Quantum nonlinear planar Hall effect in bilayer graphene: An orbital effect of a steady in-plane magnetic field

We study the quantum nonlinear planar Hall effect in bilayer graphene under a steady in-plane magnetic field. When time-reversal symmetry is broken by the magnetic field, a charge current occurs in the second-order response to an external electric field as a result of the Berry curvature dipole in momentum space. We show that a nonlinear planar Hall effect originating from the anomalous velocity is caused by an orbital effect of an in-plane magnetic field on electrons in bilayer graphene in the complete absence of spin-orbit coupling. Taking into account the symmetry analysis, we derive the dominant dependence of the Berry curvature dipole moment on the magnetic field components. Moreover, we illustrate how to control and modulate the Berry curvature dipole with an external planar magnetic field, gate voltage, and Fermi energy.