Nucleation and Antiphase Twin Control in Bi$_2$Se$_3$ via Step-Terminated Al$_2$O$_3$ Substrates

The epitaxial synthesis of high-quality 2D layered materials is an essential driver of both fundamental physics studies and technological applications. Bi$_2$Se$_3$, a prototypical 2D layered topological insulator, is sensitive to defects imparted during the growth, either thermodynamically or due to the film-substrates interaction. In this study, we demonstrate that step-terminated Al$_2$O$_3$ substrates with a high miscut angle (3$^\circ$) can effectively suppress a particular hard-to-mitigate defect, the antiphase twin. Systematic investigations across a range of growth temperatures and substrate miscut angles confirm that atomic step edges act as preferential nucleation sites, stabilizing a single twin domain. First principles calculations suggest that there is a significant energy barrier for twin boundary formation at step edges, supporting the experimental observations. Detailed structural characterization indicates that this twin-selectivity is lost through the mechanism of the 2D layers overgrowing the step edges, leading to higher twin density as the thickness increases. These findings highlight the complex energy landscape unique to 2D materials that is driven by the interplay between substrate topology, nucleation dynamics, and defect formation, and overcoming and controlling these are critical to improve material quality for quantum and electronic applications.