Kondo Insulator to Semimetal Transformation Tuned by Spin-Orbit Coupling

Anomalous Hall Effect and Quantum Criticality in Geometrically Frustrated Heavy Fermion Metals

Studies on the heavy-fermion pyrochlore iridate (Pr_{2}Ir_{2}O_{7}) point to the role of time-reversal-symmetry breaking in geometrically frustrated Kondo lattices. Here, we address the effect of Kondo coupling and chiral spin liquids in a J_{1}-J_{2} model on a square lattice and a model on a kagome lattice via a large-N method, based on a fermionic representation of the spin operators, and consider a new mechanism for anomalous Hall effect for the chiral phases. We calculate the anomalous Hall response for the chiral states of both the Kondo destroyed and Kondo screened phases. Across the quantum critical point, the anomalous Hall coefficient jumps when a sudden reconstruction of Fermi surfaces occurs. We discuss the implications of our results for the heavy-fermion pyrochlore iridate and propose an interface structure based on Kondo insulators to explore such effects further.

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.

Kondo screening in a Majorana metal

Kondo impurities provide a nontrivial probe to unravel the character of the excitations of a quantum spin liquid. In the S = 1/2 Kitaev model on the honeycomb lattice, Kondo impurities embedded in the spin-liquid host can be screened by itinerant Majorana fermions via gauge-flux binding. Here, we report experimental signatures of metallic-like Kondo screening at intermediate temperatures in the Kitaev honeycomb material α-RuCl3 with dilute Cr3+ (S = 3/2) impurities. The static magnetic susceptibility, the muon Knight shift, and the muon spin-relaxation rate all feature logarithmic divergences, a hallmark of a metallic Kondo effect. Concurrently, the linear coefficient of the magnetic specific heat is large in the same temperature regime, indicating the presence of a host Majorana metal. This observation opens new avenues for exploring uncharted Kondo physics in insulating quantum magnets.

Breakdown of the scaling relation of anomalous Hall effect in Kondo lattice ferromagnet USbTe

The interaction between strong correlation and Berry curvature is an open territory of in the field of quantum materials. Here we report large anomalous Hall conductivity in a Kondo lattice ferromagnet USbTe which is dominated by intrinsic Berry curvature at low temperatures. However, the Berry curvature induced anomalous Hall effect does not follow the scaling relation derived from Fermi liquid theory. The onset of the Berry curvature contribution coincides with the Kondo coherent temperature. Combined with ARPES measurement and DMFT calculations, this strongly indicates that Berry curvature is hosted by the flat bands induced by Kondo hybridization at the Fermi level. Our results demonstrate that the Kondo coherence of the flat bands has a dramatic influence on the low temperature physical properties associated with the Berry curvature, calling for new theories of scaling relations of anomalous Hall effect to account for the interaction between strong correlation and Berry curvature.

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.

Band theoretical approaches to topological physics in strongly-correlatedf-electron Kondo systems

First-principles band structure theory on the basis of the density functional theory (DFT) plays an essential role in the investigation of topological properties of weakly-correlated systems. DFT band structures show clear bulk band crossings for Weyl and Dirac semimetals, and surface band crossings for topological insulators and topological-crystalline insulators. In contrast, for strongly-correlatedf-electron systems, their topological properties are relatively less explored because the simple DFT does not work properly in describing the electronic structures of strongly-correlatedfelectrons. In this perspective, we examine the band theoretical approaches to topological properties of strongly-correlatedf-electron Kondo systems. We recapitulate current status of understanding of electronic structures and topological properties of strongly-correlated 4f-electron systems, such as Ce, SmB₆, and g-SmS, and also a 5f-electron system PuB₄, the electronic structures of which were investigated by the DFT combined with the dynamical mean-field theory (DFT + DMFT). Finally, we provide future directions and perspectives of improving theoretical band approaches to search for new topologicalf-electron systems, as an outlook.

Enhancement of Spin-Charge Conversion in Dilute Magnetic Alloys by Kondo Screening

We derive a kinetic theory capable of dealing both with large spin-orbit coupling and Kondo screening in dilute magnetic alloys. We obtain the collision integral nonperturbatively and uncover a contribution proportional to the momentum derivative of the impurity scattering S matrix. The latter yields an important correction to the spin diffusion and spin-charge conversion coefficients, and fully captures the so-called side-jump process without resorting to the Born approximation (which fails for resonant scattering), or to otherwise heuristic derivations. We apply our kinetic theory to a quantum impurity model with strong spin-orbit, which captures the most important features of Kondo-screened Cerium impurities in alloys such as Ce_{x}La_{1-x}Cu_{6}. We find (1) a large zero-temperature spin-Hall conductivity that depends solely on the Fermi wave number and (2) a transverse spin diffusion mechanism that modifies the standard Fick's diffusion law. Our predictions can be readily verified by standard spin-transport measurements in metal alloys with Kondo impurities.

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.

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.

