Stochastic Berry Curvature and Magneto-Optical Response in Halide Perovskites

Magneto-optical response in quantum materials is typically treated as a deterministic consequence of fixed electronic band structure and Berry curvature. Halide perovskites, however, exhibit dynamic lattice disorder, ionic fluctuations, and local symmetry variations that are capable of perturbing the underlying geometric electronic structure. This work proposes a phenomenological framework in which Berry curvature becomes configuration-dependent, producing fluctuations in optical Hall conductivity and magneto-optical response. Most importantly, the present framework distinguishes conventional transition-energy broadening from configuration-dependent redistribution of Berry-curvature weighting. A matched control calculation shows that, for the representative parameters considered here, the geometric contribution primarily redistributes the response variance across photon energy rather than substantially increasing its spectrally integrated magnitude. A minimal Monte Carlo implementation illustrates fluctuation-sensitive broadening of MCD-like spectra arising from stochastic redistribution of Berry curvature. The results suggest that optical-response variance may provide a potential probe of fluctuation-sensitive quantum geometry in structurally fluctuating quantum materials.