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 AB2 pyrite materials, respectively transforms into a crystalline rhombus-hexagon (C46) and random rhombus-pentagon-hexagon (R456) tilings, by continuously introducing 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 two-dimensional (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 the 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 metallike electronic properties, making them promising candidates for forming Schottky barriers with the semiconducting P5 material.