Oxygen vacancy-driven orbital multichannel Kondo effect in Dirac nodal line metals IrO2 and RuO2

Strong electron correlations have long been recognized as driving the emergence of novel phases of matter. A well recognized example is high-temperature superconductivity which cannot be understood in terms of the standard weak-coupling theory. The exotic properties that accompany the formation of the two-channel Kondo (2CK) effect, including the emergence of an unconventional metallic state in the low-energy limit, also originate from strong electron interactions. Despite its paradigmatic role for the formation of non-standard metal behavior, the stringent conditions required for its emergence have made the observation of the nonmagnetic, orbital 2CK effect in real quantum materials difficult, if not impossible. We report the observation of orbital one- and two-channel Kondo physics in the symmetry-enforced Dirac nodal line (DNL) metals IrO₂ and RuO₂ nanowires and show that the symmetries that enforce the existence of DNLs also promote the formation of nonmagnetic Kondo correlations. Rutile oxide nanostructures thus form a versatile quantum matter platform to engineer and explore intrinsic, interacting topological states of matter.

Strong electron correlations may give rise to an unconventional metallic state accompanying non-magnetic Kondo scattering. Here, the authors report signatures of orbital one- and two-channel Kondo physics in Dirac nodal line metals RuO₂ and IrO₂ nanowires.

Unraveling the 4felectronic structures of cerium monopnictides

We employed a state-of-the-art first-principles many-body approach, namely the density functional theory in combination with the single-site dynamical mean-field theory, to study the 4felectronic structures in cerium monopnictides (CeX, whereX= N, P, As, Sb, and Bi). We find that the 4felectrons in CeN are highly itinerant and mixed-valence, showing a prominent quasiparticle peak near the Fermi level. On the contrary, they become well localized and display weak valence fluctuation in CeBi. It means that a 4fitinerant-localized crossover could emerge upon changing theXatom from N to Bi. Moreover, according to the low-energy behaviors of 4fself-energy functions, we could conclude that the 4felectrons in CeXalso demonstrate interesting orbital-selective electronic correlations, which are similar to the other cerium-based heavy fermion compounds.

From Trivial Kondo Insulator Ce_{3}Pt_{3}Bi_{4} to Topological Nodal-Line Semimetal Ce_{3}Pd_{3}Bi_{4}

Using the density functional theory combined with dynamical mean-field theory, we have performed systematic study of the electronic structure and its band topology properties of Ce_{3}Pt_{3}Bi_{4} and Ce_{3}Pd_{3}Bi_{4}. At high temperatures (∼290  K), the electronic structures of both compounds resemble the open-core 4f density functional calculation results. For Ce_{3}Pt_{3}Bi_{4}, clear hybridization gap can be observed below 72 K, and its coherent momentum-resolved spectral function below 18 K exhibits an topologically trivial indirect gap of ∼6  meV and resembles density functional band structure with itinerant 4f state. For Ce_{3}Pd_{3}Bi_{4}, no clear hybridization gap can be observed down to 4 K, and its momentum-resolved spectral function resembles electron-doped open-core 4f density functional calculations. The band nodal points of Ce_{3}Pd_{3}Bi_{4} at 4 K are protected by the gliding-mirror symmetry and form ringlike structure. Therefore, the Ce_{3}Pt_{3}Bi_{4} compound is topologically trivial Kondo insulator while the Ce_{3}Pd_{3}Bi_{4} compound is topological nodal-line semimetal.

Evidence for undoped Weyl semimetal charge transport in Y2Ir2O7

Weyl fermions scattering from a random Coulomb potential are predicted to exhibit resistivity versus temperature [Formula: see text] in a single particle model. Here we show that, in closed-environment-grown polycrystalline samples of Y₂Ir₂O₇, [Formula: see text] over four orders of magnitude in [Formula: see text]. While the measured prefactor, [Formula: see text], is obtained from the model using reasonable materials parameters, the [Formula: see text] behavior extends far beyond the model's range of applicability. In particular, the behavior extends into the low-temperature, high-resistivity region where the Ioffe-Regel parameter, [Formula: see text]. Strong on-site Coulomb correlations, instrumental for predicting a Weyl semimetal state in Y₂Ir₂O₇, are the possible origin of such 'bad' Weyl semimetal behavior.

Magnetic field-tuned Fermi liquid in a Kondo insulator

Kondo insulators are expected to transform into metals under a sufficiently strong magnetic field. The closure of the insulating gap stems from the coupling of a magnetic field to the electron spin, yet the required strength of the magnetic field-typically of order 100 T-means that very little is known about this insulator-metal transition. Here we show that Ce[Formula: see text]Bi[Formula: see text]Pd[Formula: see text], owing to its fortuitously small gap, provides an ideal Kondo insulator for this investigation. A metallic Fermi liquid state is established above a critical magnetic field of only [Formula: see text] 11 T. A peak in the strength of electronic correlations near [Formula: see text], which is evident in transport and susceptibility measurements, suggests that Ce[Formula: see text]Bi[Formula: see text]Pd[Formula: see text] may exhibit quantum criticality analogous to that reported in Kondo insulators under pressure. Metamagnetism and the breakdown of the Kondo coupling are also discussed.

