Topological transformations in hyperuniform pentagonal two-dimensional materials induced by Stone-Wales defects

We discover two distinct topological pathways through which the pentagonal Cairo tiling (P5), a structural model for single-layer $A{B}_{2}$ pyrite materials, respectively transforms into crystalline rhombus-hexagon (C46) and random rhombus-pentagon-hexagon (R456) tilings, by continuously introducing Stone-Wales (SW) defects. find these transformations are controlled orientation correlations among neighboring $B\ensuremath{-}B$ bonds exhibit phenomenological analogy of (anti)ferromagnetic-to-paramagnetic transition in two-state Ising systems. Unlike SW defects hexagonal two-dimensional (2D) materials such as graphene, cause distortions, 2D preserve shape symmetry fundamental cell P5 associated with minimal energy cost, making intermediate R456 tilings realizable metastable states at room temperature. Moreover, structures along neither crystals nor quasicrystals, yet hyperuniformity or C46 crystal (i.e., infinite-wavelength normalized density fluctuations completely suppressed) can be viewed analogs disordered Barlow packings three dimensions. The resulting possess metallike electronic properties, them promising candidates forming Schottky barriers semiconducting material.