Selection rules of twistronic angles in two-dimensional material flakes via dislocation theory

Interlayer rotation angle couples strongly to the electronic states of twisted van der Waals layers. However, not every is energetically favorable. Recent experiments on rotation-tunable electronics reveal existence a discrete set angles at which assume most stable configurations. Nevertheless, quantitative map for locating these intrinsically preferred twist in bilayer system has been available, posing challenges on-demand design that are desired angles. Here we simple mapping between and geometry system, form geometric scaling laws wide range as function only parameters rotating flake supporting layer. We triangular hexagonal flakes since they frequently appear chemical vapor deposition growth. also present general method handling arbitrary geometry. Such dimensionless possess universality all kinds two-dimensional material systems, providing abundant opportunities intrinsic "twistronics". For example, increasing magic-sizes prefers zero-approaching sequence multiple magic-angles graphene can be revealed.