Extrinsic and Intrinsic Nonlinear Hall Effects 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.

6+9 pages

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Cited by in corpus (10)

• Unification of Nonlinear Anomalous Hall Effect and Nonreciprocal Magnetoresistance in Metals by the Quantum Geometry
• Non-linear Hall Effects: Mechanisms and Materials
• General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect
• Scaling Law for Time-Reversal-Odd Nonlinear Transport
• Disorder in the non-linear anomalous Hall effect of $\mathcal{P}\mathcal{T}$-symmetric Dirac fermions
• Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
• Berry-dipole Semimetals
• Nonlinear Hall effects with an exceptional ring
• Charge transport in chiral solids as a possible tool in search of dark matter signals
• Quantum oscillation in Hopf-link semimetals