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

TL;DR

This paper explores how nonlinear anomalous Hall effects in twisted double bilayer graphene can serve as sensitive probes for topological phase-transitions induced by electric fields, revealing sign reversals in Hall responses.

Contribution

It demonstrates that the entire family of nonlinear anomalous Hall effects can detect topological phase-transitions in moiré systems, a novel application of these Hall responses.

Findings

Nonlinear anomalous Hall signals reverse sign at topological phase-transitions.

Hall effects can be used to probe topological changes in moiré systems.

Electric fields induce topological phase-transitions detectable via Hall responses.

Abstract

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. Here, we investigate the family of second-order nonlinear anomalous Hall effects, the electrical, thermoelectric and thermal nonlinear Hall effects in the moir\'e system of twisted double bilayer graphene. We demonstrate that the nonlinear anomalous Hall signals can be used to probe the topological phase-transitions in moir\'e systems, induced by a perpendicular electric field. Specifically, we show that the whole family of nonlinear anomalous Hall responses undergo a sign reversal across a topological phase-transition.