Liquid-substrate fluctuation effects on crystal growth and disordered hyperuniformity of two-dimensional materials

We investigate the growth of two-dimensional (2D) crystals on fluctuating\nsurfaces using a phase field crystal model that is relevant on atomic length\nand diffusive time scales. Motivated by recent experiments which achieved\nunprecedented fast growth of large-size high-quality 2D crystals on liquid\nsubstrates, we uncover novel effects of liquid surfaces on microstructural\nordering. We find that substrate fluctuations generate short-ranged noise that\nspeeds up crystallization and grain growth of the overlayer, surpassing that of\nfree-standing system. Coupling to the liquid substrate fluctuations can also\nmodulate local randomness, leading to intriguing disordered structures with\nhidden spatial order, i.e., disordered hyperuniformity. These results reveal\nthe physical mechanisms underlying the fast growth of 2D crystals on liquid\nsurfaces and demonstrate a novel strategy for synthesizing disordered\nhyperuniform thin film structures.\n