Mechanistic transition of heat conduction in two-dimensional solids: A study of silica bilayers

Thermal transport in solids changes its nature from phonon propagation that suffers from perturbative scattering to thermally activated hops between localized vibrational modes as the level of disorder increases. Models have been proposed to understand these two distinct extremes that predict opposite temperature dependence of the thermal conductivity but not for the transition or the intermediate regime. Here we explore thermal transport in two-dimensional silica with varying levels of disorder a by performing atomistic simulations, as well as analysis based on the kinetic and Allen-Feldman theories. We demonstrate a crossover between the crystalline and amorphous regimes at alpha similar to 0.3, which is characterized by a turnover of the temperature dependence in thermal conductivity and explained by the dominance of thermal hopping processes. This critical disorder level is also identified in the analysis of the participation ratio of localized vibrational modes and the spatial localization of heat flux. These factors serve as key indicators in quantitatively characterizing the mechanism of heat transport in the transitional regime.