconductor UTe 2 using superconductive scanning tunnelling microscopy tips.

The intense interest in triplet superconductivity partly stems from theoretical predictions of exotic excitations such as non-Abelian Majorana modes, chiral supercurrents and half-quantum vortices 1 – 4 . However, fundamentally new and unexpected states may emerge when triplet superconductivity appears in a strongly correlated system. Here we use scanning tunnelling microscopy to reveal an unusual charge-density-wave (CDW) order in the heavy-fermion triplet superconductor UTe 2 (refs.  5 – 8 ). Our high-resolution maps reveal a multi-component incommensurate CDW whose intensity gets weaker with increasing field, with the CDW eventually disappearing at the superconducting critical field H c2 . To understand the phenomenology of this unusual CDW, we construct a Ginzburg–Landau theory for a uniform triplet superconductor coexisting with three triplet pair-density-wave states. This theory gives rise to daughter CDWs that would be sensitive to magnetic field owing to their origin in a pair-density-wave state and provides a possible explanation for our data. Our discovery of a CDW state that is sensitive to magnetic fields and strongly intertwined with superconductivity provides important information for understanding the order parameters of UTe 2 . A study using scanning tunnelling microscopy reveals a charge-density-wave state that is sensitive to magnetic fields and strongly intertwined with superconductivity in the heavy-fermion triplet superconductor UTe 2 .

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 UTe 2 with surface normal fluid response. The microwave surface impedance of the UTe 2 crystal 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 UTe 2 can be a new platform to study exotic topological excitations in higher dimension. Chiral superconductors are predicted to realize Majorana normal fluid at its boundary, but remain elusive experimentally. Here, Bae et al. report anomalous surface normal fluid response in UTe 2 single crystal which is further attributed to a chiral spin-triplet pairing state.

Reentrant superconductivity is an uncommon phenomenon in which the destructive effects of magnetic field on superconductivity are mitigated, allowing a zero-resistance state to survive under conditions that would otherwise destroy it. Typically, the reentrant superconducting region derives from a zero-field parent superconducting phase. Here, we show that in UTe 2 crystals extreme applied magnetic fields give rise to an unprecedented high-field superconductor that lacks a zero-field antecedent. This high-field orphan superconductivity exists at angles offset between 29 o and 42 o from the crystallographic b to c axes with applied fields between 37 T and 52 T. The stability of field-induced orphan superconductivity presented in this work defies both empirical precedent and theoretical explanation and demonstrates that high-field superconductivity can exist in an otherwise non-superconducting material. In addition to its low-field superconducting state, UTe 2 features a re-entrant superconducting state when high magnetic fields are applied at a particular range of angles. Here, the authors demonstrate that the high-field re-entrant superconducting state survives even when the low-field superconducting state is destroyed by disorder.

Despite their name, the bulk electrical conductivity of most topological insulators is relatively high, masking many of the important characteristics of its protected, surface conducting states. Counter-doping reduces the bulk conductivity of Bi 2 Se 3 significantly, allowing these surface states and their properties to be clearly identified. The newly discovered three-dimensional strong topological insulators (STIs) exhibit topologically protected Dirac surface states 1 , 2 . Although the STI surface state has been studied spectroscopically, for example, by photoemission 3 , 4 , 5 and scanned probes 6 , 7 , 8 , 9 , 10 , transport experiments 11 , 12 , 13 , 14 , 15 , 16 , 17 have failed to demonstrate the most fundamental signature of the STI: ambipolar metallic electronic transport in the topological surface of an insulating bulk. Here we show that the surfaces of thin (∼ 10 nm), low-doped Bi 2 Se 3 (≈10 17  cm −3 ) crystals are strongly electrostatically coupled, and a gate electrode can completely remove bulk charge carriers and bring both surfaces through the Dirac point simultaneously. We observe clear surface band conduction with a linear Hall resistivity and a well-defined ambipolar field effect, as well as a charge-inhomogeneous minimum conductivity region 18 , 19 , 20 . A theory of charge disorder in a Dirac band 19 , 20 , 21 explains well both the magnitude and the variation with disorder strength of the minimum conductivity (2 to 5 e 2 / h per surface) and the residual (puddle) carrier density (0.4×10 12 to 4×10 12  cm −2 ). From the measured carrier mobilities 320–1,500 cm 2  V −1  s −1 , the charged impurity densities 0.5×10 13 to 2.3×10 13  cm −2 are inferred. They are of a similar magnitude to the measured doping levels at zero gate voltage (1×10 13 to 3×10 13  cm −2 ), identifying dopants as the charged impurities.

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 UTe 2 using 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 superconducting T c in a comparable manner. Our work points towards an intimate connection between hidden magnetic correlations and the origin of the unusual charge density waves in UTe 2 . Understanding the physics of charge density waves in emerging superconductors may reveal insights into unconventional superconductivity mechanisms. Here, the authors study the temperature and magnetic-field dependence of charge-density-wave suppression in the unconventional superconductor UTe 2 .

The two-dimensional surface of the three-dimensional topological insulator is in the symplectic universality class and should exhibit perfect weak antilocalization reflected in positive weak-field magneto-resistance. Previous studies in topological insulator thin films suffer from high level of bulk n -type doping making quantitative analysis of weak antilocalization difficult. Here we measure the magneto-resistance of bulk-insulating Bi 2 Se 3 thin films as a function of film thickness and gate-tuned carrier density. For thick samples, the magnitude of weak antilocalization indicates two decoupled (top and bottom) symplectic surfaces. On reducing thickness, we observe first a crossover to a single symplectic channel, indicating coherent coupling of top and bottom surfaces via interlayer tunnelling, and second, a complete suppression of weak antilocalization. The first crossover is governed by the ratio of phase coherence time to the inter-surface tunnelling time, and the second crossover occurs when the hybridization gap becomes comparable to the disorder strength. Weak antilocalization is a signifier of electrical transport via topologically non-trivial surface states of a topological insulator, but it is often masked by dopant-induced scattering. Kim et al. overcome such difficulties to identify coherent transport via the topological surface states of bismuth selenide.

The Ising model—in which degrees of freedom (spins) are binary valued (up/down)—is a cornerstone of statistical physics that shows rich behaviour when spins occupy a highly frustrated lattice such as kagome. Here we show that the layered Ising magnet Dy 3 Mg 2 Sb 3 O 14 hosts an emergent order predicted theoretically for individual kagome layers of in-plane Ising spins. Neutron-scattering and bulk thermomagnetic measurements reveal a phase transition at ∼0.3 K from a disordered spin-ice-like regime to an emergent charge ordered state, in which emergent magnetic charge degrees of freedom exhibit three-dimensional order while spins remain partially disordered. Monte Carlo simulations show that an interplay of inter-layer interactions, spin canting and chemical disorder stabilizes this state. Our results establish Dy 3 Mg 2 Sb 3 O 14 as a tuneable system to study interacting emergent charges arising from kagome Ising frustration. Frustration in lattices of interacting spins can lead to rich and exotic physics, such as fractionalized excitations and emergent order. Here, the authors demonstrate a low-temperature transition from a disordered spin-ice-like phase to an emergent charge ordered phase in the bulk kagome Ising magnet Dy 3 Mg 2 Sb 3 O 14 .

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice materialHo3Mg2Sb3O14unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of theHo3+ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition atT*≈0.32Kto a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down toT≈0.12K. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. InHo3Mg2Sb3O14, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.