Emergent flat band and topological Kondo semimetal driven by orbital-selective correlations.

Flat electronic bands are expected to show proportionally enhanced electron correlations, which may generate a plethora of novel quantum phases and unusual low-energy excitations. They are increasingly being pursued in d-electron-based systems with crystalline lattices that feature destructive electronic interference, where they are often topological. Such flat bands, though, are generically located far away from the Fermi energy, which limits their capacity to partake in the low-energy physics. Here we show that electron correlations produce emergent flat bands that are pinned to the Fermi energy. We demonstrate this effect within a Hubbard model, in the regime described by Wannier orbitals where an effective Kondo description arises through orbital-selective Mott correlations. Moreover, the correlation effect cooperates with symmetry constraints to produce a topological Kondo semimetal. Our results motivate a novel design principle for Weyl Kondo semimetals in a new setting, viz. d-electron-based materials on suitable crystal lattices, and uncover interconnections among seemingly disparate systems that may inspire fresh understandings and realizations of correlated topological effects in quantum materials and beyond.

Reversible non-volatile electronic switching in a near-room-temperature van der Waals ferromagnet.

Non-volatile phase-change memory devices utilize local heating to toggle between crystalline and amorphous states with distinct electrical properties. Expanding on this kind of switching to two topologically distinct phases requires controlled non-volatile switching between two crystalline phases with distinct symmetries. Here, we report the observation of reversible and non-volatile switching between two stable and closely related crystal structures, with remarkably distinct electronic structures, in the near-room-temperature van der Waals ferromagnet Fe5-δGeTe2. We show that the switching is enabled by the ordering and disordering of Fe site vacancies that results in distinct crystalline symmetries of the two phases, which can be controlled by a thermal annealing and quenching method. The two phases are distinguished by the presence of topological nodal lines due to the preserved global inversion symmetry in the site-disordered phase, flat bands resulting from quantum destructive interference on a bipartite lattice, and broken inversion symmetry in the site-ordered phase.

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.

Shot noise in a strange metal.

Strange-metal behavior has been observed in materials ranging from high-temperature superconductors to heavy fermion metals. In conventional metals, current is carried by quasiparticles; although it has been suggested that quasiparticles are absent in strange metals, direct experimental evidence is lacking. We measured shot noise to probe the granularity of the current-carrying excitations in nanowires of the heavy fermion strange metal YbRh2Si2. When compared with conventional metals, shot noise in these nanowires is strongly suppressed. This suppression cannot be attributed to either electron-phonon or electron-electron interactions in a Fermi liquid, which suggests that the current is not carried by well-defined quasiparticles in the strange-metal regime that we probed. Our work sets the stage for similar studies of other strange metals.

Coupled topological flat and wide bands: Quasiparticle formation and destruction.

Flat bands amplify correlation effects and are of extensive current interest. They provide a platform to explore both topology in correlated settings and correlation physics enriched by topology. Recent experiments in correlated kagome metals have found evidence for strange-metal behavior. A major theoretical challenge is to study the effect of local Coulomb repulsion when the band topology obstructs a real-space description. In a variant to the kagome lattice, we identify an orbital-selective Mott transition in any system of coupled topological flat and wide bands. This was made possible by the construction of exponentially localized and Kramers-doublet Wannier functions, which, in turn, leads to an effective Kondo-lattice description. Our findings show how quasiparticles are formed in such coupled topological flat-wide band systems and, equally important, how they are destroyed. Our work provides a conceptual framework for the understanding of the existing and emerging strange-metal properties in kagome metals and beyond.

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.

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.

Control of electronic topology in a strongly correlated electron system.

