Comprehensive understanding of disorder- and interaction-induced NLHE

Establish a comprehensive theoretical understanding of disorder- and interaction-induced contributions to the intrinsic second-order DC nonlinear Hall effect in multiband dispersive systems, beyond minimal models such as the two-dimensional Dirac point, by determining how impurity and electron–phonon scattering interplay with nontrivial quantum geometry to generate and modify the nonlinear Hall response.

Background

The paper decomposes the intrinsic second-order nonlinear Hall effect (NLHE) into quantum geometric contributions—nonlinear Drude, Berry curvature dipole, interband quantum metric dipole, and a newly identified intraband quantum metric dipole—within a fully gauge-invariant projector formalism. While these intrinsic mechanisms are clarified, the authors note that combining disorder (impurity scattering) and interactions (e.g., electron–phonon coupling) with quantum geometry can produce additional nonlinear Hall responses that are not yet fully understood.

They emphasize that numerical progress exists for minimal models (such as the 2D Dirac point), but achieving a complete, general theoretical framework for disorder- and interaction-induced NLHE in realistic multiband systems remains open. This would connect microscopic scattering processes with the presented quantum geometric expansion and help explain discrepancies among semiclassical and quantum approaches.