Nonperturbative Nonlinear Hall Effect in Nonequilibrium Steady States
Abstract
The nonlinear Hall effect in quantum materials has attracted broad interest, yet most existing studies focus on the weak-field, perturbative regime. Here we develop a nonperturbative approach based on nonequilibrium steady-state Green's functions for dc-field-driven lattice systems, with dissipation and interactions incorporated through self-energies beyond the constant relaxation-time approximation and interband transitions treated alongside their intraband counterparts. Applied to a two-band semimetal model, our approach provides direct access to the strong-field Hall response beyond the nonperturbative crossover where the edge of the nonequilibrium distribution reaches Berry-curvature hot spots, a regime in which constant relaxation-time estimates and Berry curvature dipole calculations become unreliable. We further demonstrate that interaction and electron-phonon self-energies within dynamical mean-field theory can substantially change the Hall signal. Our framework enables quantitative simulations of nonequilibrium nonlinear Hall phenomena and provides guidance for strong-field transport experiments.
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BibTeX
@misc{geng2026nonperturbative,
title = {{Nonperturbative Nonlinear Hall Effect in Nonequilibrium Steady States}},
author = {Lei Geng and Martin Eckstein and Lei Chen and Shouvik Sur and Silke Paschen and Qimiao Si and Philipp Werner},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.01519},
eprint = {2607.01519},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.01519},
}
RIS
TY - UNPB
TI - Nonperturbative Nonlinear Hall Effect in Nonequilibrium Steady States
AU - Lei Geng
AU - Martin Eckstein
AU - Lei Chen
AU - Shouvik Sur
AU - Silke Paschen
AU - Qimiao Si
AU - Philipp Werner
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2607.01519
UR - https://arxiv.org/abs/2607.01519
AB - The nonlinear Hall effect in quantum materials has attracted broad interest, yet most existing studies focus on the weak-field, perturbative regime. Here we develop a nonperturbative approach based on nonequilibrium steady-state Green's functions for dc-field-driven lattice systems, with dissipation and interactions incorporated through self-energies beyond the constant relaxation-time approximation and interband transitions treated alongside their intraband counterparts. Applied to a two-band semimetal model, our approach provides direct access to the strong-field Hall response beyond the nonperturbative crossover where the edge of the nonequilibrium distribution reaches Berry-curvature hot spots, a regime in which constant relaxation-time estimates and Berry curvature dipole calculations become unreliable. We further demonstrate that interaction and electron-phonon self-energies within dynamical mean-field theory can substantially change the Hall signal. Our framework enables quantitative simulations of nonequilibrium nonlinear Hall phenomena and provides guidance for strong-field transport experiments.
ER -