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

TL;DR

The paper investigates the relationship between the Weyl semimetal (WSM) phase and the three-dimensional quantum Hall (3D QH) phase in ZrTe$_5$. Using rotatable, pressure-dependent transport, it maps how electronic polarization and the temperature scale $T_p$ control phase stability, showing WSM signals collapse under pressure while $T_p$ rises to approach the 3D QH regime. The main finding is that WSM and 3D QH are mutually exclusive, with a density-wave–like order parameter associated with $T_p$ likely stabilizing the 3D QH at higher pressure. This work reveals a tunable topological-phase competition in ZrTe$_5$ and suggests routes to realize the 3D QH phase by pressure-driven manipulation of polarization and order parameters.

Abstract

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.

Figures (4)

• Figure 1: Resistivity under different hydrostatic pressures.a, Resistivity ($\rho$) versus temperature (T) for ZrTe$_5$ under varying hydrostatic pressures (sample ZT006). The peak temperature ($\text{\rmfamily T}_{\text{\rmfamily p}}$) increases with pressure. The inset shows the crystal structure of ZrTe$_5$. b, Left panel: A pressure cell designed for 360-degree rotation measurements at low temperatures and under applied magnetic fields. Right panel: A microscope image of the ZrTe$_5$ single crystal. Scale bar is 5 mm. c, Schematic drawing of the Weyl semimetal (WSM) and 3D quantum Hall (3D QH) phases connected via order parameters. The 3D QH phase consists of stacked 2D QH layers along a specific crystallographic direction in real space, whereas the WSM phase features Weyl node pairs in momentum space, acting as Berry curvature sources/sinks. Each 2D momentum-space slice corresponds to a 2D QH system characterized by a Chern number. Crucially, the two phases are distinguished by the in-plane Hall effect: the WSM phase exhibits this effect (indicating existence of polarization), while the 3D QH phase does not. Tuning the order parameters drives transitions between these phases.
• Figure 2: 3D QH effect (sample ZT412) and in-plane Hall effect (sample ZT015) at ambient pressure. Magnetic field angle ($\theta$) definitions are provided in the insets. a, $\rho$ vs. T for the 3D QH sample ZT412 ($\text{\rmfamily T}_{\text{\rmfamily p}}$$\approx$ 90 K). b, Angle-dependent $\rho_{yx}$ vs. $\mu_0H$ for ZT412$\#$2 (field rotated in the bc plane). The near-constant resistivity ($\sim$7.5 $m\Omega$$cm$, dashed line) confirms the 3D QH phase. c, $\rho_{yx}$ vs.$\mu_0H$ for ZT412$\#$1. The matching positions of the kink in Hall resistivity and the entrance into the quantum limit provide further confirmation of the 3D QH phase. d, $\rho$ vs. T for the in-plane Hall sample ZT015 ($\text{\rmfamily T}_{\text{\rmfamily p}}$$\approx$ 2 K). Inset: Polarization direction along the c-axis. e, Angle-dependent $\rho_{yx}$ vs. $\mu_0H$ for ZT015 (field rotated in the bc plane). A prominent in-plane Hall signal as large as $\rho_{yx}$$\approx$ 13 $m\Omega$ signifies the WSM phase. f, Second-harmonic resistance ($R_{2\omega}$) vs. $\mu_0H$ (along the b-axis) for ZT015. Insets: Calculated $\left|\gamma'\right|$ and the ratio $\left|\gamma'\right|/\chi$ (representing polarization strength) vs. $\mu_0H$, showing the development of prominent electrical polarization along the c-axis (the in-plane direction).
• Figure 3: Angle- and pressure-dependent measurements for sample ZT006 in a rotatable pressure cell.a–c, Angle-dependent Hall resistivity ($\rho_{yx}$) vs. magnetic field ($\mu_0H$) at 0.2 GPa, 0.43 GPa, and 0.65 GPa, respectively. A prominent in-plane Hall signal is observed at all pressures. d, e, Hall conductivity ($\sigma_{xy}$) along the c-axis (in-plane) and b-axis (out-of-plane) at varying pressures ($\leq$0.95 GPa). A significant anomalous Hall conductivity ($\sigma^A_{xy}$) develops with the applied magnetic field in both directions, persisting up to 8 T. This is attributed to Berry curvature effects caused by the redistribution of Weyl nodes under applied magnetic fields. The magnitude of $\sigma^A_{xy}$ diminishes with increasing pressure for both directions, indicating a suppression of Berry curvature. f, Extracted anomalous Hall conductivity ($\sigma^A_{xy}$) from (d, e) vs. polarization magnitude. g, h, Polarization strength $\left|\gamma'\right|$ (derived from nonreciprocal signals) vs. magnetic field at different pressures. Insets: The corresponding polarization directions. i, Nonlinear Hall signals, plotted as $E_y^{2\omega}/E_x^2$ (proportional to Berry curvature dipole density) vs. polarization strength $\left|\gamma'\right|$, with the magnetic field applied along the b-axis.
• Figure 4: Phase diagram of ZrTe$_5$. Increasing pressure suppresses key features of the WSM phase—including Berry curvature ($\sigma^A_{xy}$), Berry curvature dipole density ($E_y^{2\omega}/E_x^2$), and polarization magnitude ($\left|\gamma'\right|$). Simultaneously, the rise in $\text{\rmfamily T}_{\text{\rmfamily p}}$ (blue dashed line) signals a progressive transition into the 3D QH phase. To correct for a systematic error, data from the QD pressure cell (except for the peak temperature, $\text{\rmfamily T}_{\text{\rmfamily p}}$) was scaled by a factor to align it with the data from the Almax pressure cell.