Magnetic Weyl semimetals with broken time-reversal symmetry are expected to generate strong intrinsic anomalous Hall effects, due to their large Berry curvature. Here, we report a magnetic Weyl semimetal candidate, Co3Sn2S2, with a quasi-two-dimensional crystal structure consisting of stacked Kagomé lattices. This lattice provides an excellent platform for hosting exotic topological quantum states. We observe a negative magnetoresistance that is consistent with the chiral anomaly expected from the presence of Weyl nodes close to the Fermi level. The anomalous Hall conductivity is robust against both increased temperature and charge conductivity, which corroborates the intrinsic Berry-curvature mechanism in momentum space. Owing to the low carrier density in this material and the significantly enhanced Berry curvature from its band structure, the anomalous Hall conductivity and the anomalous Hall angle simultaneously reach 1130 Ω−1 cm−1 and 20%, respectively, an order of magnitude larger than typical magnetic systems. Combining the Kagomé-lattice structure and the out-of-plane ferromagnetic order of Co3Sn2S2, we expect that this material is an excellent candidate for observation of the quantum anomalous Hall state in the two-dimensional limit.

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.

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

The entanglement of quantum states is both a central concept in fundamental physics and a potential tool for realizing advanced materials and applications. The quantum superpositions underlying entanglement are at the heart of the intricate interplay of localized spin states and itinerant electronic states that gives rise to the Kondo effect in certain dilute magnetic alloys. In systems where the density of localized spin states is sufficiently high, they can no longer be treated as non-interacting; if they form a dense periodic array, a Kondo lattice may be established. Such a Kondo lattice gives rise to the emergence of charge carriers with enhanced effective masses, but the precise nature of the coherent Kondo state responsible for the generation of these heavy fermions remains highly debated. Here we use atomic-resolution tunnelling spectroscopy to investigate the low-energy excitations of a generic Kondo lattice system, YbRh(2)Si(2). We find that the hybridization of the conduction electrons with the localized 4f electrons results in a decrease in the tunnelling conductance at the Fermi energy. In addition, we observe unambiguously the crystal-field excitations of the Yb(3+) ions. A strongly temperature-dependent peak in the tunnelling conductance is attributed to the Fano resonance resulting from tunnelling into the coherent heavy-fermion states that emerge at low temperature. Taken together, these features reveal how quantum coherence develops in heavy 4f-electron Kondo lattices. Our results demonstrate the efficiency of real-space electronic structure imaging for the investigation of strong electronic correlations, specifically with respect to coherence phenomena, phase coexistence and quantum criticality.