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

Abstract

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, which have received considerable attentions, yet general analytical theories that can feasibly address the stability of twist angles have not yet been available. In this work, we reveal the existence of universal analytical scaling laws to delineate the interface rotational energy landscape, capable of determining both stable angles and interlayer rotational torque. The universality of our theoretical results is fundamentally based on evolution of moiré geometry that is applicable across many material interface systems. Our results not only unify experimental observations and literature atomistic simulations, but also provide new perspectives to the rational design of nanoscale rotation-tunable electronic devices. Our theories can potentially inspire deeper understanding of moiré-correlated interface mechanics.