Strange-metal behaviour in a pure ferromagnetic Kondo lattice.

A wide range of metals exhibit anomalous electrical and thermodynamic properties when tuned to a quantum critical point (QCP), although the origins of such strange metals have posed a long-standing mystery. The frequent association of strange metals with unconventional superconductivity and antiferromagnetic QCPs1-4 has led to the belief that they are highly entangled quantum states5. By contrast, ferromagnets are regarded as an unlikely setting for strange metals, because they are weakly entangled and their QCPs are often interrupted by competing phases or first-order phase transitions6-8. Here we provide evidence that the pure ferromagnetic Kondo lattice9,10 CeRh6Ge4 becomes a strange metal at a pressure-induced QCP. Measurements of the specific heat and resistivity under pressure demonstrate that the ferromagnetic transition is continuously suppressed to zero temperature, revealing a strange-metal behaviour around the QCP. We argue that strong magnetic anisotropy has a key role in this process, injecting entanglement in the form of triplet resonating valence bonds into the ordered ferromagnet. We show that a singular transformation in the patterns of the entanglement between local moments and conduction electrons, from triplet resonating valence bonds to Kondo-entangled singlet pairs at the QCP, causes a jump in the Fermi surface volume-a key driver of strange-metallic behaviour. Our results open up a direction for research into ferromagnetic quantum criticality and establish an alternative setting for the strange-metal phenomenon. Most importantly, strange-metal behaviour at a ferromagnetic QCP suggests that quantum entanglement-not the destruction of antiferromagnetism-is the common driver of the varied behaviours of strange metals.

Anisotropic c-f Hybridization in the Ferromagnetic Quantum Critical Metal CeRh_{6}Ge_{4}.

Heavy fermion compounds exhibiting a ferromagnetic quantum critical point have attracted considerable interest. Common to two known cases, i.e., CeRh_{6}Ge_{4} and YbNi_{4}P_{2}, is that the 4f moments reside along chains with a large interchain distance, exhibiting strong magnetic anisotropy that was proposed to be vital for the ferromagnetic quantum criticality. Here, we report an angle-resolved photoemission study on CeRh_{6}Ge_{4} in which we observe sharp momentum-dependent 4f bands and clear bending of the conduction bands near the Fermi level, indicating considerable hybridization between conduction and 4f electrons. The extracted hybridization strength is anisotropic in momentum space and is obviously stronger along the Ce chain direction.The hybridized 4f bands persist up to high temperatures, and the evolution of their intensity shows clear band dependence. Our results provide spectroscopic evidence for anisotropic hybridization between conduction and 4f electrons in CeRh_{6}Ge_{4}, which could be important for understanding the electronic origin of the ferromagnetic quantum criticality.

Revealing the Heavy Quasiparticles in the Heavy-Fermion Superconductor CeCu_{2}Si_{2}.

The superconducting order parameter of the first heavy-fermion superconductor CeCu_{2}Si_{2} is currently under debate. A key ingredient to understand its superconductivity and physical properties is the quasiparticle dispersion and Fermi surface, which remains elusive experimentally. Here, we present measurements from angle-resolved photoemission spectroscopy. Our results emphasize the key role played by the Ce 4f electrons for the low-temperature Fermi surface, highlighting a band-dependent conduction-f electron hybridization. In particular, we find a very heavy quasi-two-dimensional electron band near the bulk X point and moderately heavy three-dimensional hole pockets near the Z point. Comparison with theoretical calculations reveals the strong local correlation in this compound, calling for further theoretical studies. Our results provide the electronic basis to understand the heavy-fermion behavior and superconductivity; implications for the enigmatic superconductivity of this compound are also discussed.

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.

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.

Hybridization gap and Fano resonance in SmB6.

Hybridization between conduction electrons and the strongly interacting f-electrons in rare earth or actinide compounds may result in new states of matter. Depending on the exact location of the concomitant hybridization gap with respect to the Fermi energy, a heavy fermion or an insulating ground state ensues. To study this entanglement locally, we conducted scanning tunneling microscopy and spectroscopy (STS) measurements on the "Kondo insulator" SmB6. The vast majority of surface areas investigated were reconstructed, but infrequently, patches of varying sizes of nonreconstructed Sm- or B-terminated surfaces also were found. On the smallest patches, clear indications for the hybridization gap with logarithmic temperature dependence (as expected for a Kondo system) and for intermultiplet transitions were observed. On nonreconstructed surface areas large enough for coherent cotunneling, we were able to observe clear-cut Fano resonances. Our locally resolved STS indicated considerable finite conductance on all surfaces independent of their structure, not proving but leaving open the possibility of the existence of a topologically protected surface state.

