Importance of the semimetallic state for the quantum Hall effect in ${\mathrm{HfTe}}_5$

At ambient pressure, ${\mathrm{HfTe}}_5$ is a material at the boundary between a weak and a strong topological phase, which can be tuned by changes in its crystalline structure or by the application of high magnetic fields. It exhibits a Lifshitz transition upon cooling, and three-dimensional (3D) quantum Hall effect (QHE) plateaus can be observed at low temperatures. Here, we have investigated the electrical transport properties of ${\mathrm{HfTe}}_5$ under hydrostatic pressure up to 3 GPa. We find a pressure-induced crossover from a semimetallic phase at low pressures to an insulating phase at about 1.5 GPa. Our data suggest the presence of a pressure-induced Lifshitz transition at low temperatures within the insulating phase around 2 GPa. The quasi-3D QHE is confined to the low-pressure region in the semimetallic phase. This reveals the importance of the semimetallic ground state for the emergence of the QHE in ${\mathrm{HfTe}}_5$ and thus favors a scenario based on a low carrier density metal in the quantum limit for the observed signatures of the quasiquantized 3D QHE.