Crystalline two-dimensional (2D) materials such as graphene possess unique
physical properties absent in their bulk form, enabling many novel device
applications. Yet, little is known about their amorphous counterparts, which
can be obtained by introducing the Stone-Wales (SW) topological defects via
proton radiation. Here we provide strong numerical evidence that SW defects
preserve hyperuniformity in hexagonal 2D materials, a recently discovered new
state of matter characterized by vanishing normalized infinite-wavelength
density fluctuations, which implies that all amorphous states of these
materials are hyperuniform. Specifically, the static structure factor S(k) of
these materials possesses the scaling S(k) ~ k^{\alpha} for small wave number
k, where 1<=\alpha(p)<=2 is monotonically decreasing as the SW defect
concentration p increases, indicating a transition from type-I to type-II
hyperuniformity at p ~= 0.12 induced by the saturation of the SW defects. This
hyperuniformity transition marks a structural transition from perturbed lattice
structures to truly amorphous structures, and underlies the onset of strong
correlation among the SW defects as well as a transition between distinct
electronic transport mechanisms associated with different hyperuniformity
classes