In-plane anomalous features in the 3D quantum Hall regime

TL;DR

This work reveals that applying an in-plane magnetic field to a 3D Weyl semimetal in the quantum Hall regime uncovers transport features beyond the conventional 3D QHE. A coexisting Hall quantum oscillation and a nonquantized two-terminal resistance arise from a unique 3D nonlocal backscattering pathway that couples hinge modes, chiral Landau levels, and bulk interfaces, effectively breaking a straightforward 3D Chern-number transport correspondence. The authors develop a compact picture combining quantized hinge-mode contributions with CLL short-circuiting, and demonstrate robust negative longitudinal resistance that distinguishes Weyl from Dirac semimetals. They further propose experimental configurations to recover quantization, explore hybrid lead setups, and show that these 3D transport phenomena persist under rotated field or sample orientation, highlighting a fundamental 3D transport mechanism with potential experimental signatures and diagnostic power for Weyl physics. Overall, the work argues for a breakdown of traditional 3D topological transport characterization and introduces a new class of 3D quantum transport phenomena tied to 3D nonlocal channels and geometry-sensitive lead connections.

Abstract

Studies of the 3D quantum Hall effect (QHE) have primarily emphasized transport features that mimic the well-established 2D QHE. In this work, we show that qualitatively new features arise when an in-plane magnetic field is applied to a 3D Weyl semimetal in the quantum Hall regime. An unexpected Hall quantum oscillation, distinct from the Weyl-orbit oscillation, coexists with the QHE, along with an unquantized two-terminal magnetoresistance. Moreover, unconventional antichiral transmission enables a peculiar disorder-robust negative longitudinal resistance. Quantization tunable by the lead configuration is further found in this transport geometry. A unique type of nonlocal quantum backscattering channels underlies these phenomena. Our work demonstrates a breakdown of the topological characterization of transport even with 3D Chern numbers and reveals hidden 3D QHE transport properties. It opens a new class of transport measurements and phenomena.

Figures (19)

• Figure 1: Two possible Hall-bar configurations in 3D with the magnetic field (a) perpendicular or (b) parallel to the measurement plane. Current (Voltage) leads are in green (yellow). Solid orange lines denote the top (right-going) and bottom (left-going) hinge states; bidirectional dashed orange lines in (b) represent vertical chiral Landau levels (CLLs) connecting conducting channels near the lead-sample interface. Together, they form a unique type of 3D nonlocal quantum backscattering paths.
• Figure 2: (a) The inverse Hall resistance $1/R_{yx}$ and (b) the longitudinal resistance $R_{xx}$ from the $yx$-geometry in Fig. \ref{['Fig:cartoon']}(b). The vertical dashed lines mark the magnetic fields of $zx$-QHE plateau transitions from the measurement in Fig. \ref{['Fig:cartoon']}(a), indicating that all phenomena exist in the QHE regime of the system. (c) Inverse two-terminal resistance $\tilde{R}_{xx}$ in $yx$-geometry; red line: its counterpart in $zx$-geometry shows quantization instead. (d) Residual two-terminal resistance $\Delta\tilde{R}_{xx}$ approximately linear in $B$. System size is $32\times32\times32$ and three disorder strengths $W$ are shown. Model parameters are $A=1, M=0.15, D_x=0.06, D_y=0.03, D_z=0.09, k_\text{w}=\pi/2$.
• Figure 3: The inverse Hall resistance $1/R_{yx}$ for two related narrow-lead configurations in the lower right insets (see Fig. \ref{['Fig:enlarged_insets']} for enlarged illustration), in which of (b) CLLs as vertical dashed lines connect voltage leads to hinge modes above or below. Corresponding longitudinal resistance $R_{xx}$ is shown in the upper left insets.
• Figure S1: A standard six-terminal Hall-bar measurement in a 2D QHE system with two chiral edge states represented by orange arrow lines. The current leads are in green while the voltage leads are in yellow. The lead labelling in Fig. \ref{['Fig:cartoon']} follows the same convention herein.
• Figure S2: Transport feature of the WSM-based 3D QHE measured in the $zx$-geometry in Fig. \ref{['Fig:cartoon']}(a). (a) Hall quantization of $R_{zx}$; (b) quantizied two-terminal resistance $\tilde{R}_{xx}$ identical to the Hall resistance $R_{zx}$; (c) vanishing longitudinal resistance $R_{xx}$. Three different disorder strengths are exemplified to show the robustness of the QHE.