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

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 moiré system of 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 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.

Giant nonlinear Hall effect in strained twisted bilayer graphene

“…Duan et al report the experimental observation of the NLH effect in TBG [56]. References [57,58] study the topological transition probed by the NLH effect in twisted double bilayer graphene.…”

Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions

“…Thus, although the ENHE and INHE are Fermi-surface properties that are generally not possible to determine the topological invariant associated with the whole Brillouin zone, they are possible to detect the change of band topology if the topological insulators are weakly doped. Previous works indeed found that the ENHE can manifest topological phase transitions described by low-energy Dirac Hamiltonians through the dramatic sign change of nonlinear Hall conductivity tensor (NHCT) [22,37,38]. However, since therein the tilt or warping of massive Dirac cone is necessary to have nonzero ENHE [13,26], the NHCT does not have a simple and universal form revealing the change of topological invariant.…”