Resonance from antiferromagnetic spin fluctuations for superconductivity in UTe2.

Superconductivity originates from the formation of bound (Cooper) pairs of electrons that can move through the lattice without resistance below the superconducting transition temperature Tc (ref. 1). Electron Cooper pairs in most superconductors form anti-parallel spin singlets with total spin S = 0 (ref. 2), although they can also form parallel spin-triplet Cooper pairs with S = 1 and an odd parity wavefunction3. Spin-triplet pairing is important because it can host topological states and Majorana fermions relevant for quantum computation4,5. Because spin-triplet pairing is usually mediated by ferromagnetic (FM) spin fluctuations3, uranium-based materials near an FM instability are considered to be ideal candidates for realizing spin-triplet superconductivity6. Indeed, UTe2, which has a Tc ≈ 1.6 K (refs. 7,8), has been identified as a candidate for a chiral spin-triplet topological superconductor near an FM instability7-14, although it also has antiferromagnetic (AF) spin fluctuations15,16. Here we use inelastic neutron scattering (INS) to show that superconductivity in UTe2 is coupled to a sharp magnetic excitation, termed resonance17-23, at the Brillouin zone boundary near AF order. Because the resonance has only been found in spin-singlet unconventional superconductors near an AF instability17-23, its observation in UTe2 suggests that AF spin fluctuations may also induce spin-triplet pairing24 or that electron pairing in UTe2 has a spin-singlet component.

Quantum criticality enabled by intertwined degrees of freedom.

Strange metals appear in a wide range of correlated materials. Electronic localization-delocalization and the expected loss of quasiparticles characterize beyond-Landau metallic quantum critical points and the associated strange metals. Typical settings involve local spins. Systems that contain entwined degrees of freedom offer new platforms to realize unusual forms of quantum criticality. Here, we study the fate of an SU(4) spin-orbital Kondo state in a multipolar Bose-Fermi Kondo model, which provides an effective description of a multipolar Kondo lattice, using a renormalization-group method. We show that at zero temperature, a generic trajectory in the model's parameter space contains two quantum critical points, which are associated with the destruction of Kondo entanglement in the orbital and spin channels, respectively. Our asymptotically exact results reveal an overall phase diagram, provide the theoretical basis to understand puzzling recent experiments of a multipolar heavy fermion metal, and point to a means of designing different forms of quantum criticality and strange metallicity in a variety of strongly correlated systems.

Nematic Spin Correlations Pervading the Phase Diagram of FeSe_{1-x}S_{x}.

We use resonant inelastic x-ray scattering (RIXS) at the Fe-L_{3} edge to study the spin excitations of uniaxial-strained and unstrained FeSe_{1-x}S_{x} (0≤x≤0.21) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range 0200 K in x=0.18 and reaches a maximum around the nematic quantum critical doping (x_{c}≈0.17). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and highlight the capability of uniaxial strain in tuning spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity.

Giant spontaneous Hall effect in a nonmagnetic Weyl-Kondo semimetal.

Nontrivial topology in condensed-matter systems enriches quantum states of matter to go beyond either the classification into metals and insulators in terms of conventional band theory or that of symmetry-broken phases by Landau's order parameter framework. So far, focus has been on weakly interacting systems, and little is known about the limit of strong electron correlations. Heavy fermion systems are a highly versatile platform to explore this regime. Here we report the discovery of a giant spontaneous Hall effect in the Kondo semimetal [Formula: see text] that is noncentrosymmetric but preserves time-reversal symmetry. We attribute this finding to Weyl nodes-singularities of the Berry curvature-that emerge in the immediate vicinity of the Fermi level due to the Kondo interaction. We stress that this phenomenon is distinct from the previously detected anomalous Hall effect in materials with broken time-reversal symmetry; instead, it manifests an extreme topological response that requires a beyond-perturbation-theory description of the previously proposed nonlinear Hall effect. The large magnitude of the effect in even tiny electric and zero magnetic fields as well as its robust bulk nature may aid the exploitation in topological quantum devices.

Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe.

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2×2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.

Sequential localization of a complex electron fluid.

