Topological phases of matter describe electronic structures that can be continuously tuned into one another while being characterized by a well defined global (topological) invariant. Recently, noncentrosymmetric Weyl semimetals have emerged as one of the few such phases hosting 3D relativistic fermions in the bulk; therein, pairs of Weyl nodes – each node characterized by a well defined Chern number – are stabilized by broken inversion symmetry and strong spin-orbit interaction. So far, Weyl semimetals as well as most other topologically nontrivial phases were studied in noninteracting systems, or in settings that are adiabatically connected to them. On the other hand, exploring topologically nontrivial phases in systems where electron correlation effects are strong may open the way towards entirely new quantum phases. Heavy fermion materials are canonical representatives of strongly interacting electron systems. Therein, a plethora of novel quantum phases emerge due to the Kondo entanglement of conduction electrons and a sublattice of localized magnetic moments. Therefore, they constitute an ideal setting for exploring the interplay of topology and strong electron correlations. In this work, I show that tuning the spin-orbit interaction in the canonical noncentrosymmetric Kondo insulator Ce3Bi4Pt3 via Pd-Pt substitution drives the system into a semimetal. Low-temperature specific heat experiments for the novel Pd end compound Ce3Bi4Pd3 demonstrate that this compound hosts Kondo interaction-driven Weyl cones, thus realizing a new groundstate dubbed Weyl-Kondo semimetal. To probe the Berry curvature of Ce3Bi4Pd3, zero-field temperature dependent Hall resistivity measurements were carried out. They reveal a giant nonlinear spontaneous Hall effect in this material exposing a diverging Berrycurvature at the Fermi energy. Whereas this effect was predicted for time-reversal preserving Weyl semimetals – though with orders of magnitude smaller magnitude than observed here – I show that it features additional terms that are beyond this theoretical framework, and whose description requires a non-perturbative treatment of the effect. Finally, I present magnetotransport and magnetization experiments of Ce3Bi4Pd3 and magnetization experiments of Ce3Bi4Pt3, both donein high magnetic fields and at low temperatures. The data evidence that the groundstate of Ce3Bi4Pd3 is driven across a two-step quantum phase transition with increasing magnetic field. In the first step, the Weyl-Kondo semimetal state collapses at a topological quantum phase transition. In the second step, the system undergoes an abrupt metallization featuring quantum critical behaviour, thus exposing a Kondo insulator gap underlying the Weyl nodes. The results discussed in this thesis demonstrate that strong electron correlations can drive new topologically nontrivial electronic phases with properties beyond what could have been anticipated from weakly interacting systems. I anticipate that this insight will trigger further work, both experimental and theoretical, thereby helping to establish correlation-driven electronic topology as a new field of fundamental research, with potential also in quantum applications.
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