It is becoming increasingly clear that breakthrough in quantum applications necessitates materials innovation. In high demand are conductors with robust topological states that can be manipulated at will. This is what we demonstrate in the present work. We discover that the pronounced topological response of a strongly correlated "Weyl-Kondo" semimetal can be genuinely manipulated-and ultimately fully suppressed-by magnetic fields. We understand this behavior as a Zeeman-driven motion of Weyl nodes in momentum space, up to the point where the nodes meet and annihilate in a topological quantum phase transition. The topologically trivial but correlated background remains unaffected across this transition, as is shown by our investigations up to much larger fields. Our work lays the ground for systematic explorations of electronic topology, and boosts the prospect for topological quantum devices.

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.

Pristine quantum criticality in a Kondo semimetal.

The observation of quantum criticality in diverse classes of strongly correlated electron systems has been instrumental in establishing ordering principles, discovering new phases, and identifying the relevant degrees of freedom and interactions. At focus so far have been insulators and metals. Semimetals, which are of great current interest as candidate phases with nontrivial topology, are much less explored in experiments. Here, we study the Kondo semimetal CeRu4Sn6 by magnetic susceptibility, specific heat, and inelastic neutron scattering experiments. The power-law divergence of the magnetic Grünesien ratio reveals that, unexpectedly, this compound is quantum critical without tuning. The dynamical energy over temperature scaling in the neutron response throughout the Brillouin zone and the temperature dependence of the static uniform susceptibility, indicate that temperature is the only energy scale in the criticality. Such behavior, which has been associated with Kondo destruction quantum criticality in metallic systems, could be generic in the semimetal setting.

Inhomogeneous Kondo-lattice in geometrically frustrated Pr2Ir2O7.

Magnetic fluctuations induced by geometric frustration of local Ir-spins disturb the formation of long-range magnetic order in the family of pyrochlore iridates. As a consequence, Pr2Ir2O7 lies at a tuning-free antiferromagnetic-to-paramagnetic quantum critical point and exhibits an array of complex phenomena including the Kondo effect, biquadratic band structure, and metallic spin liquid. Using spectroscopic imaging with the scanning tunneling microscope, complemented with machine learning, density functional theory and theoretical modeling, we probe the local electronic states in Pr2Ir2O7 and find an electronic phase separation. Nanoscale regions with a well-defined Kondo resonance are interweaved with a non-magnetic metallic phase with Kondo-destruction. These spatial nanoscale patterns display a fractal geometry with power-law behavior extended over two decades, consistent with being in proximity to a critical point. Our discovery reveals a nanoscale tuning route, viz. using a spatial variation of the electronic potential as a means of adjusting the balance between Kondo entanglement and geometric frustration.

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.

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.

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.

Heavy fermion quantum criticality at dilute carrier limit in CeNi2-δ(As1-xPx)2.

We study the quantum phase transitions in the nickel pnctides, CeNi2-δ(As1-xPx)2 (δ ≈ 0.07-0.22) polycrystalline samples. This series displays the distinct heavy fermion behavior in the rarely studied parameter regime of dilute carrier limit. We systematically investigate the magnetization, specific heat and electrical transport down to low temperatures. Upon increasing the P-content, the antiferromagnetic order of the Ce-4f moment is suppressed continuously and vanishes at xc ~ 0.55. At this doping, the temperature dependences of the specific heat and longitudinal resistivity display non-Fermi liquid behavior. Both the residual resistivity ρ0 and the Sommerfeld coefficient γ0 are sharply peaked around xc. When the P-content reaches close to 100%, we observe a clear low-temperature crossover into the Fermi liquid regime. In contrast to what happens in the parent compound x = 0.0 as a function of pressure, we find a surprising result that the non-Fermi liquid behavior persists over a nonzero range of doping concentration, xc < x < 0.9. In this doping range, at the lowest measured temperatures, the temperature dependence of the specific-heat coefficient is logarithmically divergent and that of the electrical resistivity is linear. We discuss the properties of CeNi2-δ(As1-xPx)2 in comparison with those of its 1111 counterpart, CeNi(As1-xPx)O. Our results indicate a non-Fermi liquid phase in the global phase diagram of heavy fermion metals.

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.

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.

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.