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Main Authors: Zhang, Yixin, Huang, H.
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.08043
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author Zhang, Yixin
Huang, H.
author_facet Zhang, Yixin
Huang, H.
contents Optical spectroscopy provides a powerful, contact-free probe of topological quantum states, yet exact constraints on antisymmetric Hall absorption remain much less well developed than their longitudinal counterparts. Motivated by earlier Hall-conductivity sum rules, we formulate the corresponding first-frequency-moment constraint for the antisymmetric optical conductivity, whose imaginary part governs chirality-dependent absorption. We then demonstrate this sum rule in two classes of time-reversal-breaking topological systems. For a zero-field moiré continuum model hosting topological bands, the moment vanishes exactly, implying that any low-frequency anomalous Hall absorption must be compensated by higher-frequency spectral weight of the opposite sign. For a Hofstadter model under a uniform magnetic field, the same moment takes a universal value fixed by the magnetic flux density, independent of microscopic model details. By linking low- and high-frequency spectral contributions, this optical Hall absorption sum rule provides a rigorous framework for quantifying circular dichroism constraints and diagnosing Landau-level mixing. Our results show how a known Hall spectral constraint acquires new and experimentally relevant content in modern interacting topological materials.
format Preprint
id arxiv_https___arxiv_org_abs_2604_08043
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Optical Hall absorption sum rule and spectral compensation in time-reversal-breaking moiré and Hofstadter systems
Zhang, Yixin
Huang, H.
Mesoscale and Nanoscale Physics
Materials Science
Strongly Correlated Electrons
Optical spectroscopy provides a powerful, contact-free probe of topological quantum states, yet exact constraints on antisymmetric Hall absorption remain much less well developed than their longitudinal counterparts. Motivated by earlier Hall-conductivity sum rules, we formulate the corresponding first-frequency-moment constraint for the antisymmetric optical conductivity, whose imaginary part governs chirality-dependent absorption. We then demonstrate this sum rule in two classes of time-reversal-breaking topological systems. For a zero-field moiré continuum model hosting topological bands, the moment vanishes exactly, implying that any low-frequency anomalous Hall absorption must be compensated by higher-frequency spectral weight of the opposite sign. For a Hofstadter model under a uniform magnetic field, the same moment takes a universal value fixed by the magnetic flux density, independent of microscopic model details. By linking low- and high-frequency spectral contributions, this optical Hall absorption sum rule provides a rigorous framework for quantifying circular dichroism constraints and diagnosing Landau-level mixing. Our results show how a known Hall spectral constraint acquires new and experimentally relevant content in modern interacting topological materials.
title Optical Hall absorption sum rule and spectral compensation in time-reversal-breaking moiré and Hofstadter systems
topic Mesoscale and Nanoscale Physics
Materials Science
Strongly Correlated Electrons
url https://arxiv.org/abs/2604.08043