Nonlinear anomalous Hall effects detect topological phase-transitions in moiré superlattices

Nonlinear anomalous Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference in response to a longitudinal electric field or temperature gradient. These are the prominent Hall responses in time reversal symmetric systems. These band-geometry induced responses in recently realized twistronics platforms provide a means to probe novel electronic and band structure and topology. Here, we discuss the family of second-order nonlinear anomalous Hall effects, the electrical, thermoelectric and thermal nonlinear Hall effects in the twisted double bilayer graphene. We demonstrate that the nonlinear anomalous Hall signals can be used to probe the topological phase-transitions in moiré systems, induced by external perturbations such as perpendicular electric field. Specifically, we show that the whole family of nonlinear anomalous Hall responses undergo a sign reversal across a topological phase-transition.