Disordered hyperuniformity and thermal transport in monolayer amorphous carbon

Disordered hyperuniformity (DHU) is a recently discovered novel state of amorphous systems characterized by strongly suppressed density fluctuations at large length scales as in crystalline materials, which offers great potential for achieving unusual mechanical, electronic, and photonic properties. However, despite the fundamental and technological importance of thermal transport in amorphous solids, the effect of DHU remains largely unexplored. Here, we theoretically study thermal transport in a class of two-dimensional DHU materials—monolayer amorphous carbon (MAC). Beginning with a perfect graphene lattice, we continuously apply Stone-Wales transformations to generate a series of MAC models with varied degrees of disorder and defects, which are quantified through comprehensive structural analysis including the so-called hyperuniformity index (H), where a smaller H indicates a higher degree of hyperuniformity. Subsequently, we conduct molecular dynamics simulations to obtain the thermal conductivity (κ). A significant correlation between the thermal transport behavior and degree of hyperuniformity is observed, with the room-temperature κ decreasing from 26.3 to 5.3 W m⁻¹ K⁻¹ while H is tuned from 0.0004 to 0.024. Remarkably, two distinct transport regimes are identified, including a nearly-DHU regime at small H (< 0.005) where κ drops sharply and a non-DHU region at larger H where κ becomes relatively flat. Mode-resolved analysis reveals longer lifetime and higher participation ratio for the heat carriers in nearly-DHU MAC, implying that the hidden long-range correlations could support extended modes that enhance transport. Our work highlights the impact of DHU on the thermal properties of amorphous materials and represents a conceptual advancement that is worthy of future exploration.