Magnetotransport in the presence of real and momentum space topology

Abstract

We investigate magnetotransport in a time-reversal symmetry-broken, untilted Weyl semimetal in the simultaneous presence of momentum-space Berry curvature and real-space topology arising from a skyrmion-induced emergent magnetic field $\mathbf{B}_{\mathrm{emer}}$. Using a semiclassical Boltzmann approach incorporating Berry-curvature corrections and intervalley scattering, we analyze the longitudinal magnetoconductivity and planar Hall conductivity in this mixed-topology regime. In the absence of $B_{\mathrm{emer}}$, increasing intervalley scattering drives a strong sign reversal of the longitudinal magnetoconductivity. A finite $\mathbf{B}_{\mathrm{emer}}$ introduces an additional shift of the parabolic magnetic-field dependence, leading to a weak sign-reversal regime without altering the curvature. The coexistence of these effects naturally produces a strong-and-weak sign-reversal regime, demonstrating that intervalley scattering and real-space topology control distinct geometric features of the response. The emergent field further induces asymmetry in the angular dependence of both longitudinal and planar Hall conductivities. We show that a finite planar Hall response can arise solely from $\mathbf{B}_{\mathrm{emer}}$ when its direction is varied, providing a transport signature of real-space topology. Our results establish that the skyrmion-induced emergent field acts as an independent topological tuning parameter, revealing measurable consequences of the interplay between real- and momentum-space Berry curvature in Weyl systems.

Figures (6)

• Figure 1: A schematic illustration of the characteristic regimes of magnetoconductivity $\sigma_{ij}$ in WSMs in the presence of both external magnetic field $B$ and emergent field $B_\mathrm{emer}$. The figure highlights weak sign reversal (shifted parabola), strong sign reversal (curvature inversion), and the coexisting strong-and-weak sign-reversal regime, in contrast to the conventional quadratic-in-$B$ response. In the present mixed-topology setting, these regimes arise from the interplay between intervalley scattering and the real-space Berry-curvature contribution encoded in $B_{\mathrm{emer}}$ahmad2023longitudinalvarma2024magnetotransportvarma2026chiral.
• Figure 2: Normalized LMC for a minimal model of a time-reversal symmetry broken, untilted WSM in the presence of an emergent magnetic field $\mathbf{B}_\mathrm{emer}$ arising from real-space topology. The angle of $\mathbf{B}_\mathrm{emer}$ and an external magnetic field $\mathbf{B}$ is set to be $\gamma_\mathrm{emer}=\gamma=\pi/2$. In all the panels, $\alpha$ varies from 0.20 to 1.50 along the red arrow. (a) $B_\mathrm{emer}=0$ T and changing $B$. At $\alpha_c\simeq$ 0.80, the anomaly-driven sign change of LMC occurs ahmad2025longitudinal. (b) $B_\mathrm{emer}=0.25$ T and changing $B$. For $\alpha<\alpha_c$ (${ \alpha}>\alpha_c)$, weak sign-reversal (strong-and-weak sign-reversal) behaviors emerge. (c) $B=0$ T and changing $B_\mathrm{emer}$. The sign change occurs at ${ \alpha_c}$. (d) $B=0.1$ T and changing $B_\mathrm{emer}$.
• Figure 3: Normalized LMC as a function of the external magnetic field $\mathbf{B}$ with $\gamma= \pi/2$ for a minimal model of an untilted time-reversal symmetry broken WSM. (a) Weak sing-reversal regime ($\alpha=0.2 < \alpha_c { \simeq}$ 0.80) and (b) strong-and-weak sing-reversal regime ($\alpha=0.90 > \alpha_c$). The progression from the blue to the green curves (indicated by the red arrow) corresponds to increasing the emergent magnetic field $B_\mathrm{emer}$ from 0 to 0.25 T with $\gamma_\mathrm{emer}=\pi/2$.
• Figure 4: Normalized LMC and PHC for a minimal model of untilted WSM as a function of $\gamma$ and $\gamma_\mathrm{emer}$. (a) Normalised LMC at $B=0.5$ T. (b) PHC at $B=0.5$ T. (c) Normalized LMC for given $B_\mathrm{emer}$ at $B=0$ T. (d) PHC for given $B_\mathrm{emer}$ at $B=0$ T. In (a)-(d), from blue to green lines, $B_{emer}$ is varied from $0$ to $0.25$ T with $\gamma = \gamma_\mathrm{emer}=\pi/2$.
• Figure 5: PHC as a function of external magnetic field $B$ for a minimal model of an untilted time-reversal symmetry broken WSM. (a) The emergent magnetic field $B_\mathrm{emer}=0$ T. (b) $B_\mathrm{emer}=0.25$ T. The angle $\gamma = \pi/4$ and $\gamma_{emer} = \pi/2$. In (a) and (b), $\alpha$ is changed from 0.20 to 1.5 from the top to bottom lines.