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.

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.

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.

Giant Isotropic Nernst Effect in an Anisotropic Kondo Semimetal.

The "failed Kondo insulator" CeNiSn has long been suspected to be a nodal metal, with a node in the hybridization matrix elements. Here we carry out a series of Nernst effect experiments to delineate whether the severely anisotropic magnetotransport coefficients do indeed derive from a nodal metal or can simply be explained by a highly anisotropic Fermi surface. Our experiments reveal that despite an almost twentyfold anisotropy in the Hall conductivity, the large Nernst signal is isotropic. Taken in conjunction with the magnetotransport anisotropy, these results provide strong support for an isotropic Fermi surface with a large anisotropy in quasiparticle mass derived from a nodal hybridization.

NMR study of Ba8Cu5Si(x)Ge(41-x) clathrate semiconductors.

We have performed (63)Cu, (65)Cu, and (137)Ba NMR on Ba8Cu5SixGe41-x, a series of intermetallic clathrates known for their potential as thermoelectric materials, in order to investigate the electronic behavior of the samples. The spectra and spin-lattice relaxation times were measured at 77 K and 290 K for the entire composition range 0 ≤ x ≤ 41. Magnetic and quadrupole shifts and relaxation rates of the Cu NMR data were extracted, and thereby carrier-induced metallic contributions identified. The observed shifts change in a nonlinear way with increasing Si substitution: from x = 0 to about 20 the shifts are essentially constant, while approaching x = 41 they increase rapidly. At the same time, Ba NMR data indicate greater Ba-site participation in the conduction band in Ba8Cu5Si41 than in Ba8Cu5Ge41. The results indicate surprisingly little change in electronic features vs. Si content for most of the composition range, while Ba8Cu5Si41 exhibits enhanced hybridization and a more metallic framework than Ba8Cu5Ge41.

Covalent embedding of Ni2+/Fe3+ cyanometallate structures in silica by sol-gel processing.

Compound [Ni(AEAPTS)2]3[Fe(CN)6]2 (AEAPTS = N-(2-aminoethyl)-3-aminopropyltrimethoxysilane), in which Ni(2+) and Fe(3+) ions are ferromagnetically coupled through cyano bridges, was prepared. Sol-gel processing of the AEAPTS derivative resulted in incorporation of the cyanometallate in silica. The obtained material is magnetically ordered below 22 K with an effective magnetic moment µeff of 4.46 µB at room temperature, a maximum of 8.60 µB at approximately 15 K and a narrow hysteresis at 2 K, with a saturation remanence of about 300 emu mol(-1) and a coercitivity of 0.03 T.

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.

Fermi-surface collapse and dynamical scaling near a quantum-critical point.

Quantum criticality arises when a macroscopic phase of matter undergoes a continuous transformation at zero temperature. While the collective fluctuations at quantum-critical points are being increasingly recognized as playing an important role in a wide range of quantum materials, the nature of the underlying quantum-critical excitations remains poorly understood. Here we report in-depth measurements of the Hall effect in the heavy-fermion metal YbRh(2)Si(2), a prototypical system for quantum criticality. We isolate a rapid crossover of the isothermal Hall coefficient clearly connected to the quantum-critical point from a smooth background contribution; the latter exists away from the quantum-critical point and is detectable through our studies only over a wide range of magnetic field. Importantly, the width of the critical crossover is proportional to temperature, which violates the predictions of conventional theory and is instead consistent with an energy over temperature, E/T, scaling of the quantum-critical single-electron fluctuation spectrum. Our results provide evidence that the quantum-dynamical scaling and a critical Kondo breakdown simultaneously operate in the same material. Correspondingly, we infer that macroscopic scale-invariant fluctuations emerge from the microscopic many-body excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finite-temperature behavior in a broad range of strongly correlated quantum systems.

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.

Are Heavy Fermion Strange Metals Planckian?

Strange metal behavior refers to a linear temperature dependence of the electrical resistivity that is not due to electron-phonon scattering. It is seen in numerous strongly correlated electron systems, from the heavy fermion compounds, via transition metal oxides and iron pnictides, to magic angle twisted bi-layer graphene, frequently in connection with unconventional or "high temperature" superconductivity. To achieve a unified understanding of these phenomena across the different materials classes is a central open problem in condensed matter physics. Tests whether the linear-in-temperature law might be dictated by Planckian dissipation-scattering with the rate ∼ k B T / ℏ -are receiving considerable attention. Here we assess the situation for strange metal heavy fermion compounds. They allow to probe the regime of extreme correlation strength, with effective mass or Fermi velocity renormalizations in excess of three orders of magnitude. Adopting the same procedure as done in previous studies, i.e., assuming a simple Drude conductivity with the above scattering rate, we find that for these strongly renormalized quasiparticles, scattering is much weaker than Planckian, implying that the linear temperature dependence should be due to other effects. We discuss implications of this finding and point to directions for further work.

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.

Introducing a magnetic guest to a tetrel-free clathrate: synthesis, structure, and properties of Eu(x)Ba(8-x)Cu16P30 (0 ≤ x ≤ 1.5).

