Magnetotransport in the presence of real and momentum space topology

TL;DR

This paper explores how real-space skyrmion-induced emergent magnetic fields and momentum-space Berry curvature jointly influence magnetotransport in Weyl semimetals, revealing unique sign-reversal behaviors and transport signatures.

Contribution

It demonstrates that real-space topology acts as an independent topological parameter affecting magnetotransport, highlighting the interplay between real- and momentum-space Berry curvature in Weyl systems.

Findings

Intervalley scattering causes sign reversal of magnetoconductivity.

Emergent magnetic field shifts magnetic-field dependence, creating weak sign-reversal regimes.

Emergent field induces asymmetry in angular dependence of conductivities.

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.