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.
A Z acknowledges the support from Shanghai Magnolia Talent Plan Youth Project and Shanghai Normal University (Grant No. 307-AF0102-24-005341). J W R was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIT) (Grant Nos. 2021R1A2C1010572, 2021R1A5A1032996 and 2022M3H3A1063074) and the Ministry of Education (Grant No. RS-2023-00285390).
