Nonlinear anomalous Hall effects probe topological phase-transitions in twisted double bilayer graphene

Nonlinear anomalous (NLA) Hall effect is the Berry curvature dipole induced second-order Hall voltage or temperature difference induced by 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 twistronic platforms can probe their novel electronic band structure and topology. Here, we investigate the family (electrical, thermoelectric, and thermal) of second-order NLA Hall effects in the moire system of twisted double bilayer graphene (TDBG). We combine the semiclassical transport framework with the continuum model of TDBG to demonstrate that the NLA Hall signals can probe topological phase transitions in moire systems. We show that the whole family of NLA Hall responses undergo a sign reversal across a topological phase transition. Our study establishes a deeper connection between valley topology and nonlinear Hall effects in time-reversal symmetric systems.