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

Shuze Zhu, Emil Annevelink, Pascal Pochet, Harley T. Johnson

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Article number115427
JournalPhysical Review B
Issue number11
StatePublished - Mar 17 2021

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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