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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.08043 |
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| _version_ | 1866915926879764480 |
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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 |