A Quantum Framework for Negative Magnetoresistance in Multi-Weyl Semimetals

TL;DR

This work develops a fully quantum, Landau-level–resolved theory of negative magnetoresistance in Weyl and multi-Weyl semimetals under $\mathbf{E}\parallel\mathbf{B}$. By incorporating a topological multi-Weyl Hamiltonian with tilt and particle-hole asymmetry, Landau quantization, and screened Coulomb disorder within the Kubo formalism, it shows that $m$ chiral Landau levels dominate anomaly-driven transport, yielding a piecewise linear $\sigma_{zz}(B)$ with $m$ distinct slopes and kink fields $B_n$ where each chiral branch depopulates. Bulk Landau levels contribute only at very low fields, leaving the chiral channels as the primary transport channels in the anomaly-active regime. The resulting negative magnetoresistance provides a direct quantum signature of multi-Weyl topology and the Landau-level hierarchy, offering testable predictions for materials with monopole charge $m=1,2,3$ and guiding extensions to tilt, interactions, and realistic disorder.

Abstract

We develop a fully quantum-mechanical theory of negative magnetoresistance in multi-Weyl semimetals in the ${\bf E}\parallel{\bf B}$ configuration, where the chiral anomaly is activated. The magnetotransport response is governed by Landau quantization and the emergence of multiple chiral Landau levels associated with higher-order Weyl nodes. These anomaly-active modes have unidirectional dispersion fixed by the node's monopole charge and dominate charge transport. As the magnetic field increases, individual chiral branches successively cross the Fermi energy, producing discrete slope changes in the longitudinal conductivity and a step-like negative magnetoresistance. This quantized evolution provides a direct experimental signature of multi-Weyl topology. Bulk Landau levels contribute only at very low fields due to strong disorder scattering and do not affect the anomaly-driven regime. Our results establish a unified, fully quantum-mechanical framework in which negative magnetoresistance arises from the discrete Landau-quantized spectrum and microscopic impurity scattering, beyond semiclassical anomaly descriptions.

Figures (4)

• Figure 1: Energy dispersion and density of states (DOS) of Landau-quantized multi-Weyl semimetals in a magnetic field. Panel (a) shows a double-Weyl node ($m=2$) and panel (b) a triple-Weyl node ($m=3$). In each case, the left plot displays the Landau-level spectrum versus $k_z$, while the right plot shows the corresponding DOS. Red lines denote the $m$ chiral Landau levels with unidirectional dispersion fixed by the node chirality, and blue curves represent bulk ($n=m$) Landau levels.
• Figure 2: (Color online) Magnetotransport response of multi-Weyl semimetals for the double-Weyl ($m=2$) and triple-Weyl ($m=3$) cases. Red, blue, and green curves correspond to $T=100$, $200$, and $300\,\mathrm{K}$, respectively. For $m=2$, two chiral channels give rise to a two-stage linear increase in $\sigma_{zz}(B)$, while the bulk contribution (b) is confined to low fields, resulting in negative magnetoresistance (MR). For $m=3$, three chiral channels produce three linear regimes in $\sigma_{zz}(B)$, with the bulk contribution (e) again negligible beyond small fields and a strongly negative MR.
• Figure 3: (Color online) Magnetotransport response of a single-Weyl node ($m=1$). Panel (a) shows the magnetic-field dependence of the normalized longitudinal conductivity $\sigma_{zz}/\sigma_0$, dominated by the chiral channel. The inset highlights the contribution from non-chiral (bulk) ($n=m$) Landau level, which is confined to the low-field regime and remains negligibly small. Panel (b) shows the corresponding magnetoresistance (MR), which is negative over the entire field range shown.
• Figure 4: Second-order impurity self-energy diagrams: (a) direct (Hartree) contribution, giving only a real energy shift; (b) exchange (crossed) contribution, producing the imaginary part of $\Sigma^{R}$ and thus the impurity scattering rate.