A first-frequency-moment constraint on antisymmetric optical conductivity vanishes exactly in zero-field moiré continuum models and equals a magnetic-flux-determined constant in Hofstadter models, implying spectral compensation for anomalous Hall absorption.
Working in the Landau gaugeA= (0,−Bx,0), we span the unper- turbed Hilbert space using the Landau-level (LL) basis |nLL, ky⟩, wheren LL denotes the LL index
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Optical Hall absorption sum rule and spectral compensation in time-reversal-breaking moir\'e and Hofstadter systems
A first-frequency-moment constraint on antisymmetric optical conductivity vanishes exactly in zero-field moiré continuum models and equals a magnetic-flux-determined constant in Hofstadter models, implying spectral compensation for anomalous Hall absorption.