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A material's electronic topology, which is generally described via its Bloch states and the associated bandstructure, will be enriched by the presence of interactions. In metallic settings, the interactions are usually treated through the concept of quasiparticles. Using the genuinely quantum critical heavy fermion compound CeRu$_4$Sn$_6$, we investigate what happens if no well-defined quasiparticles are present. Surprisingly, we discover a topological semimetal phase that emerges from the material's quantum critical state and exhibits a dome structure as a function of magnetic field and pressure. To understand these results, we study a Weyl-Kondo semimetal model at a Kondo destruction quantum critical point. Indeed, it exhibits features in the spectral function that can define topological crossings beyond the quasiparticle picture. We expect our work to stimulate the search for other emergent topological phases., Comment: 15 pages, 5 figures

The family of cubic noncentrosymmetric 3-4-3 compounds has become a fertile ground for the discovery of novel correlated metallic and insulating phases. Here, we report the synthesis of a new heavy fermion compound, Ce$_3$Bi$_4$Ni$_3$. It is an isoelectronic analog of the prototypical Kondo insulator Ce$_3$Bi$_4$Pt$_3$ and of the recently discovered Weyl-Kondo semimetal Ce$_3$Bi$_4$Pd$_3$. In contrast to the volume-preserving Pt-Pd substitution, structural and chemical analyses reveal a positive chemical pressure effect in Ce$_3$Bi$_4$Ni$_3$ relative to its heavier counterparts. Based on the results of electrical resistivity, Hall effect, magnetic susceptibility, and specific heat measurements, we identify an energy gap of 65-70 meV, about eight times larger than that in Ce$_3$Bi$_4$Pt$_3$ and about 45 times larger than that of the Kondo-insulating background hosting the Weyl nodes in Ce$_3$Bi$_4$Pd$_3$. We show that this gap as well as other physical properties do not evolve monotonically with increasing atomic number, i.e., in the sequence Ce$_3$Bi$_4$Ni$_3$-Ce$_3$Bi$_4$Pd$_3$-Ce$_3$Bi$_4$Pt$_3$, but instead with increasing partial electronic density of states of the $d$ orbitals at the Fermi energy. To understand under which condition topological states form in these materials is a topic for future studies., Comment: 28 pages, 11 figures