  Hyperuniform many-body systems in $d$-dimensional Euclidean space are
characterized by completely suppressed (normalized) infinite-wavelength density
fluctuations, and appear to be endowed with novel exotic physical properties.
In this work, we analyze the effects of localized defects on the density
fluctuations across length scales and on the hyperuniformity property of
experimental samples of two-dimensional transition metal dichalcogenides. In
particular, we extract atomic coordinates from time series annular dark
field-scanning transmission electron microscopy imaging data of 2D tungsten
chalcogenides with the 2H structure showing continuous development and
evolution of electron-beam induced defects, and construct the corresponding
chemical-bonding informed coordination networks between the atoms. We then
compute a variety of pair statistics and bond-orientational statistics to
characterize the samples. At low defect concentrations, the corresponding
materials are nearly hyperuniform. As more defects are introduced, the
(approximate) hyperuniformity of the materials is gradually destroyed, and the
system becomes non-hyperuniform even when the material still contains a
significant amount of crystalline regions. At high defect concentrations, the
structures become antihyperuniform with diverging (normalized) large-scale
density fluctuations. Overall, the defected materials possess varying degrees
of orientation order, and there is apparently no intermediate hexatic phase
emerging. We also construct a minimalist structural model and demonstrate that
the experimental samples can be essentially viewed as perturbed honeycomb
crystals with small correlated displacements and double chalcogen vacancies.
