Nonlinear Hall effect in isotropic k-cubed Rashba model: Berry-curvature-dipole engineering by in-plane magnetic field

The linear and nonlinear Hall effects in 2D systems are considered theoretically within the isotropic k-cubed Rashba model. We show that the presence of an out-of-plane external magnetic field or net magnetization is a necessary condition to induce a nonzero Berry curvature in the system, whereas an in-plane magnetic field tunes the Berry curvature leading to the Berry curvature dipole. Interestingly, in the linear response regime, the conductivity is dominated by the intrinsic component (Berry curvature component), whereas the second-order correction to the Hall current (i.e., the conductivity proportional to the external electric field) is dominated by the component independent of the Berry curvature dipole.