Magneto-nonlinear Hall effect in time-reversal breaking system

Magneto-nonlinear Hall effect is known to be intrinsic and requires time-reversal symmetry. Here we show that a new type of magneto-nonlinear Hall effect can occur in the time-reversal breaking materials within the second-order response to in-plane electric and vertical magnetic fields. Such a Hall response is generated by the oscillation of the electromagnetic field and has a quantum origin arising from a geometric quantity associated with the Berry curvature and band velocity. We demonstrate that the massive Dirac model of LaAlO3/LaNiO3/LaAlO3 quantum well can be used to detect this Hall effect. Our work widens the theory of the Hall effect in the time-reversal breaking system by proposing a new kind of nonlinear electromagnetic response.