Intrinsic in-plane magnetononlinear Hall effect in tilted Weyl semimetals

Armed with the extended semiclassical theory, we propose a Hall effect at $EB$ order, particularly in Weyl semimetals (WSMs). We dub this effect the in-plane magnetononlinear Hall effect (IMHE) since the Hall current and the driving electric and magnetic fields are confined in the same plane. Similar to the intrinsic anomalous Hall effect, the IMHE features an intrinsic nature because it arises from the field-induced anomalous velocity $\vec{E} \times \vec{\Omega}^B$, where $\vec{\Omega}^B$ is the Berry curvature induced by the magnetic field through both minimal and Zeeman couplings. Employing the low-energy effective Hamiltonian of WSMs, we reveal that the tilt of the Weyl cone is the key to triggering this effect. Notably, we find that the IMHE can survive even when the \textit{chiral anomaly} disappears because $\vect{\Omega}^B$ (as the correction of the conventional Berry curvature) does not contribute to the monopole charge. Furthermore, we elucidate the interplay between minimal and Zeeman couplings for this effect. Finally, the experimental strategy to detect the IMHE is discussed.