Hierarchical disorder in moiré exciton photoluminescence probed by spectral-descriptor correlations

Hyperspectral photoluminescence maps of moiré transition-metal dichalcogenide heterobilayers encode rich information about the underlying disorder, but extracting it is hampered by the ambiguity of assigning individual spectral peaks. We show that the spatial correlations among a set of simple, peak-decomposition-free spectral descriptors—such as the centroid energy, the dominant-peak energy, and a sharp-line fraction—provide a peak-decomposition-free route to infer features of that disorder. Different descriptors act as filters that select different components of a multiscale disorder landscape—a smooth, micron-correlated background and a dense set of localized traps—and therefore acquire different spatial correlation lengths. The central prediction is a correlation-length hierarchy, ξ ( E cent ) ≥ ξ ( E dom ) , which we derive by splitting the dominant-peak energy into a smooth background part and a short-range trap-switching fluctuation. The same picture explains the measured interdescriptor correlations, including the near-perfect anticorrelation ρ S ( Δ E cd , R HL ) ≈ − 0.978 , which we show to be a robust geometric trend for spectra dominated by a common emission-envelope asymmetry. Benchmarked against phenomenological simulations, Hamiltonian diagonalization, and the measured MoSe 2 / WSe 2 descriptor correlations, the framework turns descriptor maps into a quantitative, peak-decomposition-free probe of slow disorder and local traps in moiré excitons and, more broadly, in disordered semiconductor emitters.