Phase-Shifted Planar Hall and Magnetoresistive Responses in Weyl Semimetals

Abstract

The planar Hall resistivity and magnetoresistivity of Weyl semimetals are conventionally expected to exhibit $\sin 2\phi$ and $\cos2\phi$ angular dependences, respectively, where $\phi$ is the angle between electric and magnetic fields. However, experiments reveal shifted extrema in the planar Hall signal and sign reversals in magnetoresistivity at $\phi < \pi/4$. Here, using a diagrammatic Kubo-formula approach, we identify an intrinsic quadratic magnetic-field contribution to the planar transport response that is absent in conventional semiclassical description. This contribution introduces an additional term proportional to $\cos 2 \phi$ and $\sin 2\phi$, respectively, in transverse and longitudinal conductivities. Consequently, both planar Hall and magnetoresistive responses acquire a phase-shifted form $\sin 2(\phi+\phi_r)$ and $\cos 2(\phi+\phi_r)$, respectively. The same phase shift extracted independently from longitudinal and transverse responses quantitatively describes available experimental data. Our results establish a microscopic origin of the anomalous angular dependence observed in Weyl semimetals.