Mechanism for spiral growth of β-antimonene on a pitted substrate: vacancy line aggregation triggered by nanoscale step-loops

The rising new field of twistronics, which is centered on the mechanically twisted multilayers of two-dimensional materials (2DMs), is in need of direct growth methods for the desired samples. Here, we present a comprehensive strategy for synthesizing twisted multilayer 2DMs <i>via</i> a spiral growth mode. This strategy is based on a first-principles calculations investigation of β-antimonene (β-Sb) on a pitted Ge(111) substrate surface with step-loops. Building on previous experimental observations, we have developed a theoretical model that elucidates the growth mechanism of the twist spiral structure. Our findings reveal that the step-loops play a crucial role in maintaining the lattice-mismatch-induced compressive strain in the β-Sb. As this strain accumulates, a vacancy line is inevitably formed in the first layer, facilitating the spiral dislocation in the second layer. It is also confirmed that the formation energy of the vacancies in β-Sb is lower in the high compressive strain state, and these vacancies tend to aggregate and form a linear structure. The kinetic study reveals a lower energy barrier for vacancy migration in the high compressive state. This theory presents a detailed growth mechanism for the spiral-assisted twist structure of 2D materials, which would be candidate samples for twistronics.