Enhanced theoretical framework for bilayer stacking ferroelectricity

Sliding ferroelectricity has garnered significant research interest in recent years, and the foundational bilayer stacking ferroelectricity (BSF) theory [Ji et al., Phys. Rev. Lett. 130, 146801 (2023)] provides valuable guidelines for the design of sliding ferroelectrics. However, the current framework does not fully account for the selection of rotation operators in bilayer stacking, and is unable to determine whether and how the direction of polarization can be switched in polar bilayers. Here, we introduce two key improvements to the BSF theory through a systematic group theory analysis. First, we develop a more general method for identifying possible rotation operators, enabling a refined classification of the symmetries and polar states in bilayers that arise when stacking monolayers from oblique and rectangular crystal systems. Second, we establish an approach to determine the symmetry operators that connect the energetically degenerate configurations, thereby integrating the determination of ferroelectric switching into the BSF theory. These enhancements make the theory more comprehensive, providing a more robust and practical foundation for the design of sliding ferroelectrics.