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 surfaces using a phase-field crystal model that is relevant on atomic length and diffusive time scales. Motivated by recent experiments, which achieved unprecedented fast growth of large-size high-quality 2D crystals on liquid substrates, we uncover novel effects of liquid surfaces on microstructural ordering. We find that substrate fluctuations generate short-ranged noise that speeds up crystallization and grain growth of the overlayer, surpassing that of free-standing system. Coupling to the liquid substrate fluctuations can also modulate local randomness, leading to intriguing disordered structures with hidden spatial order, i.e., disordered hyperuniformity. These results reveal the physical mechanisms underlying the fast growth of 2D crystals on liquid surfaces, and demonstrate a novel strategy for synthesizing disordered hyperuniform thin film structures.