The europium-containing clathrate-I Eu(x)Ba(8-x)Cu(16)P(30) was synthesized from the elements. Powder X-ray diffraction in combination with energy dispersive X-ray absorption spectroscopy (EDXS) and metallographic studies showed the homogeneity range with x ≤ 1.5. Determination of the crystal structure confirmed the presence of an orthorhombic superstructure of clathrate-I and revealed that Eu atoms exclusively resided in small pentagonal-dodecahedral cages. Magnetic measurements together with X-ray absorption spectroscopy are consistent with a 4f(7) (Eu(2+)) ground state for Eu(x)Ba(8-x)Cu(16)P(30). Below 3 K the Eu moments order antiferromagnetically. Resistivity measurements revealed metallic behavior of the investigated clathrate, in line with the composition deviating from the Zintl counting scheme. Local vibrations of the guest atoms inside the cages are analyzed with the help of specific heat investigations.

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.

Thermopower evidence for an abrupt Fermi surface change at the quantum critical point of YbRh2Si2.

We present low-temperature thermopower results, S(T), on the heavy-fermion compound YbRh2Si2 in the vicinity of its field-induced quantum critical point (QCP). At B=0, a logarithmic increase of -S(T)/T between 1 and 0.1 K reveals strong non-Fermi-liquid behavior. A pronounced downturn of -S(T)/T below T{max}=0.1 K and a sign change from negative to positive S(T) values at T{0} approximately 30 mK are observed on the low-field side of the Kondo breakdown crossover line T{*}(B). In the field-induced, heavy Landau-Fermi-liquid regime, S(T)/T assumes constant, negative values below T{LFL}. A pronounced crossover in the -S(B)/T isotherms at T{*}(B) sharpens with decreasing T and seems to evolve toward a steplike function for T-->0. This is attributed to an abrupt change of the Fermi volume upon crossing the unconventional QCP of YbRh2Si2.

Structural and Thermoelectric Properties of Cu Substituted Type I Clathrates Ba8CuxSi~32-xGa~14.

With an attempt to improve the thermoelectric properties of type I clathrates in the Ba-Ga-Si system, we introduce Cu into the framework of the crystal structure. Single crystals are prepared in Ga-flux and characterized by X-ray diffraction techniques and transport measurements for the structural and thermoelectric properties. Our composition analyses show that only a small amount of Cu is determined in the clathrates. The single crystal X-ray diffraction data refinements confirm that Ga atoms prefer the 6c and 24k sites and avoid the 16i sites in the crystal structure. The small amount of Cu affects the crystal structure by compressing the tetrakaidecahedral cage along the direction perpendicular to the six-atom-ring plane. This could be the reason for the high charge carrier concentration, and low electrical resistivity and Seebeck coefficient. We analyze the principal mechanism for our observation and conclude that the Cu substitution can adjust some subtle details of the structure, maintaining the Zintl rule in the type I clathrates.

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.

Crystal Chemistry and Thermoelectric Properties of Type-I Clathrate Ba8Ni∼3.8SixGe42.2-x (x = 0, 10, 20, 42.2).

Thermoelectric materials are actively considered for waste heat recovery applications. To improve the heat to electricity conversion efficiency, fundamental understanding on composition, crystal structure, and interrelation with the thermoelectric properties is necessary. Here, we report the chemical and thermoelectric properties of type-I clathrates Ba 8 Ni 3.8 Si x Ge 42.2 - x (x = 0, 10, 20, 42.2), to show that the Si substitution can retain the low lattice thermal conductivity as in pure Ge-based clathrates by adding defects (cage distortion) scattering and/or alloying effect, and the charge carrier concentration can be optimized and thus the electronic properties can be improved by tailoring the vacancy content. We demonstrate the vacancies in the pure Ge-based compound by Rietveld refinement, and possible vacancies in the quaternary compound by transport property measurements. We also show that, for intrinsic property studies in these compounds with such a complex crystal structure, a heat treatment for as cast alloys is necessary for phase purity and composition homogeneity. The highest Z T value of 0.19 at 550 ° C is reached in the compound with x = 10 .

Direct measurement of individual phonon lifetimes in the clathrate compound Ba7.81Ge40.67Au5.33.

Engineering lattice thermal conductivity requires to control the heat carried by atomic vibration waves, the phonons. The key parameter for quantifying it is the phonon lifetime, limiting the travelling distance, whose determination is however at the limits of instrumental capabilities. Here, we show the achievement of a direct quantitative measurement of phonon lifetimes in a single crystal of the clathrate Ba7.81Ge40.67Au5.33, renowned for its puzzling 'glass-like' thermal conductivity. Surprisingly, thermal transport is dominated by acoustic phonons with long lifetimes, travelling over distances of 10 to 100 nm as their wave-vector goes from 0.3 to 0.1 Å-1. Considering only low-energy acoustic phonons, and their observed lifetime, leads to a calculated thermal conductivity very close to the experimental one. Our results challenge the current picture of thermal transport in clathrates, underlining the inability of state-of-the-art simulations to reproduce the experimental data, thus representing a crucial experimental input for theoretical developments.Phonon lifetime is a fundamental parameter of thermal transport however its determination is challenging. Using inelastic neutron scattering and the neutron resonant spin-echo technique, Lory et al. determine the acoustic phonon lifetime in a single crystal of clathrate Ba7.81Ge40.67Au5.33.