A continuous phase transition driven to zero temperature by a non-thermal parameter, such as pressure, terminates in a quantum critical point (QCP). At present, two main theoretical approaches are available for antiferromagnetic QCPs in heavyfermion systems. The conventional one is the quantum generalization of finite-temperature phase transitions, which reproduces the physical properties in many cases 1-5 . More recent unconventional models incorporate a breakdown of the Kondo effect, giving rise to a Fermi-surface reconstruction 6-8 -YbRh 2 Si 2 is a prototype of this category 5,9-11 . In YbRh 2 Si 2 , the antiferromagnetic transition temperature merges with the Kondo breakdown at the QCP. Here, we study the evolution of the quantum criticality in YbRh 2 Si 2 under chemical pressure. Surprisingly, for positive pressure we find the signature of the Kondo breakdown within the magnetically ordered phase, whereas negative pressure induces their separation, leaving an intermediate spin-liquid-type ground state over an extended range. This behaviour suggests a new quantum phase arising from the interplay of the Kondo breakdown and the antiferromagnetic QCP.In heavy-fermion systems, the Kondo effect leads to the formation of composite quasiparticles of the f and conductionelectron states with largely renormalized masses forming a Landau Fermi-liquid ground state in the paramagnetic regime well below the Kondo temperature T K . These quasiparticles are assumed to stay intact at the quantum critical point (QCP) in the conventional models in which magnetic order arises through a spin-densitywave (SDW) instability. However, the observation of magnetic correlations in CeCu 5.9 Au 0.1 being of local character 11 prompted a series of theoretical descriptions that discard this basic assumption. Rather, they focus on the breakdown of the Kondo effect, which causes the f states to become localized and decoupled from the conduction-band states at the QCP where one expects the Fermi surface to be reconstructed 7 . Consequently, a new energy scale T is predicted reflecting the finite-temperature T crossover of the Fermi-surface volume. This picture has been scrutinized in tetragonal YbRh 2 Si 2 (T K ≈ 25 K; ref. 12), a stoichiometric and very clean heavy-fermion metal that seems to be ideally suited for this kind of study 9,12 : antiferromagnetic order sets in at a very low temperature T N = 0.07 K and can easily be suppressed by a small magnetic field of µ 0 H N = 60 mT (H ⊥ c, with c being the magnetically hard axis). Hall-effect experiments 13 have detected a rapid change of the Hall coefficient along a line T (H ) that converges with H N , the width of the Hall crossover extrapolating LETTERS NATURE PHYSICS

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 manybody excitations associated with a collapsing Fermi-surface. This insight is expected to be relevant to the unconventional finitetemperature behavior in a broad range of strongly correlated quantum systems.YbRh2Si2 | Kondo effect | magnetotransport | antiferromagnetism | local quantum criticality Q uantum criticality epitomizes the richness of quantum effects in macroscopic settings (1). The traditional description is based on the framework of Ginzburg and Landau (2), which focuses on the notion of an order parameter, a classical variable. The order parameter delineates the symmetry breaking of the macroscopic phases, while its fluctuations at ever-increasing length and time scales characterize the approach toward a second-order quantum phase transition. For metallic antiferromagnets, this theory appears in the form of a spin-density-wave quantum-critical point (QCP) (3, 4). Here, the macroscopic fluctuations of the order parameter are described by a Gaussian theory at the fixed point, with a vanishing effective coupling among the collective modes in the zero-temperature (T ¼ 0), zero-energy (E ¼ 0) and infinite-length limit. Consequently (5), the collective fluctuations will violate E∕T scaling.By contrast, an unconventional class of quantum criticality, emerging from studies in recent years (1), incorporates not only the slow fluctuations of the order parameter, but also some inherent quantum modes. For heavy-fermion metals, the additional quantum modes are associated with a critical breakdown of the Kondo screening effect and the concomitant single-electron Kondo resonance excitations (6-8). These additional critical modes can lead to a critical field theory that is interacting, instead of Gaussian, and the collective fluc...

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.

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