# Linking interlayer twist angle to geometrical parameters of self-assembled folded graphene structures

## TL;DR

This study investigates the geometrical parameters of self-assembled folded twisted bilayer graphene structures, revealing a correlation between fold geometry and twist angle, modeled through energy minimization including bilayer adhesion energy.

## Contribution

It introduces a new analytical model linking the geometrical features of self-grown folded graphene to interlayer twist angles, supported by experimental AFM data.

## Key findings

- Twist-angle dependence observed in nanoribbon width and interlayer separation.
- A novel correlation between fold height (radius R) and ribbon width.
- Model predicts a relationship consistent with experimental measurements.

## Abstract

Thin adhesive films can be removed from substrates, torn, and folded in distinct geometries under external driving forces. In two-dimensional materials, however, these processes can be self-driven as shown in previous studies on folded twisted bilayer graphene nanoribbons produced by spontaneous tearing and peeling from a substrate. Here, we use atomic force microscopy techniques to generate and characterize the geometrical structure of naturally self-grown folded nanoribbon structures. Measurements of nanoribbon width and interlayer separation reveal similar twist-angle dependences possibly caused by the anisotropy in the bilayer potential. In addition, analysis of the data shows an unexpected correlation between the height of the folded arc edge -parameterized by a radius R-, and the ribbon width, suggestive of a self-growth process driven by a variable cross-sectional shape. These observations are well described by an energy minimization model that includes the bilayer adhesion energy density as represented by a distance dependent Morse potential. We obtain an analytical expression for the radius R versus the ribbon width that predicts a renormalized bending rigidity and stands in good agreement with experimental observations. The newly found relation between these geometrical parameters suggests a mechanism for tailored growth of folded twisted bilayer graphene -- a platform for many intriguing physics phenomena.