Exploring the stability of twisted van der Waals heterostructures

Recent research showed that the rotational degree of freedom in stacking 2D materials yields great changes in the electronic properties. Here we focus on an often overlooked question: are twisted geometries stable and what defines their rotational energy landscape? Our simulations show how epitaxy theory breaks down in these systems and we explain the observed behaviour in terms of an interplay between flexural phonons and the interlayer coupling, governed by Moir\'e superlattice. Our argument applied to the well-studied MoS$_2$/Graphene system rationalize experimental results and could serve as guidance to design twistronics devices.