Topological Transformations in Hyperuniform Pentagonal 2D 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 $AB_2$ pyrite materials, respectively transforms into a crystalline rhombus-hexagon (C46) tiling and random rhombus-pentagon-hexagon (R456) tilings, by continuously introducing the Stone-Wales (SW) topological defects. We find these topological transformations are controlled by the orientation correlations among neighboring $B$-$B$ bonds, and exhibit a phenomenological analogy of the (anti)ferromagnetic to paramagnetic transition in two-state Ising systems. Unlike the SW defects in hexagonal 2D materials such as graphene, which cause distortions, the defects in pentagonal 2D materials preserve the shape and symmetry of the fundamental cell of P5 tiling and are associated with a minimal energy cost, making the intermediate R456 tilings realizable metastable states at room temperature. Moreover, the intermediate structures along the two pathways are neither crystals nor quasicrystals, and yet these random tilings preserve hyperuniformity of the P5 or C46 crystal (i.e., the infinite-wavelength normalized density fluctuations are completely suppressed), and can be viewed as 2D analogs of disordered Barlow packings in three dimensions. The resulting 2D materials possess metal-like electronic properties, making them promising candidates for forming Schottky barriers with the semiconducting P5 material.