Probing topological phase transitions via nonlinear Hall response in strained moir\'e dice lattice

TL;DR

This paper demonstrates that nonlinear Hall response in strained twisted bilayer dice lattices can effectively probe topological phase transitions, with signals that reverse sign at phase boundaries and are enhanced by broken chiral symmetry.

Contribution

It introduces the use of nonlinear Hall effect as a probe for topological phase transitions in strained moiré dice lattices, highlighting the role of Berry curvature dipole and chiral symmetry breaking.

Findings

Nonlinear Hall signals reverse sign across topological phase boundaries.

Nonlinear Hall response is significantly enhanced when chiral symmetry is broken.

Berry curvature dipole governs the nonlinear Hall response in the studied system.

Abstract

Valley polarized twisted bilayer dice lattice hosts topologically nontrivial flat bands far from charge neutrality due to broken time reversal symmetry, whereas the ones in the vicinity of it remain topologically trivial. However, when both valleys are taken into consideration, the time reversal symmetry is preserved, which poses a serious hindrance to enumerate the valley specific topological phases that rely on the detection of the Berry curvature. In this work, we demonstrate that such a twisted structure with an applied uniaxial strain exhibits a nonlinear Hall effect far from charge neutrality. We ascertain that the nonlinear anomalous Hall signals can serve as a probe for topological phase transitions associated with a specific energy state that is constrained to reside at the lower edge of the middle subband and controlled via a staggered mass. Specifically, we show that the nonlinear anomalous Hall response undergoes a sign reversal across the topological phase boundaries. By tuning the carrier density, we compute the nonlinear Hall response obtained from the Berry curvature dipole, both in the chiral limit, and also when the chiral symmetry is broken. It is further seen that the nonlinear Hall effect is significantly enhanced in the broken chiral symmetry regime.