Selection rules of twistronic angles in 2D material flakes via dislocation theory

TL;DR

This paper develops a universal geometric scaling law to identify energetically preferred twist angles in 2D bilayer materials, aiding the design of stable twistronic devices.

Contribution

It introduces a simple, universal mapping between preferred twist angles and geometric parameters, applicable to various 2D material flakes and geometries.

Findings

Derived geometric scaling laws for triangular and hexagonal flakes

Presented a general method for arbitrary flake geometries

Revealed a sequence of magic-sizes in bilayer graphene

Abstract

Interlayer rotation angle couples 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 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 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 prefers zero-approaching sequence of multiple magic-angles in bilayer graphene system can be revealed.