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.

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