Complex and correlated quantum systems with promise for new functionality often involve entwined electronic degrees of freedom. In such materials, highly unusual properties emerge and could be the result of electron localization. Here, a cubic heavy fermion metal governed by spins and orbitals is chosen as a model system for this physics. Its properties are found to originate from surprisingly simple low-energy behavior, with 2 distinct localization transitions driven by a single degree of freedom at a time. This result is unexpected, but we are able to understand it by advancing the notion of sequential destruction of an SU(4) spin-orbital-coupled Kondo entanglement. Our results implicate electron localization as a unified framework for strongly correlated materials and suggest ways to exploit multiple degrees of freedom for quantum engineering.

Weyl-Kondo semimetal in heavy-fermion systems.

Insulating states can be topologically nontrivial, a well-established notion that is exemplified by the quantum Hall effect and topological insulators. By contrast, topological metals have not been experimentally evidenced until recently. In systems with strong correlations, they have yet to be identified. Heavy-fermion semimetals are a prototype of strongly correlated systems and, given their strong spin-orbit coupling, present a natural setting to make progress. Here, we advance a Weyl-Kondo semimetal phase in a periodic Anderson model on a noncentrosymmetric lattice. The quasiparticles near the Weyl nodes develop out of the Kondo effect, as do the surface states that feature Fermi arcs. We determine the key signatures of this phase, which are realized in the heavy-fermion semimetal Ce3Bi4Pd3 Our findings provide the much-needed theoretical foundation for the experimental search of topological metals with strong correlations and open up an avenue for systematic studies of such quantum phases that naturally entangle multiple degrees of freedom.

Fully gapped d-wave superconductivity in CeCu2Si2.

The nature of the pairing symmetry of the first heavy fermion superconductor CeCu2Si2 has recently become the subject of controversy. While CeCu2Si2 was generally believed to be a d-wave superconductor, recent low-temperature specific heat measurements showed evidence for fully gapped superconductivity, contrary to the nodal behavior inferred from earlier results. Here, we report London penetration depth measurements, which also reveal fully gapped behavior at very low temperatures. To explain these seemingly conflicting results, we propose a fully gapped [Formula: see text] band-mixing pairing state for CeCu2Si2, which yields very good fits to both the superfluid density and specific heat, as well as accounting for a sign change of the superconducting order parameter, as previously concluded from inelastic neutron scattering results.

Dynamical Scaling of Charge and Spin Responses at a Kondo Destruction Quantum Critical Point.

Quantum critical points often arise in metals perched at the border of an antiferromagnetic order. The recent observation of singular and dynamically scaling charge conductivity in an antiferromagnetic quantum critical heavy fermion metal implicates beyond-Landau quantum criticality. Here we study the charge and spin dynamics of a Kondo destruction quantum critical point (QCP), as realized in an SU(2)-symmetric Bose-Fermi Kondo model. We find that the critical exponents and scaling functions of the spin and single-particle responses of the QCP in the SU(2) case are essentially the same as those of the large-N limit, showing that 1/N corrections are subleading. Building on this insight, we demonstrate that the charge responses at the Kondo destruction QCP are singular and obey ω/T scaling. This property persists at the Kondo destruction QCP of the SU(2)-symmetric Kondo lattice model.

Incommensurate Spin Fluctuations in the Spin-Triplet Superconductor Candidate UTe_{2}.

Spin-triplet superconductors are of extensive current interest because they can host topological state and Majorana fermions important for quantum computation. The uranium-based heavy-fermion superconductor UTe_{2} has been argued as a spin-triplet superconductor similar to UGe_{2}, URhGe, and UCoGe, where the superconducting phase is near (or coexists with) a ferromagnetic (FM) instability and spin-triplet electron pairing is driven by FM spin fluctuations. Here we use neutron scattering to show that, although UTe_{2} exhibits no static magnetic order down to 0.3 K, its magnetism in the [0,K,L] plane is dominated by incommensurate spin fluctuations near an antiferromagnetic ordering wave vector and extends to at least 2.6 meV. We are able to understand the dominant incommensurate spin fluctuations of UTe_{2} in terms of its electronic structure calculated using a combined density-functional and dynamic mean-field theory.

