Persistent nonlinear Hall effect driven by parallel field across a topological phase transition and intraband sign-reversing integer quantum Hall effect
We investigate the linear and nonlinear Hall effects in a two-dimensional Rashba spin-orbit coupled nodal ring electronic system. We consider both the cases of linear Hall effect, the Berry curvature induced anomalous Hall and the perpendicular magnetic field-induced integer quantum Hall effect. We observe that the system exhibits a topological gap along the boundary of the nodal ring that strongly depends on the radius of the nodal ring and the strength of the Rashba spin-orbit interaction, resulting in the quantum anomalous Hall effect. Subsequently, we include a perpendicular uniform magnetic field and obtain the exact Landau levels that exhibit sign reversal in the slope with magnetic field around the ring boundary. This causes a sign reversal in the quantum Hall conductivity in the same band by tuning the magnetic field. Most importantly, we also show that when the magnetic field is strictly parallel to the system, it can induce an anisotropy to the Berry curvature that leads to the emergence of the nonlinear Hall effect. Additionally, tuning the parallel field can close and reopen the topological gap, resulting in the reverse topological phase transition from the topological Chern insulator to a trivial insulator. The nonlinear Hall effect remains persistent in both phases, but its dependence on the chemical potential exhibits distinct signatures. Noticeably, the nonlinear Hall response exhibits a sign-changing peak structure in Chern insulating phase whereas it displays a single-sign response in trivial insulating phase. These distinct signatures suggest that nonlinear Hall can serve as a probe to study such a topological phase transition.