Foundations of heavy-fermion superconductivity: lattice Kondo effect and Mott physics.

This article overviews the development of heavy-fermion superconductivity, notably in such rare-earth-based intermetallic compounds which behave as Kondo-lattice systems. Heavy-fermion superconductivity is of unconventional nature in the sense that it is not mediated by electron-phonon coupling. Rather, in most cases the attractive interaction between charge carriers is apparently magnetic in origin. Fluctuations associated with an antiferromagnetic (AF) quantum critical point (QCP) play a major role. The first heavy-fermion superconductor CeCu2Si2 turned out to be the prototype of a larger group of materials for which the underlying, often pressure-induced, AF QCP is likely to be of a three-dimensional (3D) spin-density-wave (SDW) variety. For UBe13, the second heavy-fermion superconductor, a magnetic-field-induced 3D SDW QCP inside the superconducting phase can be conjectured. Such a 'conventional', itinerant QCP can be well understood within Landau's paradigm of order-parameter fluctuations. In contrast, the low-temperature normal-state properties of a few heavy-fermion superconductors are at odds with the Landau framework. They are characterized by an 'unconventional', local QCP which may be considered a zero-temperature 4 f-orbital selective Mott transition. Here, as concluded for YbRh2Si2, the breakdown of the Kondo effect concurring with the AF instability gives rise to an abrupt change of the Fermi surface. Very recently, superconductivity was discovered for this compound at ultra-low temperatures. Therefore, YbRh2Si2 along with CeRhIn5 under pressure provide a natural link between the large group of about fifty low-temperature heavy-fermion superconductors and other families of unconventional superconductors with substantially higher T c, e.g. the doped Mott insulators of the perovskite-type cuprates and the organic charge-transfer salts.

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.

Multiband superconductivity with unexpected deficiency of nodal quasiparticles in CeCu2Si2.

Superconductivity in the heavy-fermion compound CeCu2Si2 is a prototypical example of Cooper pairs formed by strongly correlated electrons. For more than 30 years, it has been believed to arise from nodal d-wave pairing mediated by a magnetic glue. Here, we report a detailed study of the specific heat and magnetization at low temperatures for a high-quality single crystal. Unexpectedly, the specific-heat measurements exhibit exponential decay with a two-gap feature in its temperature dependence, along with a linear dependence as a function of magnetic field and the absence of oscillations in the field angle, reminiscent of multiband full-gap superconductivity. In addition, we find anomalous behavior at high fields, attributed to a strong Pauli paramagnetic effect. A low quasiparticle density of states at low energies with a multiband Fermi-surface topology would open a new door into electron pairing in CeCu2Si2.

Nernst effect: evidence of local Kondo scattering in heavy fermions.

A distinctly temperature-dependent Nernst coefficient, ν, which is strongly enhanced over that of LaCu(2)Si(2), is observed between T=2 and 300 K for CeCu(2)Si(2) and Ce(0.8)La(0.2)Cu(2)Si(2). The enhanced ν(T) is determined by the asymmetry of the on-site Kondo (conduction electron -4f electron) scattering rate. Taking into account the measured Hall mobility, µ(H), the highly unusual thermopower, S, of these systems can be semiquantitatively described by S(T)=-ν(T)/µ(H)(T), which explicitly demonstrates that the thermopower originates from the local Kondo scattering process over a wide temperature range from far above to well below the coherence temperature (≈20 K for CeCu(2)Si(2)). Our results suggest that the Nernst effect can act as a proper probe of local charge-carrier scattering. This promises to impact on exploring the unconventional enhancement of the thermopower in correlated materials suited for potential applications.

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.

Single-Ion Kondo scaling of the coherent Fermi liquid regime in Ce(1-x)La(x)Ni2Ge2.

Thermodynamic and transport properties of the La-diluted Kondo lattice CeNi(2)Ge(2) were studied in a wide temperature range. The Ce-rich alloys Ce(1-x)La(x)Ni(2)Ge(2) were found to exhibit distinct features of the coherent heavy Fermi liquid. At intermediate compositions (0.7≤x≤0.9), non-Fermi liquid properties have been observed, followed by the local Fermi liquid behavior in the dilute limit. The 4f-electron contribution to the specific heat was found to follow the predictions of the Kondo-impurity model in both the local as well as the coherent regimes, with the characteristic Kondo temperature decreasing rapidly from about 30 K for the parent compound CeNi(2)Ge(2) to about 1 K in the most dilute samples. The specific heat does not show any evidence for the emergence of a new characteristic energy scale related to the formation of the coherent Kondo lattice.

