Universal scaling laws on the rotational energy landscape for twisted van der Waals bilayers

The emerging field of twistronics utilizes the interfacial twist angle between two-dimensional materials to design and explore unconventional electronic properties. However, recent investigations revealed that not every twist angle is stable. Understanding and predicting preferred twist angles are therefore of vital importance and have received considerable attention; however, general analytical theories that can feasibly address the stability of twist angles have not yet been developed. In this work, we reveal the existence of universal analytical scaling laws that delineate the interface rotational energy landscape, enabling the determination of both stable angles and interlayer rotational torque. The universality of our theoretical results is fundamentally based on the evolution of moiré geometry, which is applicable across many material interface systems. Our results not only unify experimental observations and literature atomistic simulations, but also provide new perspectives for the rational design of nanoscale rotation-tunable electronic devices. Our theories can potentially inspire a deeper understanding of moiré-correlated interface mechanics.