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.

Automated summary

We investigate the quantum nonlinear planar Hall effect in bilayer graphene subjected to a steady in-plane magnetic field. In the presence of time-reversal symmetry breaking caused by the magnetic field, a charge current arises in the second-order response to an external electric field due to the Berry curvature dipole in momentum space. We demonstrate that the nonlinear planar Hall effect, originating from the orbital effect of an in-plane magnetic field on electrons in bilayer graphene, can occur even without spin-orbit coupling. By considering symmetry analysis, we determine the dominant dependence of the Berry curvature dipole moment on the magnetic field components. Furthermore, we illustrate how external planar magnetic field, gate voltage, and Fermi energy can be used to control and modulate the Berry curvature dipole.