Absorbance marker: Detection of quantum geometry and spread of Wannier function in disordered 2D semiconductors

The optical absorbance of 2D semiconductors is generalized to individual lattice sites through the topological marker formalism, yielding an absorbance marker. This marker allows to investigate the atomic scale variation of absorbance caused by impurities, thereby quantifies the influence of disorder on the quantum geometry and the spread of Wannier functions of valence band states. Applying this marker to transition metal dichalcogenides reveals a very localized suppression of absorbance caused by potential impurities, rendering a reduction of absorbance in the macroscopic scale proportional to the impurity density, in good agreement with the experimental results of plasma-treated WS$_{2}$.