Lifshitz transition in correlated topological semimetals

Topological quasiparticles, arising when the chemical potential is near the band crossing, are pivotal for the development of next-generation quantum devices. They are expected to exist in half-Heusler correlated topological semimetals. However, the emergence of hole carriers, which alter the chemical potential away from the quadratic-band-touching points is not yet understood. Here, we investigated the electronic structure of YPtBi and GdPtBi through ab initio many-body perturbation GW theory combined with dynamical mean-field theory and revealed that the correlation effects of 4$d$ or 4$f$ electrons can lead to the formation of hole carriers. In YPtBi, the weakly correlated Y-4$d$ electrons constitute the topological bands, and the quadratic-band-touching point is at the Fermi level at high temperatures. At low temperatures, enhanced correlations of Y-4$d$ renormalize the topological bands, leading to the formation of hole pocket. In GdPtBi, the strongly correlated Gd-4$f$ electrons form the Hubbard-like bands originate from self-energy effects associated with a topological singularity. These local bands encompass itinerant 4$f$ bands, which hybridize with topological bands to induce pronounced hole bands. This concerted effect reduces the hole doping, bringing the chemical potential closer to the quadratic-band-touching points as the temperature is lowered. The temperature-induced Lifshitz transition should be responsible for the large hole bands observed in both topological semimetals in angle-resolved photoemission spectroscopy measurements at low temperatures. Our findings indicate that the integration of correlated fermions within a topological framework can modulate the energy landscape of topological bands.