Investigating the relationship between the Weyl semimetal phase and the three-dimensional quantum Hall phase in ZrTe$_5$

The material ZrTe$_5$ exhibits distinct topological phases, including a Weyl semimetal phase, characterized by a chiral anomaly and in-plane Hall effect, and a three-dimensional quantum Hall phase. The relationship between these phases remains poorly understood. This work systematically explores their connection in ZrTe$_5$ through rotatable, pressure-dependent measurements. At ambient pressure, both phases are observed; the WSM phase requires strong electronic polarization, while the 3D QH phase appears when the characteristic resistivity peak temperature $T_p$ is approximately 90 K. Under applied pressure, the polarization diminishes, weakening the WSM phase and its associated nontrivial Hall signals. Concurrently, $T_p$ rises dramatically from 2 K at ambient pressure to 70 K at 2.2 GPa, approaching the expected regime for the 3D QH phase. These findings clarify the conditions underlying the WSM and 3D QH phases and suggest that exploring the 3D QH phase at even higher pressures is a promising direction for future research.