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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 Ce₃Bi₄Pd₃ 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.

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.

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.

Background Acute cholecystitis (AC) with concurrent cholangitis is a life-threatening condition in elderly patients. We aimed to investigate the outcome of cholecystectomy in patients aged ≥ 80 years with moderate to severe AC who underwent percutaneous cholecystostomy and subsequent interventional endoscopic retrograde cholangiopancreatography (ERCP). Methods Between January 2008 and February 2021, we retrospectively enrolled 174 patients who underwent percutaneous cholecystostomy and subsequent ERCP at Taipei Veterans General Hospital. The patients were divided into cholecystectomy and non-cholecystectomy groups after discharge. Clinical outcomes including overall survival rate, recurrence rate of biliary-related events, and complications of ERCP and cholecystectomy, were analyzed. The Kaplan–Meier model was used to interpret the overall survival and cumulative recurrence rates. Results There were 34 patients receiving cholecystectomy (cholecystectomy group), and 98 patients received conservative treatment (non-cholecystectomy group). The overall mortality rate and biliary-related mortality did not differ between the cholecystectomy and non-cholecystectomy groups (20.5% vs. 35.7%, p  = 0.082; and 0% vs. 3%, p  = 0.083, respectively). The 1-year recurrent rate, 3-year recurrent rate and 5-year recurrence rates of biliary-related events were significantly lower in the cholecystectomy group than in the non-cholecystectomy group (2.9% vs. 18.4%, p  = 0.002; 5.9% vs. 20.4%, p  = 0.014; 8.8% vs. 24.5%, p  = 0.02, respectively). There was no significant difference in the 1-year recurrence rates of cholangitis (2,9% vs. 6.1%, p  = 0.407), and pancreatitis (0% vs. 1.0%, p  = 0.320). The overall ERCP-related complication rate in the elderly population was low (4%). The overall rate of surgical complications was 11.8% in the cholecystectomy group. Conclusions Cholecystectomy lowers the recurrence rate of biliary-related events in octogenarians with moderate-to-severe cholecystitis and concurrent cholangitis after percutaneous cholecystostomy and subsequent interventional ERCP.

Heavy fermion semimetals represent a promising setting to explore topological metals driven by strong correlations. In this paper, we i) summarize the theoretical results in a Weyl-Kondo semimetal phase for a strongly correlated model with inversion-symmetry-breaking and time-reversal invariance, and the concurrent work that has experimentally discovered this phase in the non-magnetic non-centrosymmetric heavy fermion system Ce\\(_3\\)Bi\\(_4\\)Pd\\(_3\\); and ii) describe what is expected theoretically when the time-reversal symmetry is also broken.

There is considerable current interest to explore electronic topology in strongly correlated metals, with heavy fermion systems providing a promising setting. Recently, a Weyl-Kondo semimetal phase has been concurrently discovered in theoretical and experimental studies. The theoretical work was carried out in a Kondo lattice model that is time-reversal invariant but inversion-symmetry breaking. In this paper, we show in some detail how nonsymmorphic space-group symmetry and strong correlations cooperate to form Weyl nodal excitations with highly reduced velocity and pin the resulting Weyl nodes to the Fermi energy. A tilted variation of the Weyl-Kondo solution is further analyzed here, following the recent consideration of such effect in the context of understanding a large spontaneous Hall effect in Ce\\(_3\\)Bi\\(_4\\)Pd\\(_3\\) (Dzsaber et al., arXiv:1811.02819). We discuss the implications of our results for the enrichment of the global phase diagram of heavy fermion metals, and for the space-group symmetry enforcement of topological semimetals in other strongly correlated settings.

We study the long-range Coulomb interaction effects on the double-Weyl fermion system which is possibly realized in the three dimensional semimetal HgCr\\(_2\\)Se\\(_4\\) in the ferromagnetic phase. Within the one-loop renormalization group analysis, we find that there exists a stable fixed point at which the Coulomb interaction is screened anisotropically. At the stable fixed point, the renormalized Coulomb interaction induces logarithmic corrections to the physical quantities such as specific heat, compressibility, diamagnetic susceptibility, and the finite frequency (dynamic) conductivity that are obtained utilizing RG equations near the stable fixed point.

Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of freedom, how to probe them and establish their existence is a long-standing challenge. We present a general procedure to reveal the fractionalized excitations using real-space entanglement entropy in critical spin liquids that are particularly relevant to experiments. Moreover, we show how to use the entanglement entropy to construct the corresponding spinon Fermi surface. Our work defines a new pathway to establish and characterize exotic excitations in novel quantum phases of matter.

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 Ce3Bi4Pd3 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.

A co-dimension one critical surface in the momentum space can be either a familiar Fermi surface, which separates occupied states from empty ones in the non-interacting fermion case, or a novel Bose surface, where gapless bosonic excitations are anchored. Their presence gives rise to logarithmic violation of entanglement entropy area law. When they are convex, we show that the shape of these critical surfaces can be determined by inspecting the leading logarithmic term of real space entanglement entropy. The fundamental difference between a Fermi surface and a Bose surface is revealed by the fact that the logarithmic terms in entanglement entropies differ by a factor of two: \\(S^Bose_log = 2 S^Fermi_log\\), even when they have identical geometry. Our method has remarkable similarity with determining Fermi surface shape using quantum oscillation. We also discuss possible probes of concave critical surfaces in momentum space.