Second-Harmonic Bulk Response of Fractional Quantum Hall Fluids
Abstract
We develop a bulk description for the second-harmonic Hall response of fractional quantum Hall fluids with broken inversion and rotational symmetries, distinct from edge theories based on nonlinear edge-mode dispersion. By projecting a tilted massive Dirac model onto a single low-energy band, we construct a composite-boson Chern--Simons theory for the lowest Landau level that retains projection-induced nonlinear electromagnetic couplings. The nonlinear Hall resistivity vanishes in the dc limit, while its finite-frequency response retains the characteristic filling-factor dependence ρ(2)TLL∝ν−2, where ν is the Landau-level filling factor. At low frequency, its real and imaginary parts scale as (ω/ωc)2 and ω/ωc, respectively, where ωc is the cyclotron frequency, and the response is strongly anisotropic with respect to the crystalline tilt axis. Notably, the Kohn-mode resonances present in the second-order conductivity cancel in the nonlinear Hall resistivity. These results establish finite-frequency nonlinear transport as a bulk probe of fractional quantum Hall fluids without requiring nonlinear edge-mode dispersion.
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BibTeX
@misc{pimlott2026secondharmonic,
title = {{Second-Harmonic Bulk Response of Fractional Quantum Hall Fluids}},
author = {J. Luke Pimlott and Pablo Reiser and T. Hans Hansson and Habib Rostami},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33606},
eprint = {2610.33606},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33606},
}
RIS
TY - UNPB
TI - Second-Harmonic Bulk Response of Fractional Quantum Hall Fluids
AU - J. Luke Pimlott
AU - Pablo Reiser
AU - T. Hans Hansson
AU - Habib Rostami
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33606
UR - https://arxiv.org/abs/2610.33606
AB - We develop a bulk description for the second-harmonic Hall response of fractional quantum Hall fluids with broken inversion and rotational symmetries, distinct from edge theories based on nonlinear edge-mode dispersion. By projecting a tilted massive Dirac model onto a single low-energy band, we construct a composite-boson Chern--Simons theory for the lowest Landau level that retains projection-induced nonlinear electromagnetic couplings. The nonlinear Hall resistivity vanishes in the dc limit, while its finite-frequency response retains the characteristic filling-factor dependence ρ^(2)_TLL∝ν^−2, where ν is the Landau-level filling factor. At low frequency, its real and imaginary parts scale as (ω/ω_c)^2 and ω/ω_c, respectively, where ω_c is the cyclotron frequency, and the response is strongly anisotropic with respect to the crystalline tilt axis. Notably, the Kohn-mode resonances present in the second-order conductivity cancel in the nonlinear Hall resistivity. These results establish finite-frequency nonlinear transport as a bulk probe of fractional quantum Hall fluids without requiring nonlinear edge-mode dispersion.
ER -