Fractionalized Excitations Revealed by Entanglement Entropy.

Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of freedom, how to probe them and establish their existence is a long-standing challenge. We present a general procedure to reveal the fractionalized excitations using real-space entanglement entropy in critical spin liquids that are particularly relevant to experiments. Moreover, we show how to use the entanglement entropy to construct the corresponding spinon Fermi surface. Our work defines a new pathway to establish and characterize exotic excitations in novel quantum phases of matter.

Orbital Selectivity Enhanced by Nematic Order in FeSe.

Motivated by the recent low-temperature experiments on bulk FeSe, we study the electron correlation effects in a multiorbital model for this compound in the nematic phase using the U(1) slave-spin theory. We find that a finite nematic order helps to stabilize an orbital selective Mott phase. Moreover, we propose that when the d- and s-wave bond nematic orders are combined with the ferro-orbital order, there exists a surprisingly large orbital selectivity between the xz and yz orbitals even though the associated band splitting is relatively small. Our results explain the seemingly unusual observation of strong orbital selectivity in the nematic phase of FeSe, uncover new clues on the nature of the nematic order, and set the stage to elucidate the interplay between superconductivity and nematicity in iron-based superconductors.

Thermal and electrical transport across a magnetic quantum critical point.

A quantum critical point (QCP) arises when a continuous transition between competing phases occurs at zero temperature. Collective excitations at magnetic QCPs give rise to metallic properties that strongly deviate from the expectations of Landau's Fermi-liquid description, which is the standard theory of electron correlations in metals. Central to this theory is the notion of quasiparticles, electronic excitations that possess the quantum numbers of the non-interacting electrons. Here we report measurements of thermal and electrical transport across the field-induced magnetic QCP in the heavy-fermion compound YbRh(2)Si(2) (refs 2, 3). We show that the ratio of the thermal to electrical conductivities at the zero-temperature limit obeys the Wiedemann-Franz law for magnetic fields above the critical field at which the QCP is attained. This is also expected for magnetic fields below the critical field, where weak antiferromagnetic order and a Fermi-liquid phase form below 0.07 K (at zero field). At the critical field, however, the low-temperature electrical conductivity exceeds the thermal conductivity by about 10 per cent, suggestive of a non-Fermi-liquid ground state. This apparent violation of the Wiedemann-Franz law provides evidence for an unconventional type of QCP at which the fundamental concept of Landau quasiparticles no longer holds. These results imply that Landau quasiparticles break up, and that the origin of this disintegration is inelastic scattering associated with electronic quantum critical fluctuations--these insights could be relevant to understanding other deviations from Fermi-liquid behaviour frequently observed in various classes of correlated materials.

Fermi surface reconstruction and multiple quantum phase transitions in the antiferromagnet CeRhIn5.

Conventional, thermally driven continuous phase transitions are described by universal critical behavior that is independent of the specific microscopic details of a material. However, many current studies focus on materials that exhibit quantum-driven continuous phase transitions (quantum critical points, or QCPs) at absolute zero temperature. The classification of such QCPs and the question of whether they show universal behavior remain open issues. Here we report measurements of heat capacity and de Haas-van Alphen (dHvA) oscillations at low temperatures across a field-induced antiferromagnetic QCP (Bc0 ≈ 50 T) in the heavy-fermion metal CeRhIn5. A sharp, magnetic-field-induced change in Fermi surface is detected both in the dHvA effect and Hall resistivity at B0* ≈ 30 T, well inside the antiferromagnetic phase. Comparisons with band-structure calculations and properties of isostructural CeCoIn5 suggest that the Fermi-surface change at B0* is associated with a localized-to-itinerant transition of the Ce-4f electrons in CeRhIn5. Taken in conjunction with pressure experiments, our results demonstrate that at least two distinct classes of QCP are observable in CeRhIn5, a significant step toward the derivation of a universal phase diagram for QCPs.

Antiferroquadrupolar Order and Rotational Symmetry Breaking in a Generalized Bilinear-Biquadratic Model on a Square Lattice.

