Hyperuniform Structure and Mobility Edge in the Random Truchet Tiling

Motivated by recent realizations of Truchet-tiling structures in DNA molecular networks and metal-organic frameworks, we study a metal-insulator transition driven by disorder following the random Truchet tiling. We uncover a hidden hyperuniform organization encoded in the coordination-number distribution of the random Truchet tiling. This structural hyperuniformity suppresses long-wavelength fluctuations in local connectivity in a strongly anisotropic way, giving rise to correlated disorder that crucially affects the electronic states. Using a tight-binding model on the random Truchet tiling and inverse participation ratio, we show that the electron system exhibits an extended-to-localized transition accompanied by a mobility edge at a finite disorder strength. Our results indicate that the hidden hyperuniformity provides a possible structural origin of the appearance of delocalized states and mobility edge.