Hierarchical Disorder in Moiré Exciton Photoluminescence Probed by Spectral-Descriptor Correlations

Abstract

Hyperspectral photoluminescence (PL) 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 multi-scale 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, $\xi (E_{\mathrm{cent}})\ge \xi (E_{\mathrm{dom}})$, 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 inter-descriptor correlations, including the near-perfect anticorrelation ${\rho }_{\mathrm{S}}(\Delta E_{\mathrm{cd}},R_{\mathrm{HL}})\approx -0.978$, 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.

31 pages, 11 figures

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