The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an S=1 generalized bilinear-biquadratic model with multineighbor interactions. We find a large parameter regime for a (π, 0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C_{4}-symmetry-breaking quadrupolar phase is also provided by an unbiased density matrix renormalization group analysis. We discuss the implications of our results for FeSe and related iron-based superconductors.

Local Orthorhombicity in the Magnetic C_{4} Phase of the Hole-Doped Iron-Arsenide Superconductor Sr_{1-x}Na_{x}Fe_{2}As_{2}.

We report on temperature-dependent pair distribution function measurements of Sr_{1-x}Na_{x}Fe_{2}As_{2}, an iron-based superconductor system that contains a magnetic phase with reentrant tetragonal symmetry, known as the magnetic C_{4} phase. Quantitative refinements indicate that the instantaneous local structure in the C_{4} phase comprises fluctuating orthorhombic regions with a length scale of ∼2 nm, despite the tetragonal symmetry of the average static structure. Additionally, local orthorhombic fluctuations exist on a similar length scale at temperatures well into the paramagnetic tetragonal phase. These results highlight the exceptionally large nematic susceptibility of iron-based superconductors and have significant implications for the magnetic C_{4} phase and the neighboring C_{2} and superconducting phases.

Strain-Driven Approach to Quantum Criticality in AFe_{2}As_{2} with A=K, Rb, and Cs.

The iron-based superconductors AFe_{2}As_{2} with A=K, Rb, Cs exhibit large Sommerfeld coefficients approaching those of heavy-fermion systems. We have investigated the magnetostriction and thermal expansion of this series to shed light on this unusual behavior. Quantum oscillations of the magnetostriction allow identifying the band-specific quasiparticle masses which by far exceed the band-structure derived masses. The divergence of the Grüneisen ratio derived from thermal expansion indicates that with increasing volume along the series a quantum critical point is approached. The critical fluctuations responsible for the enhancement of the quasiparticle masses appear to weaken the superconducting state.

Heavy-fermion quantum criticality and destruction of the Kondo effect in a nickel oxypnictide.

A quantum critical point arises at a continuous transformation between distinct phases of matter at zero temperature. Studies in antiferromagnetic heavy-fermion materials have revealed that quantum criticality has several classes, with an unconventional type that involves a critical destruction of the Kondo entanglement. To understand such varieties, it is important to extend the materials basis beyond the usual setting of intermetallic compounds. Here we show that a nickel oxypnictide, CeNiAsO, exhibits a heavy-fermion antiferromagnetic quantum critical point as a function of either pressure or P/As substitution. At the quantum critical point, non-Fermi-liquid behaviour appears, which is accompanied by a divergent effective carrier mass. Across the quantum critical point, the low-temperature Hall coefficient undergoes a rapid sign change, suggesting a sudden jump of the Fermi surface and a destruction of the Kondo effect. Our results imply that the enormous materials basis for the oxypnictides, which has been so crucial in the search for high-temperature superconductivity, will also play a vital role in the effort to establish the universality classes of quantum criticality in strongly correlated electron systems.

Antiferroquadrupolar and Ising-nematic orders of a frustrated bilinear-biquadratic Heisenberg model and implications for the magnetism of FeSe.

Motivated by the properties of the iron chalcogenides, we study the phase diagram of a generalized Heisenberg model with frustrated bilinear-biquadratic interactions on a square lattice. We identify zero-temperature phases with antiferroquadrupolar and Ising-nematic orders. The effects of quantum fluctuations and interlayer couplings are analyzed. We propose the Ising-nematic order as underlying the structural phase transition observed in the normal state of FeSe, and discuss the role of the Goldstone modes of the antiferroquadrupolar order for the dipolar magnetic fluctuations in this system. Our results provide a considerably broadened perspective on the overall magnetic phase diagram of the iron chalcogenides and pnictides, and are amenable to tests by new experiments.

Finite-temperature spin dynamics in a perturbed quantum critical Ising chain with an E8 symmetry.

A spectrum exhibiting E8 symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E8 description for CoNb2O6.