Interlayer Registry Index of Layered Transition Metal Dichalcogenides

Inspired by the fascinating electronic properties of twisted transition metal dichalcogenides, we extend the registry index approach to quantify the interlayer commensurability of homogeneous and heterogeneous interfaces of MoS₂, WS₂, MoSe₂, and WSe₂. The developed geometric measure provides quantitative information about their sliding energy landscape with vast mechanical and tribological implications. Furthermore, the registry index is highly suitable for characterizing surface reconstruction in twisted transition metal dichalcogenide interfaces that dictates their intricate electronic and ferroelectric properties. The simple and intuitive nature of the registry index marks it as a powerful computational tool for studying the fascinating physical phenomena demonstrated by these materials.