Spin fluctuations in normal state CeCu2Si2 on approaching the quantum critical point.

We report on the magnetic excitation spectrum in the normal state of the heavy-fermion superconductor CeCu92)Si(2) on approaching the quantum critical point (QCP). The magnetic response in the superconducting state is characterized by a transfer of spectral weight to energies above a spin excitation gap. In the normal state, a slowing-down of the quasielastic magnetic response is observed, which conforms to the scaling expected for a QCP of spin-density-wave type. This interpretation is substantiated by an analysis of specific heat data and the momentum dependence of the magnetic excitation spectrum. Our study represents the first direct observation of an almost critical slowing-down of the normal state magnetic response at a QCP when suppressing superconductivity. The results strongly imply that the coupling of Cooper pairs in CeCu(2)Si(2) is mediated by overdamped spin fluctuations.

Localized 4f-electrons in the quantum critical heavy fermion ferromagnet CeRh6Ge4.

Ferromagnetic quantum critical points were predicted to be prohibited in clean itinerant ferromagnetic systems, yet such a phenomenon was recently revealed in CeRh6Ge4, where the Curie temperature can be continuously suppressed to zero under a moderate hydrostatic pressure. Here we report the observation of quantum oscillations in CeRh6Ge4 from measurements using the cantilever and tunnel-diode oscillator methods in fields up to 45 T, clearly demonstrating that the ferromagnetic quantum criticality occurs in a clean system. In order to map the Fermi surface of CeRh6Ge4, we performed angle-dependent measurements of quantum oscillations at ambient pressure, and compared the results to density functional theory calculations. The results are consistent with the Ce 4f electrons remaining localized and not contributing to the Fermi surface, suggesting that localized ferromagnetism is a key factor for the occurrence of a ferromagnetic quantum critical point in CeRh6Ge4.

BaGe(5): a new type of intermetallic clathrate.

BaGe(5) constitutes a new type of intermetallic clathrate obtained by decomposition of clathrate-I Ba(8)Ge(43)(3) at low temperatures. The crystal structure consists of characteristic layers interconnected by covalent bonds. BaGe(5) is a semiconducting Zintl phase.

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.

Crystal chemistry and physical properties of the nonmagnetic Kondo compound HfAs1.7Se0.2.

Single crystals of HfAs(1.7)Se(0.2) are grown by chemical transport reaction and their chemical composition characterized in detail by various analytical methods. Chemical analyses and crystal structure investigations by single-crystal X-ray diffraction as well as powder diffraction with synchrotron radiation reveal a tetragonal PbFCl structure type with strong disorder caused by a significant arsenic deficiency (As(0.9)) on the 2a site and mixed occupancy of the 2c site (As(0.8)Se(0.2)). HfAs(1.7)Se(0.2) is a diamagnetic metal which transforms into a superconducting state at T(c)=0.52 K. Similar to other PbFCl-type arsenide selenides, the title compound displays a magnetic-field-independent -AT(1/2) term in the low-temperature electrical resistivity. This unusual term presumably originates from the electron scattering of structural two-level systems. According to the experimental results, HfAs1.7Se0.2 appears to be a rare example of a nonmagnetic Kondo material.

Magnetic and defect probes of the SmB6 surface state.

The impact of nonmagnetic and magnetic impurities on topological insulators is a central focus concerning their fundamental physics and possible spintronics and quantum computing applications. Combining scanning tunneling spectroscopy with transport measurements, we investigate, both locally and globally, the effect of nonmagnetic and magnetic substituents in SmB6, a predicted topological Kondo insulator. Around the so-introduced substitutents and in accord with theoretical predictions, the surface states are locally suppressed with different length scales depending on the substituent's magnetic properties. For sufficiently high substituent concentrations, these states are globally destroyed. Similarly, using a magnetic tip in tunneling spectroscopy also resulted in largely suppressed surface states. Hence, a destruction of the surface states is always observed close to atoms with substantial magnetic moment. This points to the topological nature of the surface states in SmB6 and illustrates how magnetic impurities destroy the surface states from microscopic to macroscopic length scales.