Magnetochiral anisotropy-induced nonlinear Hall effect in spin-orbit coupled Rashba conductors

We theoretically predict the existence of a non-zero magnetochiral anisotropy-induced nonlinear Hall effect or a second harmonic Hall voltage transverse to an applied current in spin-orbit coupled Rashba conductors in the presence of an in-plane magnetic field B. This is distinct from the Berry curvature dipole (BCD)-induced nonlinear Hall effect in systems with non-trivial bandstructure because the former requires broken time-reversal symmetry while the BCD-induced effect is non-zero even in time-reversal symmetric systems. This result is independent of the existence of other types of interactions, such as hexagonal warping or cubic Dresselhaus interactions. We find that for E||B, the magnitude of the nonlinear Hall current flowing in a direction perpendicular to the applied electric field is exactly 1/3 of the magnitude of the non-linear rectification current responsible for magnetoresistance parallel to the applied electric field obtained in the E\perp B configuration.