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How strong correlations and topology interplay is a topic of great current interest. In this perspective paper, we focus on correlation-driven gapless phases. We take the time-reversal symmetric Weyl semimetal as an example because it is expected to have clear (albeit nonquantized) topological signatures in the Hall response and because the first strongly correlated representative, the noncentrosymmetric Weyl–Kondo semimetal Ce₃Bi₄Pd₃, has recently been discovered. We summarize its key characteristics and use them to construct a prototype Weyl–Kondo semimetal temperature-magnetic field phase diagram. This allows for a substantiated assessment of other Weyl–Kondo semimetal candidate materials. We also put forward scaling plots of the intrinsic Berry-curvature-induced Hall response vs the inverse Weyl velocity—a measure of correlation strength, and vs the inverse charge carrier concentration—a measure of the proximity of Weyl nodes to the Fermi level. They suggest that the topological Hall response is maximized by strong correlations and small carrier concentrations. We hope that our work will guide the search for new Weyl–Kondo semimetals and correlated topological semimetals in general, and also trigger new theoretical work.

 

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 CeRu 4 Sn 6 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. 

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 C e 3 B i 4 P d 3 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. 

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.