Extrinsic and Intrinsic Nonlinear Hall Effects across Berry-Dipole Transitions

TL;DR

This paper investigates the nonlinear Hall effects in three-dimensional Hopf insulators, revealing universal functions and quantized behavior across Berry-dipole transitions, linking nonlinear Hall responses to topological invariants.

Contribution

It introduces a novel connection between nonlinear Hall effects and Hopf invariants in Hopf insulators, highlighting universal behaviors at Berry-dipole critical points.

Findings

Nonlinear Hall conductivities are characterized by universal functions of doping and energy gap ratios.

Hall effects are directly proportional to changes in Hopf invariant across transitions.

Quantized nonlinear Hall responses are observed across Berry-dipole transitions.

Abstract

Three-dimensional Hopf insulators are a class of topological phases beyond the tenfold-way classification. The critical point separating two rotation-invariant Hopf insulator phases with distinct Hopf invariants is quite different from the usual Dirac-type or Weyl-type critical points and uniquely characterized by a quantized Berry dipole. Close to such Berry-dipole transitions, we find that the extrinsic and intrinsic nonlinear Hall conductivity tensors in the weakly doped regime are characterized by two universal functions of the ratio between doping level and bulk energy gap, and are directly proportional to the change in Hopf invariant across the transition. Our work suggests that the nonlinear Hall effects display a general-sense quantized behavior across Berry-dipole transitions, establishing a correspondence between nonlinear Hall effects and Hopf invariant.