Magnetic and transport properties of low-carrier-density Kondo semimetal CeSbTe

Single crystals of CeSbTe with a ZrSiS-type structure were synthesized using vapor transport method. The stoichiometry is deviated from the nominal composition, which may cause some disorder in this compound. The physical properties were characterized by measuring the magnetic susceptibility, electrical resistivity, Hall resistivity and specific heat. One antiferromagnetic (AFM) transition related to Ce³⁺ ions was found at [Formula: see text] K, and a field-induced metamagnetic transition was observed below [Formula: see text]. The moderately enhanced Sommerfeld coefficient [Formula: see text] mJ mol^-1 · K^-2 and the estimated Kondo temperature [Formula: see text] K, indicate that CeSbTe is a moderately correlated AFM Kondo lattice compound with crystalline electric field effect. The carrier concentration of CeSbTe derived from the Hall coefficient is in the order of 10²¹ cm^-3, lower than most Kondo metals, which indicates that CeSbTe is a low-carrier-density Kondo semimetal.

Oswald IW, Ban W, Huang CL, Loganathan V, Hallas AM, Wilson MN, Luke GM, Harriger L, Huang Q, Li Y, Dzsaber S, Chan JY, Wang NL, Paschen S, Lynn JW, Nevidomskyy AH, Dai P, Si Q, Morosan E. Low-carrier density and fragile magnetism in a Kondo lattice system

Kondo-based semimetals and semiconductors are of extensive current interest as a viable platform for strongly correlated states in the dilute carrier limit. It is thus important to explore the routes to understand such systems. One established pathway is through the Kondo effect in metallic nonmagnetic analogs, in the so called half-filling case of one conduction electron and one 4f electron per site. Here, we demonstrate that Kondo-based semimetals develop out of conduction electrons with a low-carrier density in the presence of an even number of rare-earth sites. We do so by studying the Kondo material Yb3Ir4Ge13 along with its closed-4f -shell counterpart, Lu3Ir4Ge13. Through magnetotransport, optical conductivity, and thermodynamic measurements, we establish that the correlated semimetallic state of Yb3Ir4Ge13 below its Kondo temperature originates from the Kondo effect of a low-carrier conduction-electron background. In addition, it displays fragile magnetism at very low temperatures, which in turn, can be tuned to a Griffiths-phase-like regime through Lu-for-Yb substitution. These findings are connected with recent theoretical studies in simplified models. Our results can pave the way to exploring strong correlation physics in a semimetallic environment.

Evidence for Weyl fermions in a canonical heavy-fermion semimetal YbPtBi

The manifestation of Weyl fermions in strongly correlated electron systems is of particular interest. We report evidence for Weyl fermions in the heavy fermion semimetal YbPtBi from electronic structure calculations, angle-resolved photoemission spectroscopy, magnetotransport and calorimetric measurements. At elevated temperatures where 4f-electrons are localized, there are triply degenerate points, yielding Weyl nodes in applied magnetic fields. These are revealed by a contribution from the chiral anomaly in the magnetotransport, which at low temperatures becomes negligible due to the influence of electronic correlations. Instead, Weyl fermions are inferred from the topological Hall effect, which provides evidence for a Berry curvature, and a cubic temperature dependence of the specific heat, as expected from the linear dispersion near the Weyl nodes. The results suggest that YbPtBi is a Weyl heavy fermion semimetal, where the Kondo interaction renormalizes the bands hosting Weyl points. These findings open up an opportunity to explore the interplay between topology and strong electronic correlations.

Thermoelectricity in correlated narrow-gap semiconductors

We review many-body effects, their microscopic origin, as well as their impact on thermoelectricity in correlated narrow-gap semiconductors. Members of this class-such as FeSi and FeSb₂-display an unusual temperature dependence in various observables: insulating with large thermopowers at low temperatures, they turn bad metals at temperatures much smaller than the size of their gaps. This insulator-to-metal crossover is accompanied by spectral weight-transfers over large energies in the optical conductivity and by a gradual transition from activated to Curie-Weiss-like behaviour in the magnetic susceptibility. We show a retrospective of the understanding of these phenomena, discuss the relation to heavy-fermion Kondo insulators-such as Ce₃Bi₄Pt₃ for which we present new results-and propose a general classification of paramagnetic insulators. From the latter, FeSi emerges as an orbital-selective Kondo insulator. Focussing on intermetallics such as silicides, antimonides, skutterudites, and Heusler compounds we showcase successes and challenges for the realistic simulation of transport properties in the presence of electronic correlations. Further, we explore new avenues in which electronic correlations may contribute to the improvement of thermoelectric performance.

Weyl-Kondo semimetal in heavy-fermion systems

While electronic states with nontrivial topology have traditionally been known in insulators, they have been evidenced in metals during the past 2 years. Such Weyl semimetals show topological protection while conducting electricity both in the bulk and on the surface. An outstanding question is whether topological protection can happen in metals with strong correlations. Here, we report theoretical work on a strongly correlated lattice model to demonstrate the emergence of a Weyl–Kondo semimetal. We identify Weyl fermions in the bulk and Fermi arcs on the surface, both of which are associated with the many-body phenomenon called the Kondo effect. We determine a key signature of this Weyl–Kondo semimetal, which is realized in a recently discovered heavy-fermion compound.

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.