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.

Figure 1

(a) Longitudinal resistivity (${\rho }_{xx}$) as a function of temperature at various pressures. The inset presents a schematic drawing of the sample used in the experiments. (b) Activation energy ($\mathrm{\Delta }$) as a function of temperature at selected pressures. The inset shows a detailed view of the low-temperature region.

Figure 2

(a) Temperature-pressure phase diagram of ${\mathrm{HfTe}}_5$. (b) Maximum values of the high-temperature gap (${\mathrm{\Delta }}_{\mathrm{HT}}$) (left axis) and low-temperature gap (${\mathrm{\Delta }}_{\mathrm{LT}}$) (right axis) as a function of pressure. (c) Cross-sectional area of the Fermi surface ($S_{FZ}$) as a function of pressure. The inset presents a Landau fan diagram at selected pressures. (d) Calculated ${\rho }_{xy,\mathrm{plat}.}^{\mathrm{cal}.}$ and measured Hall resistivity ${\rho }_{xy,\mathrm{plat}.}^{\exp .}$ at the last plateau of the QHE. (e) Carrier density ($n$) and mobility ($\mu$) as a function of pressure. The jump in $n\left(p\right)$ is accompanied by a change in carrier type from electronlike to holelike.

Figure 3

Longitudinal (${\rho }_{xx}$) and Hall resistivity (${\rho }_{xy}$) as a function of magnetic field at 1.8 K and at (a) 0.1, (b) 0.8, and (c) 1.5 GPa. The magnetic field was applied parallel to the $b$ axis in both measurements. The arrows mark the last plateau.